A Review of Linear Motor Electromagnetic Energy Regenerative Suspension and Key Technologies

Abstract

Linear motor electromagnetic energy regenerative suspension (LMEERS), integrating dual functionalities of energy regeneration and active control, possesses the potential to overcome the performance limitations inherent in existing suspension architectures. Research on key technologies for LMEERS aligns with the contemporary automotive development theme of “enhanced comfort, improved safety, and optimized energy efficiency”. This paper reviews the research progress of the configuration design, performance optimization, functionality switching criterion identification, and top-layer control strategies of LMEERS. Regarding configuration design, a systematic summary is provided for the design schemes of fundamental configuration and the technical features of three composite configurations. In the aspect of performance optimization, the specific approaches and their effectiveness in enhancing LMEERS comprehensive characteristics are analyzed. Concerning functionality switching criterion identification, the operating principles and performance differences among various estimation methods in identifying road surface information are discussed. For top-layer control strategies, the characteristics and applicability of various control methods in exploiting the dual functionalities of LMEERS are summarized. Future developments in LMEERS are anticipated to trend towards integration, lightweighting, standardization, intellectualization, and multi-mode operation. This review provides a theoretical reference for the design optimization and technological innovation of LMEERS, contributing to the advancement of automotive chassis systems in terms of electrification, intellectualization, and energy conservation.

1. Introduction

Automobiles serve as the most frequently utilized mode of daily transportation, offering substantial convenience to the public. However, the continuous growth of the global vehicle population has precipitated numerous societal challenges, including frequent traffic accidents, resource depletion, and environmental pollution, which adversely impacts quality of life. Therefore, extensive attention has been focused on automotive energy-saving technologies. In general, vehicle energy conservation primarily refers to subsystem-level energy efficiency, such as engine energy conservation (for internal combustion engine vehicles) [1,2], motor energy conservation (for electric vehicles) [3,4], braking system energy regeneration [5,6], and suspension system energy regeneration [7,8]. This approach aims to achieve comprehensive vehicle energy efficiency through optimization of individual subsystems. Additionally, advancements in battery chemistry, such as the development of high-energy-density lithium batteries and solid-state batteries, have significantly contributed to the further energy saving of vehicles by reducing weight and improving charge–discharge efficiency [9,10].

The suspension system serves as a critical automotive subsystem and is responsible for transmitting forces and moments between the vehicle body and wheels. It works to mitigate impacts, attenuate vibrations, and regulate vehicle body posture, thereby influencing all key vehicle dynamic performances, including ride comfort, handling stability, and driving safety [11]. Based on control methodologies, suspension systems are categorized as passive suspensions, semi-active suspensions, and active suspensions [12].

Conventionally, passive suspensions employing the traditional “spring-damper” architecture have difficulties in effectively balancing diverse vehicle dynamic performance requirements. Furthermore, the kinetic energy generated from suspension vibration is dissipated as heat into the atmosphere, representing significant energy loss. Although hydraulic active suspension and air active suspension demonstrably enhance vehicle dynamic performance [13,14], they are inherently constrained by the operating principles and intrinsic characteristics of their actuators. These systems commonly exhibit shared limitations, such as high energy consumption, response lag, and limited controllable bandwidth [15], hindering their ability to satisfy the future automotive imperatives. Addressing this technical challenge necessitates, first and foremost, the structural innovation of suspension systems. The design objective is to develop a novel suspension architecture capable of simultaneously fulfilling demanding dynamic performances and energy-saving properties for vehicles. This pursuit represents a major current focus and developmental direction in the automotive industry.

Currently, electromagnetic energy regenerative suspension (EERS) systems have garnered worldwide attention due to their significant advantages, including high power output, simple control implementation, extended service life, superior environmental adaptability, and the capability of seamless switching between vibration suppression and energy harvesting. Fu et al. [16] have laid a valuable foundation for understanding the general advancements in EERSs, particularly in the areas of structural research, optimal design methods, and control methods. These works provide a broad overview of various electromagnetic actuator types and their integration into vehicle suspensions, offering important insights into the field’s developmental trajectory.

However, most existing reviews predominantly tend to analyze and discuss the research progress in structural design and control strategies for all types of EERSs from a generalized perspective. In contrast, this paper focuses specifically on linear motor electromagnetic energy regenerative suspension (LMEERSs), which utilizes the linear motor as its actuator, integrating dual functionalities of energy regeneration and active control. On one hand, it enables the conversion of kinetic energy generated by suspension vibration into electrical energy for recovery and reuse, realizing indirect sub-system energy conservation. On the other hand, it can be actively controlled, significantly reducing the response time and expanding the controllable bandwidth of the control system [17]. Therefore, LMEERS possesses the potential to overcome the performance limitations inherent in existing suspension architectures. Research on its key technologies aligns with the current automotive development imperatives of electrification and energy conservation, holding significant theoretical importance and engineering application value for achieving a leap forward in the comprehensive performances of vehicles.

Unlike broader surveys, this paper delves deeply into the dual-functionality nature of LMEERS, emphasizing four key technologies:

• Principles and schemes of configuration design tailored to linear motors.
• Multidisciplinary performance optimization addressing critical operational characteristics of linear motors.
• Integration of functionality switching criterion identification for trade-off between dual functionalities.
• Selection of top-layer control strategies that fully exploit the dual-functionality capability of LMEERS.

Specifically, configuration design serves as the foundation for satisfying the functionality and reliability requirements of LMEERS. Performance optimization, focusing on structural refinement, parametric optimization, and intelligent control, represents a crucial pathway for further enhancing overall performance. Accurate road surface information identification is a prerequisite for the rational switching between LMEERS’s dual functionalities and the effective implementation of top-layer control strategies. Finally, efficient top-layer control strategies are the key to exploiting the dual functionalities.

By concentrating on these aspects, this review offers a specialized and in-depth analysis that distinguishes it from more generalized surveys on EERS. It aims to serve as a targeted reference for researchers and engineers working on next-generation high-performance energy regenerative suspension systems centered on linear motor technology. The research framework is illustrated in Figure 1.

This paper is organized as follows. Section 2 analyzes the structural features of fundamental and composite configurations of LMEERS. In Section 3, optimization pathways for the four primary operational characteristics, namely damping characteristics, thermal characteristics, thrust characteristics, and regenerative characteristics, are systematically summarized. Identification methodologies for two types of road surface information are reviewed in Section 4. A performance comparison of various top-layer control strategies applicable for LMEERS is conducted in Section 5. Section 6 discusses the existing challenges and future development trends in LMEERS. Conclusions are drawn in Section 7.

2. Configuration Design of LMEERS

2.1. Principle and Classification of Vibration Energy Regenerative Systems

According to the underlying mechanisms for the conversion of vibration energy into electrical energy, energy regenerative approaches are categorized into four types: electrostatic, piezoelectric, triboelectric, and electromagnetic [18]. Their underlying mechanisms are illustrated in Figure 2, with a comparative summary provided in

Table 1. Underlying mechanisms, core characteristics, and application status of vibration energy regenerative systems.

Type	Underlying Mechanism	Core Characteristics	Application Status in Suspension Field
Electrostatic	Changes in the capacitor electrode separation induced by vibration, then generating charge variation and forming current in the external circuit	Advantages: High output voltage, adjustable electromechanical coupling coefficient, compact size, etc. Limitations: High operating frequency requirement, limited load-bearing capacity, etc.	No documented applications
Piezoelectric	Deformation of piezoelectric semiconductors induced by vibration, then generating charge and forming current in the external circuit	Advantages: High output voltage, electromechanical coupling coefficient, and energy density, small space requirement, etc. Limitations: Narrow displacement range, limited load-bearing capacity, etc.	Extremely limited engineering applications
Triboelectric	Contact sliding induced by vibration, then generating electrostatic charge and forming current in the external circuit	Advantages: Low material cost, simple structural design, high energy-feedback efficiency at low frequencies, etc. Limitations: Lower energy density, reliability and durability challenges, etc.	No documented applications
Electromagnetic	Relative motion between magnets and coils induced by vibration, then generating induced electromotive force and forming current in the external circuit	Advantages: High power output, strong environmental adaptability, high reliability, long service life, compatibility with active control implementation Limitations: Higher cost, larger weight and volume	Already assembled in mass-production models

. Among them, electrostatic systems exhibit a high operating frequency range but suffer from limited load-bearing capacity [19]. Piezoelectric systems are constrained by a narrow operational bandwidth [20]. And triboelectric systems face challenges in reliability and durability [21]. Consequently, these three energy harvesting approaches are not viable for engineering applications in automotive suspension systems. In contrast, electromagnetic systems operate on Faraday’s law of electromagnetic induction, converting suspension vibration energy into electricity through the relative motion between coils and permanent magnets (PMs). This mechanism exhibits high compatibility with suspension systems in terms of structural characteristics and operating principles. Furthermore, electromagnetic systems offer significant advantages, including high power output, simple control implementation, extended service life, superior environmental adaptability, and the capability of seamless switching between vibration suppression and energy harvesting.

According to Faraday’s law of electromagnetic induction, the power generation capacity of the electromagnetic energy regenerative suspension (EERS) is closely related to the arrangement scheme, motion form, and relative velocity of PMs and coils. Based on the structure and arrangement features of the actuator, EERS can be classified into three primary configurations: rotary motor type [22], linear motor type [23], and composite type [24].

2.2. Fundamental Configuration of LMEERS

Unlike the rotary motor type, the actuator configuration of the linear motor type shares greater structural similarity with conventional hydraulic dampers. It comprises a stator and a mover, in which the mover is functionally analogous to the piston rod of a damper and connects to the vehicle body, and the stator corresponds to the damper cylinder tube and attaches to the wheel. During suspension vibration, relative linear motion occurs between the stator and mover. According to Faraday’s law of electromagnetic induction, the electric current is induced in the coils, thereby converting kinetic energy into electrical energy to achieve energy regeneration. Conversely, when alternating current is supplied to the coils, the mover generates an active force to suppress motion between the vehicle body and wheels, enabling active control functionality. It can be seen that LMEERS possesses dual functionalities of energy regeneration and active control.

Currently, linear motors exhibit diverse structural forms. Based on their topological configuration, they are classified into the cylindrical, flat-plate, and U-channel types [25,26,27], as illustrated in Figure 3. According to their operating principles, they fall into four categories: permanent magnet synchronous motors (PMSMs), alternating current induction motors (ACIMs), brushless direct current motors (BLDCs), and switched reluctance motors (SRMs) [28,29,30,31,32]. Performance comparisons of two classification schemes are presented in

Table 2. Performance comparison of classification scheme based on topological configuration.

Type	Advantages	Limitations	Application Fields
Cylindrical	High winding utilization, absence of transverse end effects, high thrust density, superior servo performance, etc.	Limited stroke, stringent manufacturing requirements, inefficient heat dissipation, etc.	Short-stroke high-acceleration systems such as automotive suspensions and electromagnetic catapults
Flat-plate (with iron core)	Excellent heat dissipation, high power density, exceptional control precision, etc.	Significant thrust ripple, low lateral force resistance, etc.	Long-stroke high-precision positioning systems such as precision machine tools, photolithography machines, and medical imaging devices
U-channel	Minor thrust ripple, simplified installation process, etc.	Low thrust density, limited positioning accuracy, higher cost, etc.	Long-stroke high-speed heavy-load systems such as high-speed conveyors and vibration testing platforms

and

Table 3. Performance comparison of classification schemes based on operating principles.

Index	PMSM	ACIM	BLDC	SRM
Operating temperature	★★★★★	★★★☆☆	★★★★★	★☆☆☆☆
Control complexity	★★☆☆☆	★☆☆☆☆	★★★☆☆	★★★★★
Compactness	★★★★★	★★★☆☆	★★★★★	★★★★☆
Noise emission	★★★★★	★★★☆☆	★★★★★	★☆☆☆☆
Manufacturing cost	★☆☆☆☆	★★★★★	★★☆☆☆	★★★★★
Reliability	★★★★☆	★★★★★	★★★★★	★★★★★
Thrust ripple	★★★★★	★★★★★	★★★☆☆	★★★☆☆
Efficiency	★★★★★	★★★☆☆	★★★☆☆	★★★☆☆
Response speed	★★★★★	★★★★★	★★★★☆	★★★★★
Comprehensive score	37/45★	33/45★	35/45★	32/45★

.

Analysis of Table 3 reveals that PMSMs demonstrate superior efficiency, more compact dimensions, and simpler control systems compared to ACIMs. While BLDCs and SRMs exhibit certain advantages in manufacturing cost, control complexity, and reliability, both suffer from inherent drawbacks, including significant thrust ripple and lower efficiency, rendering them unapplicable for high-precision automotive suspension actuators. Furthermore, rapid advancements in motor PM materials and control technologies have substantially improved the manufacturing cost-effectiveness and control performance of PMSMs. Therefore, PMSMs have emerged as the predominant choice for actuators of automotive suspension systems.

Moreover, while cylindrical motors offer high thrust density and superior servo performance, their limited stroke and challenging heat dissipation pose significant design constraints for suspension applications. Flat-plate motors, in contrast, excel in heat dissipation and control precision, making them theoretically better suited for high-performance applications, but their significant thrust ripple and sensitivity to lateral forces could degrade ride comfort and necessitate more complex control algorithms to compensate. The choice of motor topology, therefore, is not a straightforward decision but a critical design compromise based on the prioritization of stroke, force density, thermal management, and cost.

Additionally, the arrangement schemes of two critical components, PMs and coils, exert a profound influence on motor performance [33]. Three primary classification schemes exist: the relative position of PMs and coils categorizes configurations into moving-magnet and moving-coil types, PMs magnetization orientation differentiates axial, radial, and Halbach arrays, while coil core structural form separates into slotless and slotted designs [34,35,36,37]. Schematic illustrations of these three arrangement schemes are provided in Figure 4, with performance comparisons summarized in

Table 4. Performance comparison of classification based on arrangement scheme of PMs and coils.

Arrangement Scheme		Advantages	Limitations
Relative position	Moving-coil	Low moving inertia, lower cost, etc.	Low thrust density, poor heat dissipation, cable fatigue susceptibility, etc.
	Moving-magnet	High power density, reliable electrical connections, efficient heat dissipation, etc.	Significant copper loss, low mechanical reliability of PMs, etc.
Magnetization orientation	Radial	Minimal manufacturing cost	Significant thrust ripple, minimum air-gap magnetic flux density
	Axial	Minimal thrust ripple, moderate air-gap magnetic flux density	Higher manufacturing cost
	Halbach	Maximum air-gap magnetic flux density	Highest manufacturing complexity, maximal cost, severe thrust ripple
Coil core structural form	Slotless	Low thrust ripple	Reduced air-gap magnetic flux density
	Slotted	Significant air-gap magnetic flux density	High thrust ripple

.

2.3. Composite Configuration of LMEERS

The single-motor configuration of LMEERS cannot simultaneously ensure fundamental dynamic characteristics during energy regeneration and fail-safe properties during active control [38]. To address this limitation, composite configurations integrating complementary advantages of different types of shock absorbers are proposed to enhance the comprehensive performance of LMEERS. They are classified based on their operating principles into electro-hydraulic, electro-electro, and electro-inerter composite systems.

2.3.1. Electro-Hydraulic Composite LMEERS

The electro-hydraulic composite (EHC) configuration typically integrates a linear motor with a passive hydraulic damper or a solenoid valve damper. It utilizes the base damping provided by the latter to compensate for the shortcomings of the linear motor in damping characteristics, thereby enhancing the dynamic performance and reliability of the suspension system.

Ding et al. [39,40,41] proposed a hybrid electromagnetic actuator structure where a hydraulic damper was positioned inside a linear motor, as shown in Figure 5. In this configuration, the PM mover of the motor is rigidly connected to the damper piston rod, and the stator coils are rigidly connected to the damper cylinder barrel, thereby achieving a parallel arrangement of the damper and motor. They conducted in-depth research on the working mechanism and control scheme for this EHC configuration, revealing the influence law of damping on energy regeneration and vehicle body vibration isolation. Furthermore, a switching control strategy matching the adjustable damping of the linear motor and the fixed damping of the hydraulic damper was devised. Wei et al. [42] designed an EHC-type LMEERS applicable to MacPherson independent suspensions by employing a coaxially nested arrangement of a linear motor, a hydraulic damper, and a coil spring. The developed configuration ensures the safety and stability of the MacPherson suspension.

Acknowledging that hydraulic dampers can only provide fixed damping, a hybrid electromagnetic actuator structure integrating a linear motor with a solenoid valve shock absorber was proposed by Kou et al. [43,44]. Here, the former is utilized for active control or energy recovery, while the latter provides variable hydraulic damping by adjusting the solenoid valve opening. A multi-mode switching control strategy was designed for this composite configuration, achieving effective coordination of ride comfort, handling stability, and energy regeneration capability for suspension systems.

In contrast to hydraulic and solenoid valve dampers, which adjust damping by changing the fluid flow, magnetorheological (MR) dampers utilizing smart rheological materials can continuously adjust damping within milliseconds, offering a significantly larger control bandwidth and damping adjustment range. Consequently, MR dampers have become a current research focus in the automotive suspension field. Self-powered electromagnetic damping systems combining an energy-harvesting linear motor with an MR damper represent another common EHC configuration.

Chen et al. [45] positioned a linear motor outside an MR damper for energy regeneration, while the MR damper provided semi-active control. In this setup, the linear motor consistently operates at its maximum energy regeneration power state, and the regenerated electrical energy directly powers the MR damper, thereby achieving self-powered semi-active control. Wang et al. [46] designed a self-powered electromagnetic vibration suppression and absorption system by externally integrating a linear motor and an MR damper in parallel. Within this system, the linear motor functions for vibration absorption and energy regeneration, while the MR damper provides vibration suppression. Simulation results demonstrated that, in comparison with the sole MR suspension, this system achieved superior dynamic performances. Furthermore, the regenerated energy covered the power consumption required for semi-active control.

2.3.2. Electro-Electro Composite LMEERS

The electro-electro composite (EEC) configuration typically integrates an eddy current damper or constitutes a dual-motor structure. Ebrahimi et al. [17] proposed a hybrid electromagnetic damper featuring a highly integrated linear motor and eddy current damper. In this structure, an eddy current damper, composed of an outer conductor tube and outer magnet, is placed concentrically outside a cylindrical linear motor. When relative motion occurs in the damper, the varying magnetic field induces the eddy current within the conductor, providing an additional passive damping coefficient of 1570 Ns/m. As a result, system energy consumption was reduced by over 70%. Furthermore, Zhang et al. [47] employed a Halbach PMs array within an EEC structure to enhance the magnetic field variation rate, thereby increasing the magnitude of the induced eddy current damping. They also investigated the influence law of the dislocation ratio between the inner and outer PMs on the motor’s energy regeneration power and the composite damping coefficient.

Hu et al. [48] developed a hybrid generator integrating a sliding-mode triboelectric nanogenerator (S−TENG) with a linear motor, as depicted in Figure 6. This dual-motor structure achieved self-powering for onboard sensors without compromising vehicle ride comfort. Suda et al. [49] designed a self-powered electromagnetic active vibration isolation system for heavy-duty truck cabins with the coaxial arrangement of two linear motors. One motor operates in the generator mode to recover energy and simultaneously to provide passive electromagnetic damping. The other utilizes the recovered energy to output active control forces for suspension system. In contrast to Suda’s coaxial arrangement, Li et al. [50] employed the parallel-axis arrangement of dual linear motors, as illustrated in Figure 7. In this configuration, the primary motor functions as the actuator for active vibration suppression and energy recovery, while the secondary motor acts as a vibration absorber to absorb wheel vibration energy. Hardware-in-loop testing results demonstrated that this configuration effectively balanced the vertical dynamic performance and energy-harvesting capability, exhibiting a regeneration potential of 72 W on the B-class random road. The dual-motor structure employing a linear motor and a rotary motor was developed by Wang et al. [51].

2.3.3. Electro-Inerter Composite LMEERS

The electro-inerter composite (EIC) configuration introduces an inerter element into the electromagnetic system, breaking through the traditional two-element (spring-damper) parallel configuration and broadening the vibration isolation frequency band of suspension systems. Yang et al. [52] investigated the influence of series and parallel arrangements of the linear motor and inerter on the energy regeneration capability and ride comfort of suspensions, as shown in Figure 8. They concluded that the parallel arrangement is more conducive to energy harvesting efficiency, while the series arrangement benefits vehicle ride comfort. Shen et al. [53,54] integrated a linear motor with a hydraulic piston type inerter, designing a split-type EIC actuator, as illustrated in Figure 9. This design features primary and secondary hydraulic cylinders arranged side-by-side and connected via fluid circulation tubes. And the linear motor is integrated with the secondary cylinder. During suspension operation, fluid circulating between the primary and secondary cylinders generates a hydraulic inerter effect. Simultaneously, the motor can recover energy driven by the secondary cylinder piston rod or actively output electromagnetic force to the secondary cylinder. Subsequently, Hu [55] implemented active control for this EIC configuration, exploring its potential for improving vehicle dynamic performance.

He et al. [56] compared the performance indexes of EIC actuators with a linear motor and a rotary motor. They concluded that the ball-screw-based rotary motor combined with the inerter achieved a higher inerter–mass ratio, which was more advantageous for reducing actuator volume and mass towards commercialization. Gonzalez-Buelga et al. [57] proposed a novel electrical inerter, formed by connecting a parallel inductor–resistor circuit in series with a capacitor, and then integrated this inerter into the linear motor winding circuit to create an EIC configuration. This structure has minimal impact on the motor’s physical dimensions; however, it exhibits relatively lower energy regeneration power.

The single-motor based LMEERS configuration faces challenges in simultaneously ensuring satisfactory suspension dynamic performance during energy recovery and reliability during active control. To address these limitations, LMEERS is commonly integrated with auxiliary devices, primarily forming three composite configurations: EHC, EEC, and EIC.

• Currently, composite configurations centered around linear motors are predominantly EHC types, which underscores a fundamental engineering trade-off: reliability and “hard damping” versus energy efficiency and integration. The hydraulic component provides a fail-safe property and robust impact resistance, which is a critical advantage for automotive safety. However, this comes at the cost of energy that is intrinsically dissipated within the hydraulic fluid rather than being recovered, thereby reducing the net energy-saving potential of the entire system.
• In contrast, EEC types, exemplified by those integrating eddy current dampers, offer higher integration levels and pure electromagnetic operation but provide only “soft damping”, which may be insufficient for extreme driving conditions or failure modes. Other EEC configurations, such as the dual-motor structure, face challenges related to structural complexity and high cost, hindering commercialization prospects.
• EIC types introduce an inerter element into the electromagnetic system, breaking through the traditional two-element (spring-damper) parallel configuration and broadening the vibration isolation bandwidth. However, they encounter similar issues, including large volume, complex structure, elevated cost, etc.

Therefore, the selection of a composite configuration involves a strategic decision: prioritizing functional safety and robustness (favoring EHC) versus pursuing maximum energy regeneration and integration (favoring EEC/EIC), with the current industry trend leaning towards the former due to safety-critical considerations.

3. Performance Optimization of LMEERS

Commercial validation of LMEERS was demonstrated when Bose Corporation conducted public testing of its in-house developed suspension system in the Lexus LS400 model, revealing its capacity to recover vibration energy during compression strokes. The total energy consumption of LMEERS was reduced to merely one-third of the vehicle’s air conditioning load while excellent vibration attenuation was also achieved [58]. Similarly, BYD Auto has implemented its DiSus-Z, a linear motor electromagnetic suspension system, in the Yangwang U7 model, achieving comprehensive vehicle body control characterized by effective vibration isolation and negligible lateral tilt [59].

Extensive research substantiates LMEERS’s significant improvements in vehicle dynamic performance and energy conservation capability [60,61]. However, inherent limitations of linear motors constrain LMEERS performance in the aspects of damping, thermal, thrust, and regenerative characteristics. Addressing these deficiencies necessitates the conduction of performance optimization in terms of structural refinement, parametric optimization, and intelligent control. These three approaches all involve optimization processes, where advanced optimization algorithms serve as pivotal enablers for enhancing design efficiency [62,63,64]. Given that performance optimization for LMEERS constitutes a complex multidisciplinary, multi-objective problem, nonlinear programming methods are typically employed for systematic optimization design. The specific optimization workflow is detailed in Figure 10.

3.1. Optimization in Damping Characteristics

Linear motors are functionally equivalent to passive dampers when operating in energy regeneration mode. Yet, fundamentally distinct from hydraulic damping, the electromagnetic damping generated by motors constitutes “soft damping”, characterized by a significantly lower magnitude than hydraulic systems, thereby failing to rapidly attenuate suspension vibrations. For instance, the linear motor designed by Tang et al. [65] achieved a maximum damping coefficient of merely 940 N·s/m, while conventional passenger vehicles require 1500~2000 N·s/m for adequate vibration suppression. To address this deficiency, Gysen et al. [66,67] proposed embedding aluminum rings within motor stator slots. Relative motion between coils and PMs induces eddy currents in these rings, generating supplemental eddy current damping that reduces energy consumption during active control and enhances damping characteristics.

Building upon this concept, Ebrahimi et al. [17] added an additional layer of PMs concentrically outside the linear motor’s outer conductor tube. Relative stator–mover motion creates varying magnetic fields that induce eddy currents in the outer conductor tube, providing additional passive damping of 1570 N·s/m and reducing total motor mass by 53%. Tang et al. [68] further employed the Finite Element Method (FEM) to optimize motor parameters, aiming to boost power density and damping density. Additionally, they refined the motor structure by introducing a dual-layer laminated configuration and a radial PM array, which further enhanced the power density. Prototype testing results confirmed that the damping coefficient provided by the optimized linear motor met or exceeded the performance standards of conventional hydraulic shock absorbers.

It is noteworthy that the aforementioned solutions primarily focus on optimizing the linear motor structure and parameters to improve its intrinsic damping. Nevertheless, this enhanced damping fundamentally remains “soft damping”, exhibiting potential reliability concerns and failing to meet suspension dynamic demands under extreme operating conditions. Therefore, it is proposed that the reliable “hard damping” provided by hydraulic elements can be directly integrated in parallel with the linear motor to substantially increase the suspension system’s damping coefficient.

Asadi et al. [69,70] placed the linear motor inside a hydraulic damper. In this configuration, the hydraulic damper provides the base damping for the suspension system, while the linear motor recovers vibration energy. The motor’s equivalent damping can be adjusted by varying its load resistance to meet vehicle dynamic requirements under different driving conditions. Xu et al. [71] filled the interior of a linear motor with hydraulic fluid and set solenoid valves onto the piston coaxial with the motor mover. By controlling the solenoid valve opening, the damping coefficient of the hydraulic unit can be modulated. Based on this hybrid structure, the actuator can operate in three modes. In active mode or regeneration mode, the linear motor outputs electromagnetic thrust or recovers energy, while the hydraulic unit provides the base damping, ensuring suspension dynamic performance. In semi-active mode, both the motor and the hydraulic unit can simultaneously provide variable damping.

3.2. Optimization in Thermal Characteristics

Temperature rise directly deteriorates the output thrust and winding losses of linear motors, consequently degrading vibration suppression effectiveness and energy regeneration efficiency of LMEERS. In severe cases, it can even lead to PM demagnetization and winding insulation failure. Common mitigation approaches involve parametric optimization of the motor structure, implementing cooling systems, and developing thermal management control strategies.

3.2.1. Structural Optimization in Thermal Characteristics

In the aspect of parametric optimization, Wang et al. [72] proposed a bidirectional electromagnetic-thermal coupled model, accounting for the influence of variations in material thermal properties on temperature rise. With winding temperature rise and motor detent force as optimization objectives, the Response Surface Methodology (RSM) was employed for multi-objective optimization of sensitive structural parameters. The optimized design reduced winding temperature rise and electromagnetic losses by 11.02% and 17.50%, respectively. Zhu [73] established an electro-magnetic-thermal multiphysics coupled model for the linear motor, the accuracy of which was validated by a constructed temperature rise test platform. Subsequently, a neural network surrogate model was used for co-optimization of motor structural parameters. The results indicated a 6.3% reduction in the optimized coil peak temperature.

BYD Auto has conducted structural refinement of LMEERS by arranging various cooling systems in order to improve its thermal characteristics. Several liquid-cooling schemes have been designed, such as installing external radiators [74] and incorporating internal heat exchange cavities or cooling chambers within motors [75,76,77]. An air-cooling solution featuring a novel rectifier design capable of generating stable, high-speed airflow within the motor housing for stator cooling was also developed [78].

3.2.2. Thermal Management

For the dynamic operating environment of automotive suspensions, precise tracking of the linear motor’s transient temperature response is essential for implementing effective thermal management and improving the utilization efficiency of the motor’s electromagnetic output. Available monitoring methods include sensor-based and model-based approaches. The former involves direct sensor placement within motors but poses significant challenges regarding system cost, reliability, and signal accuracy. Therefore, research should prioritize the latter approach [79,80].

Common thermal monitoring models can be categorized into Lumped Parameter Thermal Networks (LPTNs) or numerical modeling. Both methods can effectively predict motor temperature distribution [81,82]. Lu et al. [83] investigated the thermal distribution of a PM linear motor during operation on the basis of LPTN. This enabled real-time optimization of the coolant flow rate in the liquid-cooling system. Furthermore, the optimal relationship between the short-time large current and working time, as well as the optimal duty cycle for the drive current, were determined. Chow et al. [84,85] modeled the motor with the Finite Difference Method (FDM), as shown in Figure 11, to calculate the internal heat transfer. Experiments confirmed the high accuracy of this method for temperature prediction.

3.3. Optimization in Thrust Characteristics

The thrust output of a linear motor is proportional to its volume, while the compact installation space within a suspension system imposes significant constraints on the dimension design of motors requiring high thrust. Furthermore, several factors such as end effects and cogging effects cause thrust ripple, which deteriorates the positioning accuracy and operational stability of motors [86,87,88]. To optimize the thrust characteristics of linear motors, three approaches are typically employed, namely structural refinement, parametric optimization, and intelligent control.

3.3.1. Structural Optimization in Thrust Characteristics

Regarding refinement and optimization, for the primary unit, Refs [89,90,91] proposed to optimize the primary core length to reduce end forces. Refs [92,93] demonstrated that incorporating an auxiliary pole structure on the primary unit could effectively suppress thrust ripple. Makki et al. [94] investigated the influence of primary core slotting design on the magnetic reluctance force. A tubular linear PMSM featuring a double primary structure was designed by Wu et al. [95,96]. The electromagnetic characteristics of the dual primaries was superimposed, and the end tooth structure was optimized, which effectively suppressed the even harmonics within the detent force, thereby reducing motor thrust ripple. The optimized structure exhibited low thrust ripple and excellent working performance. Zhang et al. [97,98] proposed a modulation method for cogging force and end force based on the destructive interference theory. Accounting for both cogging and end effects, they established an integrated subdomain analytical model to optimize the primary core structural parameters, thereby reducing detent force. The proposed method achieved a thrust ripple below 1.5%.

In addition to considering the primary structure, Yan et al. [23] also investigated the influence of secondary PM parameters on thrust ripple. Multi-objective optimization with the Taguchi method and RSM resulted in an 11.9% increase in average thrust and a 76.6% reduction in ripple for the optimized motor. A novel skewing pole structure for PM was proposed by Li et al. [99], which further reduced thrust ripple. Xu et al. [100] suggested employing the Halbach array for PM to suppress thrust ripple. Refs [101,102,103] investigated the impact of PM shape on thrust performance, such as the arc-shaped PMS shown in Figure 12, while complex shapes increased the manufacturing complexity. Cheng [104] discovered that motor detent force would reach its minimum when the number of slots and poles were coprime. Lu et al. [105] further clarified that in single-sided linear motors, thrust characteristics are superior when the slot–pole combination differs by 1 or 2. For double-sided structures, thrust density is higher when the slot–pole combination differs by 1.

3.3.2. Intelligent Control in Thrust Characteristics

Implementing advanced control strategies to compensate for linear motor behavior and improve dynamic response proved to be an effective approach for detent force suppression. Common suppression strategies include active disturbance rejection control [106,107,108], sliding mode control [109,110], predictive control [111,112,113], and iterative learning control [114,115,116].

Kim et al. [117] compensated for thrust ripple with a feedforward controller. Zhang et al. [118] designed a Proportional Resonant Internal Model Extended State Observer (PR-IMESO) specifically targeting detent force. This designed disturbance observer possessed excellent capabilities of observing and compensating for detent forces, and effectively suppressed thrust ripple caused by other unmodeled factors. Model-based feedforward and observers do not change the controller structure and require less computational resources, but their optimization effectiveness is limited in high-frequency, high-speed environments. In contrast, intelligent control strategies, such as neural network and iterative learning, offer superior compensation for thrust ripple. However, they inherently suffer from substantial computational burdens, potentially compromising the real-time performance of the control system.

3.4. Optimization in Regenerative Characteristics

The energy regeneration power in energy recovery mode and the electromagnetic thrust in active control mode are fundamentally determined by the air-gap magnetic flux density between the primary and secondary components. To enhance motor energy regeneration efficiency, optimization efforts are focused on three aspects: structural refinement, parametric optimization, and intelligent control.

3.4.1. Structural Optimization in Regenerative Characteristics

Regarding structural refinement, the layout of PMs and coils is primarily optimized. In the aspect of PM design, Gupta et al. [119] designed an electromagnetic energy regenerative damper featuring a coaxial arrangement of inner and outer dual-layer annular PMs for improving regenerative characteristics. Although increasing the number of PMs could readily enhance the air-gap flux density, it concomitantly increases the actuator’s volume and weight, hindering practical application.

To address this limitation, Halbach [120] innovatively proposed a novel PM array. Unlike conventional arrays, adjacent PMs in this array are magnetized at 90° angles relative to each other. This design significantly strengthens the magnetic field on one side while nearly eliminating it on the opposite side, thereby achieving high field strength within a compact volume. Zhu et al. [121,122] investigated the application potential of Halbach arrays for vibration energy recovery. Simulation results demonstrated that single-layer and double-layer Halbach arrays increased the energy regeneration power of linear motors by 40% and 88%, respectively. Dai [123] compared the air-gap flux density of different arrays on the basis of FEM. As shown in Figure 13, the Halbach array exhibited the highest density. The Halbach-like array was designed by Xiong et al. [124] to increase motor energy regeneration power. Additionally, Kopylov et al. [125] found that implementing a back-iron architecture for PMs yielded higher energy harvesting power.

Additionally, regarding coil layout, factors such as turn number, layer number, phase number, and the core slotting design also influence energy recovery power. Tang et al. [65] indicated that a larger winding phase number could increase power. Figure 13, above, also illustrates that the slotted core design yields a greater magnetic flux density.

For parametric optimization, Hasani et al. [126] proposed an optimization method based on the electromagnetic damping model to improve motor energy regeneration efficiency. Abdelkareem et al. [127] conducted frequency-based parametrical bandwidth sensitivity analyses on suspension vibration energy recovery potential with Monte Carlo sensitivity simulations. The correlation between energy-harvesting potential and various suspension parameters were revealed, providing the theoretical foundation for subsequent parametric optimization and facilitating the conceptual design of EERS.

3.4.2. Intelligent Control in Regenerative Characteristics

Once the topology and parameters of LMEERS are finalized, efficient and reliable intelligent control strategies are essential to fully exploit its energy regeneration potential. Li et al. [128] proposed a pavement-level-based switching control strategy for LMEERS. Its core logic involves adjusting the control parameters of the top-layer controller according to the road profile to ensure the maximum energy harvesting efficiency under high-frequency excitation. Simulation results showed that this switching strategy improved regenerative efficiency by 30.5%. Azmi et al. [129] designed an optimal control strategy based on a continuous predictive approach. The energy regeneration power increased by 31% due to the suspension control focus steered towards high-efficiency regenerative regions by adjusting weighting coefficients. The time-delay control was employed by Wu et al. [130] to enhance the energy recovery capability. The existing literature demonstrates that the introduction of active control can effectively improve energy harvesting potential. However, it is noteworthy that extracting excessive energy from suspension vibration will degrade other performance indexes, highlighting an inherent trade-off between the dynamic performance and energy regeneration capability of LMEERS.

3.5. Emerging Optimization Methods

While the optimization methods discussed in the preceding sections have significantly enhanced the comprehensive performances of LMEERS, they often face inherent limitations. These include the computational complexity of high-fidelity multi-physics models, challenges in handling system nonlinearities and uncertainties in real-time, and the difficulty in achieving a globally optimal trade-off between dynamic performance and energy regeneration capability. Recent advancements in Artificial Intelligence (AI) and Digital Twin (DT) technologies offer a transformative paradigm to overcome these limitations and unlock new frontiers in LMEERS performance optimization [131,132].

DT technology, characterized by the creation of a high-fidelity virtual replica of the physical suspension system, moves beyond the traditional static modeling. This cyber-physical system synchronizes with its physical counterpart in real-time via sensor data, enabling unprecedented capabilities for optimization [133,134,135,136,137]. The DT framework integrates high-fidelity electromagnetic, thermal, and structural models, facilitating the virtual prototyping and design validation, real-time performance prediction, and closed-loop online calibration. Prusa et al. [138] conducted a comparative analysis of the performance differences between DT technology and the traditional Finite Element Method (FEM) in the development of linear motors, arguing that DT can simultaneously achieve both simulation accuracy and real-time capability. This led to the conclusion that DT is highly important for the motor development process. Luo et al. [139] proposed a data-driven DT method for real-time estimation of the motor operating temperature, with experimental results demonstrating the method’s effectiveness in achieving thermal management for motors. Antonelli et al. [140] developed a DT of a suspension system after performing nonlinear modeling, which was utilized for the development and optimization of the suspension control system. Furthermore, online calibration of the controller was also conducted on the DT.

Meanwhile, AI-driven methodologies are revolutionizing control and optimization strategies [141,142,143,144]. Deep Learning (DL), particularly through deep neural networks, excels at identifying complex, non-linear patterns from operational data [145,146]. DL can be employed to develop data-driven surrogate models that approximate the system’s dynamics with less computational cost than full physical models, or to enhance road information identification algorithms for more precise functionality switching [147,148]. Iwata et al. [149] employed a pre-trained deep learning model to predict the degree of influence of transitions from air to magnetic materials in a PMSM, thereby facilitating the topological optimization of the motor. Both the development efficiency and the motor’s electromagnetic and mechanical performance were significantly improved. Khan et al. [150] introduced a novel method using deep learning to predict the efficiency map of motor drives, which demonstrated higher accuracy and efficiency compared to FEM. In addition, this method is proven to be applicable to the design and optimization processes of motors.

The convergence of DT and AI creates a powerful symbiotic relationship where DT provides the realistic environment necessary for training and validating AI algorithms, while AI provides the intelligent core to analyze data and make decisions within the DT framework. This integrated approach promises a future where LMEERS can autonomously self-optimize its performance in real-time, achieving a truly adaptive and intelligent suspension system. Although these technologies are still immature in their application to LMEERS, they signify a pivotal shift from conventional methodologies towards a more holistic, data-driven, and self-adaptive optimization paradigm, setting a clear direction for future research and development.

In summary, due to performance limitations inherent in the linear motor, LMEERS exhibits shortcomings in damping, thermal, thrust, and regenerative characteristics. Three aspects of structural refinement, parametric optimization, and intelligent control are typically focused on to improve the comprehensive performance of LMEERS.

• Damping characteristics is typically enhanced by integrating the eddy current or hydraulic damping modules.
• Parametric optimization and implementing cooling systems are simple and effective approaches to mitigate motor temperature rise.
• Thrust and regenerative characteristics, being critical to the functional behavior of LMEERS, require a comprehensive set of approaches for improvement.
• Emerging optimization methods, such as DT and AI, demonstrate substantial application potential, representing a promising and critical direction for future research.

4. Functionality Switching Criterion Identification of LMEERS

An inherent trade-off exists between the energy regenerative capability and dynamic performance of LMEERS. Consequently, the working modes of LMEERS must be judiciously switched according to driving conditions to balance its dual functionalities of energy regeneration and active control. Road excitation, as the primary input source generating vibration for suspension systems, also constitutes a critical component of the vehicle’s driving conditions. Therefore, road surface information serves as the most appropriate switching criterion for determining whether LMEERS should prioritize active control or energy recovery [18].

Furthermore, the extraction and identification of road surface information can offer more precise and rational front-end decision-making for subsequent top-layer control. This ensures the organic combination and efficient coordination between energy regeneration and active control, ultimately achieving the control objective of optimal overall performance across all road conditions. With the rapid development of high-level autonomous driving, multi-sensor fusion-based environment recognition technologies are maturing daily. This maturation provides the technical foundation for LMEERS to perform functionality switching based on road surface information. Hence, researchers worldwide have begun to prioritize road surface information as a key criterion for LMEERS mode switching.

For vertical dynamic control of suspension systems, road surface information primarily comprises road surface roughness and road surface type.

• Road surface roughness, defined as the random variation in road surface profile (as illustrated in Figure 14), is the direct vertical excitation input to the wheels [151]. Through the tire–suspension–body transmission path, it induces vibrations. These vibrations influence the vehicle’s demand for either dynamic performance or energy regeneration capability—essentially determining which functionality mode is the optimal choice at any given moment. Therefore, road surface roughness is the core road information considered during LMEERS functionality switching, particularly in single-wheel suspension application scenarios.
• Regarding the road surface type, it reflects the statistical characteristics of road surface roughness, typically serving as prior knowledge to assist in estimating road surface roughness [152]. The fundamental methods for road surface information identification are summarized in Figure 15. The identification methods of road surface roughness are primarily divided into three categories, namely direct measurement, non-contact measurement, and system state response-based estimation [153,154,155]. And road surface type identification methods are categorized into two main classes, namely image-based direct recognition and vehicle dynamic characteristic-based indirect recognition [156,157].

Figure 14. Road surface roughness visualization: (a) vertical road surface profile; (b) contact between a rough road surface and tire (the road vertical profile is exaggerated for better visualization).

Figure 14. Road surface roughness visualization: (a) vertical road surface profile; (b) contact between a rough road surface and tire (the road vertical profile is exaggerated for better visualization).

Figure 15. Fundamental methods for road surface information identification.

Figure 15. Fundamental methods for road surface information identification.

4.1. Identification of Road Surface Roughness

4.1.1. Direct Measurement Methods

Direct measurement methods utilize specialized equipment, such as road roughness meters, installed on or connected to vehicles to directly measure the road surface profile in the case of maintaining continuous contact with the ground [158,159]. Guo et al. [160] conducted a comparative analysis of various measurement techniques, concluding that direct measurement methods could yield high-precision road surface roughness data, thereby accurately reflecting road surface profile information.

A novel compact pavement profilometer was employed by Abulizi et al. [153] to conveniently collect data for assessing the roughness condition of public roads. Lushnikov et al. [161] compared the operational characteristics and measurement accuracy of several profilometers used for measuring road surface longitudinal roughness. Currently, a widely adopted road roughness meter within the industry is the Longitudinal Profile Analyzer (LPA) developed by the Laboratoire Central des Ponts et Chaussées (LCPC) in Nantes, France. Its structure is shown in Figure 16. This instrument can accurately measure road surface profiles with amplitudes around ±100 mm and wavelengths spanning 0.5–20 m to 1–50 m. Since that the LPA feeler wheel maintains contact with the road surface via a spring and damper system, the spring stiffness and damper damping coefficient influence the amplitude–frequency characteristics of the LPA, thereby affecting the measurement accuracy within its resonance frequency range [162]. Besides the French LPA, other commonly applied road roughness meters include the articulated multi-wheeled profilograph developed by the UK’s Transport Research Laboratory (TRL) [163], and the vibratory cumulative measuring device adopted by the US Federal Highway Administration (FHWA) [164].

Limitations inherent in the structure and installation requirements of road roughness meters result in the poor transplant ability of these instruments. Furthermore, the measurement process necessitates that vehicles must travel at relatively low speeds. Therefore, direct measurement methods based on specialized equipment are mainly applied to pavement maintenance and repair and inapplicable for real-time road information acquisition on conventional vehicles.

4.1.2. Non-Contact Measurement Methods

Non-contact measurement methods operate based on the inertial reference principle. Distance sensors (e.g., Light Detection And Ranging (LiDAR), Radar) or vision sensors (e.g., optic camera) installed on vehicles are utilized to directly measure road surface profile [165]. With the advancement of automotive intellectualization, these methods exhibit broad application prospects. Babu et al. [154] proposed a novel semi-empirical model for road surface roughness identification based on the high-resolution airborne Polarimetric Synthetic Aperture Radar (PolSAR). The measurement results demonstrated high agreement with ground truth data. Furthermore, the proposed model is adaptable to lower-performance SAR systems, thereby reducing identification costs. Gao et al. [166] applied high-precision point cloud data from a 3D LiDAR to measure urban pavement roughness. This approach accurately estimated the International Roughness Index (IRI) values of actual roads and the distribution characteristics of their spatial roughness. The LiDAR data-based identification algorithm developed by Kumar et al. [167] estimated pavement roughness by calculating the profile residual values between the LiDAR points and road surface mesh. Their experimental results validated the algorithm’s effectiveness. Blasiis et al. [168] designed the identification workflow illustrated in Figure 17. It demonstrates the minor deviations between road surface profiles calculated from LiDAR data and those directly acquired by a profilometer.

Current research indicates that LiDAR-based non-contact measurement methods achieve high accuracy but they impose a significant cost burden on vehicles. Consequently, the relatively lower-cost optic cameras attain expanded concerns. Khalifeh et al. [169] constructed 3D road surface models according to the color and depth images captured by cameras. The road profile under a single wheel track was then extracted to ultimately derive the IRI value. This method offered high measurement accuracy and low equipment costs. Aleadelat et al. [170] employed a low-cost depth camera to estimate IRI values, achieving accuracy of 83%.

Although non-contact measurement methods show high identification accuracy and good transplant ability, enabling on-board measurement on conventional vehicles, they necessitate additional expensive sensors and image processors. Moreover, due to lengthy processing times, measurement effectiveness remains constrained by vehicle speed (typically 20~100 km/h). Additionally, commonly used LiDARs and cameras exhibit poor environmental adaptability, making it difficult to guarantee their measurement accuracy under rainy or snowy weather [171].

4.1.3. System State Response-Based Estimation Methods

To address the limitations of direct measurement methods, such as poor transplant ability, and those of non-contact measurement methods, such as high cost and poor environmental adaptability, estimation methods based on vehicle dynamic responses using low-cost sensors commonly equipped in conventional vehicles have garnered significant attention. The type of suspension signals used obviously impacts the applicability and estimation accuracy of different state response-based estimation methods.

Acceleration is one of the most common signals and boasts the highest sensor equipment rate in suspension systems. It directly reflects vehicle vibration intensity; hence, identification methods based on acceleration signals have been extensively researched. Liu et al. [172] designed an online road level identification algorithm based on vehicle body acceleration signal, with its principle illustrated in Figure 18. First, they constructed an inverse dynamic model of a quarter-car suspension system with the adaptive neural fuzzy network, then the time-domain road surface profile estimator was designed. Finally, the frequency-domain road level estimator was developed based on Power Spectral Density (PSD) estimation. Experimental results demonstrated that this algorithm achieved estimation accuracy exceeding 90% across various random roads and exhibited excellent adaptability to varying vehicle speed. Liu et al. [155] proposed a speed-decoupled road level identification method. Vehicle body and wheel accelerations were selected as input signals, and an improved Least-Squares Method (LSM) was applied to obtain pure spatial-domain pavement roughness parameters independent of vehicle speed, with estimation accuracy exceeding 95%. Axle acceleration was utilized by Ngwangwa et al. [173] to design a road identification method based on an artificial neural network for mining trucks. Notably, this method exhibits high estimation accuracy for discrete road obstacles, such as bumps, depressions, and potholes. Based on the Long Short-Term Memory (LSTM) model, Im et al. [174] designed a deep learning identification system for entire vehicles to estimate the roughness of unknown roads. This method worked with the data from accelerometers and gyroscopes at the vehicle’s center of gravity without a physical suspension system model, rendering it more lightweight and efficient.

In addition to the acceleration signal, suspension working stroke is another readily measurable vibration characteristic parameter. Guo et al. [175] proposed that suspension working stroke has the potential to be employed for pavement roughness identification. For this purpose, a novel road level evaluation index was defined, and its explicit expression in terms of suspension working stroke and vehicle speed was derived. Gong et al. [176] introduced the new Relative Roughness Index (RRI) according to IRI as the basis for identifying complex road roughness encountered by heavy-duty rescue vehicles. Furthermore, with suspension working stroke as the sole input, the road level identification method based on a Takagi–Sugeno (T-S) fuzzy controller was developed. A discrete Kalman observer considering unknown inputs was designed by Kang et al. [177]. Suspension working stroke, vehicle body acceleration, and wheel acceleration were selected as the state variables for online road surface roughness estimation. Due to significant simplifications of suspension system nonlinearities, this method exhibited certain identification errors. To address this limitation, Kim et al. [178] incorporated a vehicle parameter identification module to enhance the Kalman observer’s accuracy. Focusing on a half-car model, Li et al. [179] selected eight suspension signals as inputs, namely suspension working stroke, vehicle body acceleration, wheel acceleration, vehicle body pitch angular velocity, and displacement, and then employed the orthogonal experimental design to analyze the performance of four typical neural networks, namely BackPropagation (BP), Radial Basis Function (RBF), wavelet, and Nonlinear AutoRegressive with eXogenous inputs (NARX). Simulation results verified NARX as the optimal neural network for road roughness identification. Wang et al. [180] investigated the application potential of pavement roughness identification for multi-axle heavy vehicles. Using displacement and oil pressure signals from hydro-pneumatic suspension cylinders as response signals, a Support Vector Machine (SVM) trained by both model and real vehicle data was employed to recognize the road level.

System state response (e.g., acceleration, suspension working stroke)-based road surface roughness identification can be categorized into three core methodologies. The first type is the dynamic model-based inverse method, in which the road profile is directly estimated from sensor data according to the dynamic relationship between vehicle body and wheels. The second type is the state observer method, in which an observer designed based on the vehicle physical model fuses multi-sensor data to simultaneously estimate road information and suspension states. In contrast, the last type bypasses physical modeling and directly establishes end-to-end mapping from sensor data to road roughness, which is referred to as the data-driven method. A comparative analysis of these three methods is presented in

Table 5. Performance comparison of three system state response-based estimation methods.

Method	Real-Time Performance	Accuracy	Model Dependency	Exemplary Cases
Dynamic inverse	★★★★☆	★★★☆☆	Medium	[155,172]
State observer	★★★☆☆	★★★☆☆	High	[177,178]
Data-driven	★★☆☆☆	★★★★☆	Low	[173,174,179,180]

.

Road surface roughness identification methods have been primarily classified into three major categories: direct measurement methods, non-contact measurement methods, and system state response-based estimation methods. Each category possesses distinct characteristics and respective strengths.

Table 6. Performance comparison of three road surface roughness identification methods.

Type	Advantages	Limitations	Application Fields
Direct measurement	High accuracy, technologically mature, etc.	Poor transplant ability and real-time capability, sensitive to road surface conditions, etc.	Road maintenance
Non-contact measurement	Good real-time capability, relatively high accuracy, high efficiency, etc.	High cost, poor environmental adaptability, substantial computational load, etc.	Intelligent automotive chassis control
System state response-based estimation	Low cost, excellent environmental adaptability, strong robustness, etc.	Sensitive to vehicle parameters, poor performance on discontinuous random roads, etc.	Traditional automotive suspension control

summarizes the features and applicable scenarios of these three identification methods.

4.2. Identification of Road Surface Type

One fundamental function of suspension systems is to transmit and dynamically distribute the vertical loads acting on the tires. This ensures that tires maintain continuous contact with uneven road surfaces, thereby maximizing effective adhesion utilization between the tires and pavements. Furthermore, this enhances the traction performance, braking performance, and handling stability of vehicles. The same pavement under different environmental conditions, or different types of pavements under the same conditions, exhibit distinct surface characteristics. For instance, road adhesion significantly deteriorates on wet or icy surfaces, while gravel roads present a broadband random excitation. In addition, discrete pavement features, such as potholes, bumps, and cracks, impose more stringent demands on suspension system performance. Therefore, research on road surface type identification, followed by adaptive switching of suspension operating modes, constitutes a critical pathway for ensuring that vehicles maintain superior dynamic performance and energy regeneration capability even under complex road conditions. Additionally, different road types typically exhibit characteristic statistical features of the roughness, which can serve as prior knowledge to assist in estimating road surface roughness. Image-based direct recognition methods and vehicle dynamic characteristic-based indirect recognition methods are typically employed in the estimation of road surface types.

4.2.1. Image-Based Direct Recognition Methods

Direct recognition methods comprehensively utilize sensors, such as optic cameras and imaging radar, to acquire road surface images. Target information is then directly identified through image processing [181]. Sabery et al. [156] employed the Convolutional Neural Network (CNN) to classify road surfaces with images captured by an imaging radar. Liu et al. [182] also utilized the CNN to process the collected road surface image data via cameras for type identification. The recognition accuracy exceeded 99.9% for different road surfaces, with a processing time of approximately 9.5 ms per image. Subsequently, the control parameters of a semi-active control strategy were optimized based on the identified road information, enabling the suspension system to achieve superior dynamic performance. Zhao et al. [183] proposed a vision-based road classification method with the recognition accuracy of 94.84%. This method extracted texture features from road surface images captured by a camera, and then a deep learning classification model incorporating specific training strategies was employed to infer the road surface type. Furthermore, advancing this approach, Zou et al. [184] combined transfer learning with the Visual Geometry Group Network (VGGNet) model to design a network architecture specifically tailored for road classification. Its processing workflow is illustrated in Figure 19. Compared to other classical network models, this approach has significantly improved identification accuracy and training speed, making it applicable for preemptive perception of road types. The recognition method combining visual data with a Deep Neural Network (DNN), developed by Šabanovič et al. [185], exhibited high identification efficiency and was capable of monitoring every half-meter of road surface at vehicle speeds of 100 km/h.

For suspension control, discrete road surfaces, such as potholes, bumps, and cracks, significantly impact ride comfort and driving safety. Therefore, with road structural features as classification criterion, vision sensor-based road type identification methods have also been investigated. These methods aim to preemptively adjust suspension control parameters, thereby mitigating the deterioration of vehicle dynamic performance under transient excitations. Wang [186] proposed a semi-global block matching algorithm to construct a road profile model from 2D images captured by binocular cameras, and then extracted the road slope and bump features to train a multi-class SVM. As a result, the SVM could identify four characteristic road types: uphill, downhill, flat roads, and speed bumps.

The effectiveness of image-based direct recognition methods hinges on the efficiency of the image processing techniques. Common techniques are categorized into traditional methods and deep learning methods [187,188]. The former involves two steps: feature extraction and classifier construction. These typically require manual intervention, consuming significant labor and time resources, and exhibit limited performance in complex scenarios [189,190]. In contrast, deep learning methods can directly process raw data. They enable machines to autonomously learn feature representations and abstractions, thereby avoiding tedious manual feature construction and enhancing image recognition accuracy [191,192].

4.2.2. Vehicle Dynamic Characteristic-Based Indirect Recognition Methods

Direct recognition methods are inherently dependent on image quality, and their operational performances under harsh environmental conditions are difficult to guarantee. In addition, when actual driving conditions deviate from the algorithm training conditions, the estimation accuracy for road surface type tends to decrease. In contrast, vehicle dynamic characteristic-based indirect recognition methods exhibit superior environmental adaptability. Their fundamental principle is illustrated in Figure 20. Additionally, dynamic characteristic-based classification models inherently imply the interaction mechanics between the vehicle and the road surface. Therefore, their identification results possess greater applicability value for vehicle control.

Ward et al. [157] posited that the wheel acceleration directly reflected the road profile, thus selecting this signal as the algorithm input and employing an SVM for the identification. Notably, the vehicle speed was decoupled by performing spatial estimation on the road profile. Wang et al. [193] utilized accelerometers to capture triaxial accelerations during tire rolling, and then extracted time-domain and frequency-domain statistical features from the longitudinal and lateral acceleration signals. Following dimensionality reduction via principal component analysis, an SVM was used to classify and train the feature parameters, ultimately achieving road type estimation. With wheel vertical forces selected as the response signals, Yang et al. [194] applied wavelet packet transform for feature extraction, followed by an SVM for unpaved road classification. Zhao [195] selected wheel speed fluctuation, rolling resistance, and vertical acceleration as inputs and adopted the SHapley Additive exPlanations (SHAP) approach to elucidate the correlation between dynamic features and road surface types. A Random Forest (RF)-based road classifier was subsequently designed, and its recognition accuracy and recall rate both exceeded 93%.

The acoustic footprint varies significantly across different road types, and the frequency of tire–road noise on the same surface differs under varying moisture levels. On this basis, Alonso et al. [196] proposed a method to identify the dry/wet state of asphalt pavements by measuring tire–road noise. Paulo et al. [197] investigated the correlation between the acoustic signals generated at the tire–road interface and the road profile based on statistical learning methods. Combining Bayesian analysis with a neural network for road type classification achieved accuracy exceeding 90%. Furthermore, Kalliris et al. [198] evaluated the practical performance of various machine learning algorithms for road type identification using tire noise. Results demonstrated that second-order and third-order SVMs yielded the best performance.

The working principle underlying indirect road type identification is fundamentally identical to the data-driven method for road surface roughness identification introduced in Section 4.1.3. Both bypass system modeling to directly establish a mapping relationship between sensor data and road characteristics (roughness or type). However, the sensors employed for road type identification are not limited to those typically deployed within suspension systems.

To utilize the complementary strengths of both direct and indirect methods, multi-sensor fusion-based road type identification methods have been proposed. Wang et al. [199] introduced an identification method fusing the features of mechanical and visual sensor data. This approach first reconstructed the road profile via a vehicle dynamic model with wheel acceleration and vehicle speed information. Subsequently, feature extraction and classification of road surface images captured by cameras were conducted. Finally, the data features from all sensors were fused for road type identification. Experimental results revealed that identification accuracy based on the sole dynamic characteristics was relatively low, averaging 67%, while sole image-based identification averaged 88% accuracy. Notably, multi-sensor fusion significantly improved the average accuracy to 90%, with enhanced reliability and adaptability. Although multi-sensor fusion offers higher accuracy and reliability, providing a novel direction for road information identification research, vigilance is required regarding the “barrel effect” (where overall performance is limited by the weakest sensor), introduced by multiple sensors.

4.3. Decision-Making Algorithms for Functionality Switching

Accurate identification of road surface information (roughness and type) serves as an essential input for suspension control, but it is the decision-making algorithms that act as the intelligent gateway, determining the functional mode of LMEERS. The core objective of these algorithms is to resolve the inherent conflict between vibration isolation and energy harvesting by the intelligent switching between active control and energy regeneration modes based on real-time driving conditions. The prevailing decision-making algorithms can be categorized as follows.

• Rule-Based Threshold Switching: This is the most straightforward approach, where predefined thresholds on identified road indexes (e.g., IRI [176], root mean square of suspension state variables [177,178,179]) trigger functionality switching. For instance, if the road roughness exceeds a certain threshold, indicating poor road conditions, the algorithm prioritizes active control to ensure ride comfort and driving safety. Conversely, on smooth roads (low roughness), it switches to energy regeneration mode to maximize energy recovery [19,148]. While simple and computationally efficient, this method lacks flexibility and can lead to frequent or oscillatory switching if thresholds are not carefully tuned for complex road scenarios.
• Fuzzy Logic Inference: Fuzzy Logic Control (FLC) is highly suited for this application due to its ability to handle imprecise inputs with expert knowledge. The identified road information (e.g., “smooth”, “rough”) and vehicle states (e.g., “high speed”, “low speed”) are fuzzified and processed through a set of IF-THEN rules formulated by domain experts to output a decision or a continuous weighting factor between the two functionalities [64,200]. For example, a rule could state: “IF road is very rough AND vehicle speed is high, THEN prioritize active control.” This method offers smoother transitions between modes and better handles the ambiguity in road classification compared to rule-based thresholds.
• Learning-Based Adaptive Strategies: With the advancement of onboard processing power, data-driven learning algorithms are emerging for more intelligent and predictive switching. These strategies can adapt the switching policy online based on historical performance or driver preferences. Reinforcement Learning (RL) is a promising framework where an agent learns an optimal policy (switching strategy) by maximizing a reward function that balances ride comfort, driving safety, and energy recovery efficiency [201]. Neural network can also be trained to map identified road features and vehicle states directly to the optimal functionality mode [202,203]. Although these methods promise superior performance and adaptability, they require significant computational resources and extensive training data.

The selection of decision-making algorithms involves a trade-off between computational complexity, performance, and ease of calibration. The ultimate goal is to seamlessly integrate this algorithm with the top-layer control strategies (in Section 5) to form a cohesive hierarchical control architecture that fully exploits the potential of the dual functionality of LMEERS.

In summary, in-depth investigations into road surface information identification have been conducted, establishing it as a crucial switching criterion between the dual functionalities of energy regeneration and active control for LMEERS. Road surface information primarily encompasses road surface roughness and road surface type, typically identified with two on-vehicle approaches, namely image-based methods and dynamic response-based methods.

• The former offers preemptive perception of the road ahead and high identification accuracy but suffers from high equipment costs and poor environmental adaptability.
• The latter provides superior robustness and cost advantages, yet struggles to identify complex road surfaces.
• Multi-sensor fusion-based road information identification methods, capitalizing on the advantages of both methods, represent the future direction for on-vehicle solutions, contingent upon further reductions in sensor costs.

5. Top-Layer Control Strategies of LMEERS

Structural design and top-layer control constitute two pivotal aspects in LMEERS development. The former establishes the physical foundation and defines performance boundaries for the latter, while the latter exploits application potential and compensates for inherent deficiencies of the former. This synergy fundamentally determines the ultimate performance ceiling of LMEERS systems. Currently, extensive and in-depth research has achieved profound advancements in structural design and performance optimization, establishing robust feasibility for active control and energy regeneration within current configurations. Consequently, the imperative now shifts toward developing structure feature-based top-layer control methodologies to maximize operational efficiency across diverse working environments. Top-layer control strategies applicable for LMEERS are typically categorized into three types, namely classical control methods, modern control methods, and intelligent control methods.

5.1. Classical Control Methods

Classical control methods are typically applicable for single-input single-output linear time-invariant systems, the core tools of which are the frequency-domain analysis and transfer function models. These have the advantages of intuitiveness, practicality, and outstanding engineering solution capabilities [204,205]. Presently, the classical control methods commonly applied to LMEERS include skyhook control, groundhook control, and PID control.

5.1.1. Skyhook and Groundhook Control

Skyhook control was first proposed by Karnopp [206] in the 1974s. Its operating principle involves virtually connecting the vehicle body to an ideal inertial sky via a damper, thereby suppressing vertical vibrations of the sprung mass. This approach circumvents suspension nonlinearities by requiring the actuator to output a force proportional to the absolute velocity of the sprung mass but in the opposite direction. However, since the “ideal sky” is physically unrealizable, actuators mounted between the vehicle body and wheels must emulate this skyhook force, which inevitably amplifies unsprung mass oscillations. To address this limitation, Hong et al. [207] developed a modified skyhook strategy incorporating supplemental passive damping to suppress wheel vibrations, thereby effectively balancing ride comfort and handling stability. Groundhook control operates on a similar principle but targets vibration suppression of the unsprung mass. Comparative ideal models of both strategies are illustrated in Figure 21.

Ding et al. [208,209] designed an energy-saving modified skyhook algorithm for an electro-hydraulic composite LMEERS. The skyhook damping in the algorithm was provided by the linear motor while the passive damping was delivered by the hydraulic damper. This algorithm matching damping and regenerative characteristics of the actuator realizes the superior satisfaction of LMEERS control requirements, where ride comfort is obviously improved without substantial handling stability deterioration, overcoming traditional skyhook limitations. Furthermore, this algorithm enables the linear motor to recover energy to offset active control consumption, thereby reducing net system energy expenditure. Wang et al. [210] combined skyhook control with active disturbance rejection control, employing an extended state observer to online estimate and compensate for switching disturbances. This hybrid strategy ensured stable mode switching and effective vibration attenuation across random, impulse, and sinusoidal road profiles.

Jiang et al. [211] implemented a hybrid skyhook–groundhook damping control, optimizing strategy coefficients via Genetic Algorithms (GAs) to enhance ride comfort and wheel grounding performance. Kou et al. [212] established four workings modes, namely economy, safety, comfort, and comprehensive mode, and developed a corresponding hybrid skyhook–groundhook controller for LMEERS. In this hybrid strategy, the skyhook component worked for vehicle body vibration isolation while the groundhook component worked for wheel vibration suppression. Compared with passive suspensions, the proposed strategy reduced vehicle body acceleration by 45.5% at vehicle body resonance frequencies and decreased tire dynamic load by 54.7% at wheel resonance frequencies, with the average regenerative power reaching 70.9 W.

Skyhook-based algorithms effectively exploit LMEERS’s functionality of active vibration suppression without precise suspension models and are characterized by simple control laws, thereby having potential to achieve widespread commercial adoption.

5.1.2. PID Control

Proportional–Integral–Differential (PID) control and its variants are extensively applied in engineering fields, such as suspension systems, due to their structural simplicity, operational reliability, and easy implementation [213,214]. As illustrated in Figure 22, the algorithm comprises three core components: a proportional unit, an integral unit, and a differential unit, each of which makes a unique contribution to the control effect. Among them, the proportional unit is responsible for rapid adjustment of control output according to the deviation to enhance response speed. The integral unit works to improve steady-state accuracy through accumulated error correction, and the differential unit predicts deviation trends to preemptively adjust for oscillation mitigation. While fundamentally straightforward and practical, the parameters of the three PID control units require manual calibration in advance, presenting challenges such as low efficiency and limited adaptability. However, these limitations have been mitigated to some extent through the application of machine learning techniques and online tuning methodologies.

To enhance the PID control performance, advanced optimization algorithms have been employed for tuning PID parameters, such as surrogate model-based algorithms [215,216,217], multi-objective evolutionary algorithms [218,219,220], and heuristic and meta-heuristic algorithms [221,222,223]. However, these methods are exclusively applicable for offline updates and cannot dynamically adjust PID parameters according to real-time driving conditions during vehicle operation, exhibiting inherent limitations. Wei et al. [224] designed a fuzzy PID controller for LMEERS, which employed a fuzzy control principle to adjust PID parameters online, thereby further improving control effectiveness. This strategy effectively rejects external disturbances and handles system uncertainties, particularly applicable for complex nonlinear systems like LMEERS. Furthermore, Ahmed et al. [225] recognized that the fuzzy rules in fuzzy PID controllers constitute an offline-constructed knowledge base, resulting in poor adaptability to varying road conditions. To address this limitation, the online modified Differential Evolution (DE) optimization algorithm-based Fuzzy-DE-PID control strategy was proposed, which reduced the control system’s dependency on offline fuzzy knowledge base. Li et al. [226] tackled issues of inaccurate parameter tuning and performance deterioration of traditional PID control for complex nonlinear systems by introducing a novel Fractional-Order PID (FOPID) control strategy. This approach combined the fractional-order theory with conventional PID control, expanding the actuator’s control bandwidth, thereby outperforming fuzzy PID in enhancing vehicle ride comfort.

5.2. Modern Control Methods

Classical control theory offers straightforward control laws and easy implementation, yet its limited control performance struggles to reconcile conflicting requirements in vehicle dynamic performances. Modern control methods, founded on state-space equations, represent an advanced extension of classical control theory. They typically focus on the evolution law of state variables in multi-input multi-output (MIMO) control systems [227,228]. For LMEERS, common modern control methods primarily include adaptive control, optimal control, and robust control.

5.2.1. Adaptive Control

Initially developed for aerospace control challenges, adaptive control maintains desired system performance amidst model uncertainties or external disturbances, with online adjustment to control parameters [229,230]. Vehicles in operation constitute stochastically varying nonlinear systems, making them well-suited for adaptive control applications [231]. Cai et al. [232] designed an energy regenerative adaptive controller enabling LMEERS to simultaneously achieve energy regeneration and active vibration suppression. The controller could attain regeneration efficiency of 35%, and improved vibration attenuation by 27% compared to viscous damping systems. Basaran et al. [233] proposed a Lyapunov-based adaptive backstepping control strategy, as illustrated in Figure 23, wherein the adaptive term estimated motor parameters to compute the desired drive current for LMEERS motors. This method effectively reduced the vertical displacement and pitch angle of the sprung mass, and the adaptive parameter estimation process exhibited rapid convergence.

To mitigate the impact of linear motor nonlinearities on LMEERS active control performance, Li et al. [234] introduced adaptive control to compensate for response errors in the ideal motor drive current. The system dynamic responses at low frequencies were significantly improved compared to uncompensated control, thereby enhancing vehicle ride comfort. Gu et al. [235] developed a model-free adaptive sliding mode controller to mitigate the effects of modeling inaccuracies and time-varying parameters on LMEERS control performance. On the basis of the pseudo-gradient concept, the complex, hard-to-model dynamic model of LMEERS was transformed into a full-form dynamic linearized data model, thereby reducing the top-layer controller’s dependence on precise LMEERS modeling.

The core objective of adaptive control is to achieve online identification and compensation for system time-varying parameters, nonlinear dynamics, and external disturbances through real-time adjustments to controller parameters or structures. It is frequently embedded within other control theory frameworks, thereby forming composite control structures (e.g., adaptive robust control, adaptive sliding mode control), to enhance system robustness and tracking performance under unknown disturbances and model mismatches.

5.2.2. Optimal Control

The Linear Quadratic Regulator (LQR) represents the most mature and widely applied control strategy within optimal control [236]. Its principle involves constructing system state-space equations, defining control objectives, optimizing weighting coefficients, and applying control theory to derive the optimal control law under the defined control objectives. Skyhook control can be regarded as a special case of optimal control, alternatively termed suboptimal control.

Wu et al. [237] compared the vehicle body vibration isolation performance of the LQR and H∞ control strategies for linear motor-based electromagnetic active suspensions, with results demonstrating the superiority of LQR. Chen et al. [238] designed a hierarchical control strategy for electromagnetic active suspension, wherein LQR served as the top-layer controller to compute the optimal active force, and a GA was employed to optimize the LQR weighting coefficients. Wu et al. [239] investigated the dynamic behavior of a full-vehicle LMEERS system with LQR control under extreme operating conditions, as illustrated in Figure 24. The co-simulation results verified that LQR control significantly enhanced vehicle handling stability and driving safety.

Considering its multi-input nature in enabling more effective balance between ride comfort and driving safety, Lu et al. [240] adopted LQR control as the top-layer strategy for LMEERS in its active control mode, thereby achieving a 22.5% reduction in vehicle body acceleration compared to energy regeneration mode. To reduce motor energy consumption during LMEERS active control, Sun et al. [241] designed a modified LQR controller incorporating an energy consumption constraint into the traditional LQR weighting coefficient optimization model. In comparison with conventional LQR, this modified LQR reduced motor power by 80%, thereby effectively mitigating motor energy consumption and temperature rise issues, while still outperforming passive suspensions in dynamic performance. Azmi et al. [149] augmented the LQR optimal control law with a weighting factor of the suspension relative velocity, guiding the LMEERS operating point towards the high-efficiency regeneration zone, which enabled an additional 31% energy recovery. Bazios et al. [242] incorporated three performance indexes, namely vehicle body acceleration, dynamic tire load, and regeneration power, into the LQR objective function and investigated the influence of their weighting coefficients on LMEERS ride comfort, handling stability, and energy regeneration capability across varying excitation frequencies.

The above research collectively indicates that by modifying the LQR control model or selecting LQR as the controller for active mode, the conflicting demands of active vibration suppression and passive energy regeneration for LMEERS can be effectively reconciled.

5.2.3. Robust Control

Robust control primarily addresses uncertainties in suspension systems, such as parameter variations and unmodeled dynamics [243,244], with its main implementation approaches including H∞ control and Sliding Mode Control (SMC). The former enhances system robustness by minimizing the infinity norm of the closed-loop transfer function to reduce system sensitivity to various disturbances. Conversely, SMC delivers high robustness without requiring system identification during controller design, but it inherently suffers from chattering phenomena [245,246].

Hu et al. [247] designed a constrained H2/H∞ robust controller for linear motor-based electromagnetic active suspension, compensating for the motor’s output force to align actual suspension control force with the ideal target, thereby eliminating the impact of motor nonlinearities on suspension performance. Wu et al. [248] developed an H∞ robust controller based on Lyapunov stability theory to mitigate adverse effects of parameter uncertainties, actuator faults, and electromagnetic interference on LMEERS. Sande et al. [249] incorporated frequency-dependent weighting filters into the H∞ robust controller to balance ride comfort and handling stability in linear motor-based electromagnetic suspensions. Under convex pavement conditions, the active suspension achieved a 53% improvement in ride comfort over the passive suspension. To address the negative impact of actuator motion inertia and suspension structural nonlinearities on LMEERS control stability, Chen et al. [250] designed an H∞ robust controller and explicitly accounted for sensor noise effects on controller working performance. This strategy enhanced robust stability across diverse driving conditions.

Xie et al. [251] employed an integral SMC to suppress vertical vibration of the sprung mass in electromagnetic active suspensions, as illustrated in Figure 25, showing superior anti-disturbance performance compared to state feedback control. Zhang et al. [252] devised a model-independent SMC to improve robustness in electromagnetic active suspensions, featuring low computational complexity for reduced system latency. Li et al. [148] proposed an adaptive SMC to eliminate sprung mass variation effects and incorporated convergence-guaranteed constraints in the SMC design. Furthermore, performing online parameter optimization according to the real-time road surface information identification, ultimately the efficient coordination between LMEERS dynamic performances and energy regeneration capability was achieved.

5.3. Intelligent Control Methods

Modern control methods struggle to achieve automatic parameter adjustment through self-organization or self-learning, limiting LMEERS performance under complex driving conditions. Intelligent control methods construct control strategies in imprecise ways by employing expert knowledge and empirical rules [253]. Representative intelligent control approaches primarily include fuzzy control, neural network control, and hybrid variants combining these with other algorithms.

5.3.1. Fuzzy Control

Fuzzy control comprises four core components: a fuzzification interface, a knowledge base, an inference machine, and a defuzzification interface [254,255]. Its operational principle is illustrated in Figure 26. This strategy exhibits strong robustness, as it does not rely on precise mathematical models of the controlled system, making it applicable for addressing the nonlinearities, strong couplings, and time-varying characteristics inherent in control processes, and demonstrating considerable fault tolerance [256]. However, the construction of the knowledge base is inherently subjective, and the fuzzification processing of information will lead to reduced control precision and deteriorated dynamic performance [257].

Kou et al. [258] designed an endocrine feedback-based fuzzy control strategy for LMEERS, demonstrating enhanced dynamic performance over conventional fuzzy control. Wei et al. [224] utilized fuzzy control to optimize PID parameters online, significantly improving ride comfort under random and impulse road excitations for linear motor-based electromagnetic suspensions. Min et al. [259] employed fuzzy control to identify bounded disturbances and unknown steady-state parameters in the nonlinear electromagnetic active suspension system. Liu et al. [200] proposed a PD control strategy based on the variable universe fuzzy theory, enabling EERS to recover over 18% of vibration energy and simultaneously optimizing ride comfort and handling stability. Fuzzy control was introduced by Deng et al. [260] to eliminate chattering in SMC, and a fuzzy sliding mode variable structure control strategy was developed. Subsequently, the multi-mode switching control scheme for electro-hydraulic composite LMEERS was designed, thereby concurrently improving the dynamic performances and energy regeneration capability of LMEERS. When designing the energy regeneration control strategy for an electro-hydraulic composite LMEERS, Yin [261] applied fuzzy control to the real-time voltage stabilization of the regeneration circuit, achieving a regeneration power of 70 W under C-class roads. Soudani et al. [262] proposed a novel three-input fuzzy logic controller that substantially reduced vehicle body acceleration compared to widely used two-input controllers, thereby enhancing ride comfort. Ren et al. [263] adopted T-S fuzzy theory to address uncertainties in active suspension systems, introducing a homogeneous polynomial parameter-dependent fuzzy controller that significantly increases the flexibility of fuzzy control.

5.3.2. Neural Network Control

Neural network control possesses nonlinear adaptive information processing capabilities, overcoming limitations of traditional artificial intelligence methods in handling intuitive tasks such as pattern identification, speech recognition, and unstructured information processing. This enables its successful application in fields such as neural expert systems, pattern identification, intelligent control, combinatorial optimization, and prediction [264,265]. However, as a black-box system, neural network control cannot explain its reasoning process or rationale, and it struggles to achieve effective control without sufficient training data [266].

Liu et al. [267] designed a BP neural network PID controller for EERS, wherein the BP neural network provided adaptive parameters for the PID control strategy. Compared with conventional PID, BP-PID demonstrated superior performance in enhancing both dynamic performance and energy regeneration capability. Notably, the regeneration efficiency of BP-PID remained nearly constant across varying road conditions, indicating the excellent adaptability and stability of the neural network control. Li et al. [148] employed an adaptive neural network algorithm to identify road surface levels, and then switched the optimal control parameters, thereby enabling balance between the vibration suppression and energy regeneration of LMEERS. Focusing on the critical engineering challenges in active suspension systems, including high consumption, input delay, and unknown/uncertain disturbances, Zhang et al. [268] proposed an adaptive neural network control method, wherein the neural network worked to estimate system disturbances. This hybrid strategy could facilitate online updates of input and output weights for neural networks and intentionally incorporate beneficial nonlinearities into vibration control. To resolve the issues of unmeasurable states and control input saturation constraints in active suspensions, Wang et al. [202] developed a state observation-based adaptive neural network output feedback control algorithm, ensuring robust vehicle dynamic performance.

Benefitting from strong nonlinear modeling capacity and multi-objective adaptability, neural network algorithms are frequently deployed as decision-makers for multi-mode switching control in suspension systems. Confronted with the difficulty of single-strategy control systems in simultaneously optimizing driving safety, ride comfort, and energy feedback of regenerative suspensions, Qu et al. [203] implemented adaptive switching of key top-layer controller parameters with a BP neural network, as illustrated in Figure 27.

5.3.3. Hybrid Variants with Other Algorithms

Currently, combining classical and modern control methods represents the development trend of intelligent control methods, utilizing their self-learning capabilities to further enhance classical and modern controller performances. Li et al. [269] employed fuzzy logic theory to perform online estimation of the nonlinear dynamic model of the electromagnetic suspension actuator and unmeasurable suspension state variables. And then an adaptive fuzzy output feedback fault-tolerant control strategy was proposed, guaranteeing vertical dynamic performance even during actuator failures. Homayoun et al. [270] introduced a Radial Basis Function Neural Network (RBFNN)-based minimal learning backstepping control method to address the stochastic disturbances and actuator output saturation in nonlinear active suspension systems.

Intelligent optimization algorithms, such as GA and Particle Swarm Optimization (PSO), valued for their broad applicability, high robustness, and conceptual simplicity, are widely used to optimize control strategy parameters for maximizing control effectiveness or enabling multi-mode switching control [271,272,273]. Hu et al. [274] aimed at comprehensively improving ride comfort and handling stability, achieving optimal matching between suspension parameters and LQR controller via a multi-objective PSO algorithm. The optimized LQR significantly enhanced overall vehicle dynamic performances. Kou et al. [275] utilized the Gravitational Search Algorithm (GSA) to globally optimize the weighting coefficients of LQR controllers across three working modes of an electro-hydraulic composite LMEERS, thereby satisfying dynamic demands under varying driving conditions.

With the increasing computational power of on-vehicle chips and decreasing hardware costs, deep learning-based intelligent control methods are gradually becoming popular in vehicle suspension control. The high-dimensional fitting capability of intelligent algorithms can replace mathematical modeling, solving complex control problems through end-to-end learning [276]. Addressing the challenge of electromagnetic suspension systems adapting to vibration suppression demands in time-varying environments due to nonlinearities and uncertainties, Zhan et al. [201] modified a Deep Reinforcement Learning (DRL) network based on the actuator dynamic model, and then proposed a semi-active control strategy utilizing Neural Ordinary Differential Equations (NODEs) with the Proximal Policy Optimization (PPO) algorithm. Compared to fuzzy PID control, this hybrid strategy achieved superior vibration attenuation performance. Wang et al. [277] presented a DRL-based active suspension control algorithm, employing Deep Deterministic Policy Gradients (DDPGs) to significantly improve control performance, thereby yielding a faster response speed than the LQR controller.

In summary, the top-layer control methods critically influence the coordination between active control and energy regeneration of LMEERS, thereby directly impacting overall vehicle dynamic performance and energy economy. Different control strategies exhibit distinct advantages and limitations. A comparative analysis of the characteristics of control strategies commonly employed for LMEERS is provided in

Table 7. Comparative analysis of the characteristics of control strategies for LMEERS.

Strategy	Characteristics
Skyhook control	Implementation of damping control via velocity feedback Model-free property, simple control laws, mature commercialization, applicability for vibration suppression of the sprung mass, etc. Challenges in balancing ride comfort and handling stability, etc.
PID control	Linear combination of proportional, integral, and differential actions Model-free property, simple control laws, rapid response, etc. Prone to overshoot and oscillation, etc.
Adaptive control	Real-time adjustment to control parameters according to road excitation variations Effective trade-off between active control and energy regeneration of LMEERS, etc. High computational complexity for online implementation, etc.
LQR control	Optimal regulation of control objectives through controller model design Effective trade-off between active control and energy regeneration of LMEERS, high computational efficiency, etc. Complex control laws, poor robustness, etc.
Robust control	Design of control laws to actively counteract impacts of model errors and unknown disturbances Significant stability, etc. High design complexity, conservatism, poor real-time, etc.
Fuzzy control	Processing uncertain system control via “if-then” logic Effective trade-off between active control and energy regeneration of LMEERS, high robustness, etc. Over-reliance on subjective knowledge bases, etc.
Neural network control	Data-driven-based deep learning, more applicable for switching decisions of LMEERS dual functionalities High applicability for nonlinear systems, high robustness, etc. Black-box nature, huge computational load, etc.

, serving as a technical reference for subsequent selection and design of control methods. The selection of a control strategy is a multifaceted decision that extends beyond mere performance indexes. While modern and intelligent control methods often provide superior theoretical performance, their practicability is a major concern. Strategies like LQR and adaptive control can be computationally intensive and require accurate system models, which are difficult to obtain for nonlinear suspension systems and may not be robust to parameter variations. Sliding mode control offers robustness but introduces undesirable chattering. Although intelligent methods, like fuzzy logic and neural network, handle nonlinearities well, they often suffer from a lack of transparency (“black-box” nature), significant calibration effort, and high computational load, posing challenges for deployment on low-cost automotive microcontrollers. In contrast, classical methods, like Skyhook and PID, while less optimal in complex scenarios, offer simplicity, ease of implementation, and proven reliability, explaining their continued prevalence in commercial applications.

Therefore, the evolution of LMEERS control methods is not just about pursuing algorithmic complexity but also about advancing computational hardware and developing simplified yet effective strategies that bridge the gap between performance and practicality.

6. Current Challenges and Development Trends in LMEERS

6.1. Current Principal Challenges

Integrating dual functionalities of active control and energy regeneration, LMEERS performs better alignment with automotive demands of dynamic performance and energy efficiency, representing a pivotal structural configuration for next-generation high-performance suspension systems. However, several persistent technical challenges impede their commercialization, necessitating solutions in future research.

1.

Conflict between energy recovery efficiency and net energy-saving effectiveness:

On one hand, LMEERS faces intrinsic energy regeneration efficiency limitations. Under specific conditions, such as low-frequency, small-amplitude excitations of urban congestion, the linear motor yields insufficient regeneration voltage, resulting in poor energy recovery. On the other hand, energy losses occur throughout the regeneration pathway from LMEERS to storage systems, involving multi-stage conversions (rectification, voltage stabilization and storage), leading to low net regeneration rates. Furthermore, active suspension control algorithms with high energy consumption struggle to achieve net energy gain. Studies indicate that actual on-road recovered energy only accounts for a small part of the total suspension dissipated energy.

2.

Engineering challenges in thrust density versus volume/weight:

LMEERS’s linear motor must simultaneously deliver long stroke and high thrust, inevitably increasing the volume and weight of suspension actuators. Conventional cylindrical PMSMs offer limited thrust density, failing to meet requirements for ample thrust within compact structures. Consequently, developing novel high-performance motor topologies is imperative. Additionally, liquid-cooling systems implemented to manage motor thermal loads further escalate structural complexity and mass. Excessive motor weight drastically increases unsprung mass, consequently deteriorating suspension dynamic performance.

3.

Limitations in control algorithm hysteresis and complexity:

On one hand, high-frequency road excitation induces severe fluctuations in LMEERS feedback signals, necessitating dynamic motor load adjustments for stable force output. However, existing control strategies exhibit response hysteresis and control overshoot, hindering precise attainment of desired control objectives. On the other hand, intelligent algorithms (top-layer control coupled with road surface identification) capable of concurrently optimizing ride comfort, driving safety, and energy regeneration capability entail substantial online computational resources. This elevates hardware requirements for sensors and control chips on conventional vehicles, increasing manufacturing costs and control risks.

6.2. Future Development Trends

The commercialization of LMEERS hinges on overcoming the challenges detailed in Section 6.1, which are not of equal priority but exist in a hierarchical relationship. Among them, the primary and fundamental challenge is the inherent trade-off between energy recovery efficiency and vehicle dynamic performance (Challenge #1). This is the core dilemma that defines the LMEERS system and is the ultimate problem that all other research must solve. The goal is not to maximize one at the complete expense of the other but to develop strategies for intelligent trade-off management. The key enabling challenge is the thrust density versus volume/weight constraint of the linear motor (Challenge #2). This is a primary technological bottleneck because a bulky, low-efficiency actuator directly undermines both the dynamic performance (by increasing unsprung mass) and the energy-saving capability (by lowering regeneration power). Advancements here are prerequisites for achieving a viable system capable of effectively implementing any high-level control strategy. The critical implementation challenge is the computational complexity and hysteresis of advanced control algorithms (Challenge #3). This challenge becomes paramount once the hardware is capable. The most effective control strategy is irrelevant if it cannot be reliably executed in real time on affordable automotive hardware. Research must focus not only on algorithmic performance but also on their computational efficiency and robustness.

Therefore, future development trends should be prioritized to address these challenges in a logical sequence: firstly, by developing high-performance actuators to alleviate hardware limitations; secondly, by creating intelligent and computationally efficient algorithms to manage the fundamental performance–energy trade-off; and finally, by integrating these solutions into a robust and scalable system. The following trends are discussed within this prioritized framework.

1.

Optimal design of motor topology and peripheral circuits:

Optimize the primary and secondary structural design and dimensional parameters, employing high-performance magnetic materials and Halbach arrays to enhance magnetic field unidirectionality, thereby increasing air-gap flux density. This approach will comprehensively improve the motor’s damping, thrust, and regenerative characteristics. Meanwhile, reduce the volume and weight of motors to achieve lightweighting objectives. In addition, design safe and efficient regeneration–storage systems and optimize energy recovery hardware circuits and control algorithms to enhance regeneration responsiveness, thereby elevating net energy recovery efficiency.

2.

Application of high-voltage platforms and advanced thermal management:

Adopt high-voltage driving configurations to reduce copper losses in linear motor windings and to increase thrust density, ensuring the compatibility with electrical architectures of new energy vehicles. Realizing high-voltage operation in LMEERS necessitates breakthroughs in some key technologies, such as primary winding, insulation materials, and power electronics. Integrate motor cooling within the vehicle thermal management system, optimizing cooling channel topology and applying novel thermal interface materials. Synergistically combine thermal management control with suspension control to implement predictive cooling.

3.

Enhancing the energy efficiency ratio via composite configurations:

Integrate hydraulic, electro, and inerter components with linear motors to ensure that LMEERS maintains dynamic characteristics during energy regeneration and fail-safe properties during active control. Furthermore, develop tailored control schemes according to the performance advantages of various composite configurations to improve comprehensive suspension performance. Among these configurations, the electro-hydraulic composite types, which offer easy implementation, high reliability, and sufficient hard damping, will dominate mainstream solutions, yet their lightweighting and integration remain a critical research focus.

4.

Intelligent control and vehicle-road coordination:

Enable LMEERS with multiple working modes (e.g., comfort, sport, and economy modes) to balance active control and energy recovery across diverse driving scenarios. Utilize road surface information as the multi-mode switching criterion, and integrate intelligent control methods into suspension top-layer controller to enhance the road adaptability of LMEERS. Realize automatic adjustment to control parameters and adaptive switching of working modes, further elevating overall vehicle performance. Additionally, stability control during mode switching also requires focused attention.

7. Conclusions

Automotive energy-saving technologies have garnered extensive global research attention. As the critical subsystem, the suspension system’s performance in vibration attenuation and energy recovery directly influence vehicle dynamic performance and energy efficiency. Its configuration design stands as a key factor constraining its properties. Linear motor electromagnetic energy regenerative suspension (LMEERS), which integrates dual functionalities of active control and energy regeneration, demonstrates significant potential to overcome the performance limitations of conventional suspension architectures. It represents a pivotal development direction for next-generation high-performance suspension systems. Therefore, this review comprehensively synthesizes the state-of-the-art of the key technologies of LMEERS across four dimensions: configuration design, performance optimization, functionality switching criterion identification, and top-layer control strategies. To succinctly encapsulate the core insights of this review, the main findings across the four primary technological domains are summarized in

Table 8. Summary of main findings of key technologies for LMEERS.

Key Technology	Main Findings
Configuration design	LMEERS demonstrates superior distinct advantages and possesses dual functionalities of energy regeneration and active control, representing a pivotal structural paradigm for next-generation high-performance suspension system. Cylindrical PMSM is typically employed as the system actuator due to high thrust density, superior servo performance, and maturity. Composite configurations (EHC, EEC, EIC) are essential to overcome the limitations of single-motor designs. Electro-Hydraulic Composite (EHC) configurations are prevalent for their reliability and fail-safe “hard damping”.
Performance optimization	Damping characteristics are enhanced by integrating the hydraulic damping or eddy current modules. Thermal characteristics are managed through parametric optimization and equipped with cooling systems. Thrust and Regenerative characteristics are improved by a comprehensive set of approaches, including structural refinement, parametric optimization, and intelligent control. Emerging optimization methods, such as DT and AI, demonstrate substantial application potential, representing a promising and critical direction for future re-search.
Functionality switching criterion identification	Road surface information primarily encompasses roughness and type, typically identified with two on-vehicle approaches, namely image-based methods and dynamic response-based methods. Both approaches offer distinct advantages. Multi-sensor fusion (vision + dynamics) is the most promising direction for high accuracy and versatility.
Top-layer control strategies	No single optimal strategy exists, and the choice is a trade-off. Classical methods (Skyhook, PID) offer simplicity and reliability. Modern and intelligent methods (adaptive, LQR, SMC, fuzzy, neural network) offer higher performance but at the cost of complexity and computational load.

.

• In terms of configuration design, the cylindrical PMSM is typically employed as the system actuator. To further enhance system reliability and overcome the limitations of a single-motor structure in damping characteristics and fault-safe performance, LMEERS is commonly integrated with auxiliary devices, primarily forming three composite configurations: electro-hydraulic, electro-electro, and electro-inerter types. Among these, the electro-hydraulic type is considered the most promising for engineering applications owing to its simple structure, high reliability, and ability to provide inherent hard damping.
• Regarding performance optimization, efforts focus on damping, thermal, thrust, and regenerative characteristics, which are enhanced through structural refinement, parametric optimization, and intelligent control. Currently, damping characteristics is typically enhanced by integrating the eddy current or hydraulic damping modules. Parametric optimization and implementing cooling systems are simple and effective approaches to mitigate motor temperature rise. Thrust and regenerative characteristics, being critical to the functional behavior of LMEERS, require a comprehensive set of approaches for improvement. Additionally, emerging optimization methods, such as DT and AI, demonstrate substantial application potential.
• In the aspect of functionality switching criterion identification, road information (including road roughness and road type) serves as the key criterion for coordinating the dual-functionality switching of LMEERS. Two on-vehicle approaches, namely image-based methods and dynamic response-based methods, have been developed and compared. The former offers preemptive perception of the road ahead and high identification accuracy, but it suffers from high equipment costs and poor environmental adaptability. In contrast, the latter provides superior robustness and cost advantages, yet struggles to identify complex road surfaces. Therefore, multi-sensor fusion-based road information identification methods, capitalizing on the advantages of both methods, represent a future direction for on-vehicle solutions.
• Concerning top-layer control strategies, classical control (e.g., skyhook control, PID), modern control (e.g., adaptive control, LQR, robust control), and intelligent control (e.g., fuzzy control, neural network control) methods are widely applied and increasingly integrated. The introduction of intelligent optimization algorithms (e.g., PSO, GA) and deep learning methods has further improved the adaptive capability and multi-objective coordination performance of control systems.

Nonetheless, LMEERS still faces challenges, such as unsatisfactory net energy saving effectiveness, limited feasibility in engineering application, and limitations in control algorithm hysteresis and complexity. Future development of LMEERS will trend towards integration, lightweighting, standardization, intellectualization, and multi-modal operation. Specific development directions include the following:

• Optimize motor topology and peripheral circuit design to enhance magnetic field orientation and energy recovery responsiveness.
• Apply high-voltage platforms and advanced thermal management technologies for compatibility with electrical architectures in new energy vehicles.
• Develop composite configurations and cooperative control strategies to improve overall system energy efficiency ratio and reliability.
• Integrate vehicle–road coordination with intelligent decision-making to achieve adaptive switching between multiple operational modes for global performance optimization.