Optimal Control Method of Semi-Active Suspension System and Processor-in-the-Loop Verification

Featured Application

An implementation of PID controller optimized with PSO to improve the road holding and ride comfort simultaneously on a real suspension test setup was proposed. The manuscript contains valuable experimental results for suspension system controller researchers.

Abstract

This study presents an implementation of a proportional–integral–derivative (PID) controller utilizing particle swarm optimization (PSO) to enhance the compromise on road holding and ride comfort of a quarter car semi-active suspension system (SASS) through simulation and experimental study. The proposed controller is verified with a processor-in-the-loop (PIL) approach before real-time suspension tests. Using experimental data, the magnetorheological damper (MR) is modeled by an artificial neural network (ANN). A series of experiments are applied to the system for three distinct bump disturbances. The algorithm performance is evaluated by various key metrics, such as suspension deflection, sprung mass displacement, and sprung mass acceleration for simulation. The phase plane method is used to prove the stability of the system. The experimental results reveal that the proposed controller for the SASS significantly improves road holding and ride comfort simultaneously.

1. Introduction

Reducing the forces affecting the vehicle body through the suspension system improves ride comfort. Suspension systems also enhance the road-holding ability by increasing the physical contact point between the tire and the surface of the road [1,2,3,4]. Road-holding and ride comfort parameters show a trade-off behavior [5]. This means that improving one of them declines the other. In the design of traditional suspension systems, elements of the system are determined by establishing a balance between these parameters.

In view of controllability, passive, semi-active, and active suspension systems are the configuration for the suspension systems. Passive systems, which contain fixed-value components, cannot be controllable. Semi-active suspension systems (SASSs) usually contain magnetorheological (MR), electrorheological or variable orifice-type damping elements. These damping elements provide an adjustable damping ratio. Active suspension systems and SASS try to suppress the conflict between road holding and ride comfort by arranging unsprung mass acceleration, suspension deflection, and tire deflection by using several control algorithms [2,4,6].

SASS is widely preferred due to its low cost and low power consumption [7,8]. The most important suspension element that provides this advantage is the damper. An MR damper is a controllable semi-active damping device used for vibration mitigation in several fields, such as seismic isolation, knee prosthesis, weapon recoil damper, engine mounts, seat suspension, and especially automotive suspension systems. In controllable suspension systems, the effectiveness of the controller on the suspension performance is quite high, as well as the damper. The proportional–integral–derivative (PID) controller is commonly preferred in engineering applications, owing to its cost effectiveness, ease of implementation, resilience, and low cost compared to the other methods. However, just a few studies on PID controllers have been carried out in the context of the SASS applications because regulating three controller coefficients (proportional ($K_d$), integral ($K_i$), and derivative ($K_d$) coefficients) requires a significant duration. The primary critical issue to obtain proper consistency on road holding and ride comfort is designing a robust controller with an appropriate optimization method. The proper design of the PID controller is possible with the appropriate gains. A common but time-consuming approach to determining these gains is to use a trial-and-error method [9]. This method involves adjusting the parameters in small increments and observing the system’s response to define the optimal values. Alternatively, there are various tuning techniques, including the Ziegler–Nichols method, Cohen–Coon method, etc. On the other hand, using a linear controller structure to control nonlinear systems may not be effective in providing maximum performance for all states of the system. Therefore, there is a need to optimize the controller parameters over the entire operating range. Different performance parameters can be merged in controller optimization as an objective function. Optimizing the controller parameters is crucial to obtaining the global best values in the objective function [10]. For this reason, optimization algorithms, for instance, particle swarm optimization (PSO), gradient descent, genetic algorithm, and ant colony optimization, have been used to adjust these parameters. PSO is a population and stochastic-based optimization method stimulated by the social roles of fish and bird swarms [11]. This optimization method is used in many real-world problems thanks to its flexibility and easy adaptation to the problems. Furthermore, it also has a strong global search ability and robust performance [12].

MR damper models are in two main categories as parametric and non-parametric. Damper behavior can be characterized using a parametric model, such as a modified Bouc–Wen model. In addition, a non-parametric model can be employed, which utilizes measured data to establish input/output relationships without requiring knowledge of the damper’s internal structure. The artificial neural network (ANN) is a popular method for obtaining non-parametric models of the MR dampers. The damper coil current is generally taken as an input of the ANN model [13]. Alternatively, the damping characteristics can be changed by the section area of the throttle valve instead of the current [14].

Many different and innovative design studies are in the literature to enhance the damping capability of the MR damper [15,16,17]. In some studies, the damping performance was enhanced by optimizing the dimensions, which have a direct effect on the damping performance [18,19,20]. MR dampers use four different operating modes: squeeze mode, mixed mode, valve mode, and shear mode [15,20,21,22,23,24,25]. The operating mode can be selected according to the features required by the application. In this experimental study, the MR damper was used in mixed mode.

Alternatively, studies using different types of dampers are also included in the literature. Seifi and Hassannejad put forward the critical importance of considering uncertainties in vehicle components during design to ensure passenger safety and optimal performance. They introduced a novel suspension system with inverters and asymmetric dampers, demonstrating significant improvements in ride comfort, road-holding, and rollover probability compared to conventional damper designs [26]. Shen et al. studied a novel combined suspension system, incorporating a power-driven damper (PDD) and inerter-spring damper (ISD). They could address vibration issues in vehicles across a wide frequency spectrum with a fractional-order derivative sliding mode controller (FD-SMC) [27].

In addition to the design of suspension systems with different damping elements, the control of suspension systems with various controllers is also a studied subject. An adaptive controller algorithm was proposed by Paksoy and Metin to overcome parameter changes in suspension systems [28]. However, measuring changes in the parameters of the suspension system is quite difficult. Therefore, the prediction of damping force methods has been developed. Tudon-Matinez et al. proposed a linear parameter-varying H-infinity filter based on linear matrix inequality theory dependent on parameters [29]. Prediction-based methods can also be used in controller design. In recent years, controllers using prediction-based models have become increasingly popular. Pinon et al. studied the prediction-based controllers for SASS and proposed an external-input autoregressive model predictive controller [30]. Model predictive controllers generate the optimal control signal for the next iteration with the designed system model. Therefore, the accuracy of the designed model is crucial. In addition, they require advanced microcontrollers for real-time applications, which increases the system’s complexity and cost. Gu et al. presented a robust control technique for a nonlinear vehicle suspension system dealing with uncertainties, time-delayed actuation, and bounded disturbances. They overcame these challenges by combining sliding mode and back-stepping methods, demonstrating superior performance in active suspension through MATLAB simulations [31]. Oh and Choi designed a SASS with multiple orifice holes and controlled it with a sliding mode controller [32]. By their nature, sliding mode controllers make the system resistant to disturbances and uncertainties. However, the chattering and variable frequency of the controller’s output make it difficult to use directly for the MR damper control. Considering these challenges, the optimized PID controller is prevalent in many fields of industry.

Researchers have extensively investigated the application of PSO for the fine-tuning of the controllers designed. Samsuria et al. designed a sliding mode controller utilizing PSO by changing a sliding surface [33]. Ma et al. enhanced the vehicle’s dynamic characteristics in the vertical direction with a PSO-optimized sliding mode surface controller in the SASS for the hydraulic adjustable damper [34]. He et al. evaluated frequency-weighted RMS values with different optimization methods, such as PSO, cuckoo search, and genetic algorithm, for improving driving comfort in a commercial vehicle [35]. A genetic algorithm with a multi-objective function was used for SASS by Papaioannou and Koulocheris. They considered not only road holding and ride comfort characteristics but also the conflict on the vibration reduction effectivity and the dissipated energy [36].

The other issue that should be addressed in the control of SASS is verifying the control algorithm through real-time testing on the MR damper model. Challenges encountered in the design process can be solved swiftly and cost-effectively with the help of rapid prototyping methods [37]. Processor in the loop (PIL) is frequently employed for test and performance verification of the system to be controlled in various fields as reported in [38,39,40]. Tramacere et al. verified the control performance of an autonomous vehicle with a PIL architecture [41]. The path-planning algorithm of an autonomous vehicle was verified using a combination of model-in-the-loop (MIL) and PIL architecture by Sun et al. [42]. El-bakkouri et al. obtained theoretical stability results for the control algorithm developed for an anti-lock braking system. They experimentally verified with the PIL method for different road conditions [43]. Verification and validation processes using model-based approaches also play an essential role in safety-critical systems. Dini and Saponara validated the model predictive control algorithm used for assisted driving in the automotive industry with PIL [44]. Moreover, the PIL architecture is widely used in the verification of power electronics systems. Motahhir et al. verified the maximum power point tracking algorithms using a V-cycle development process [45]. Ulah et al. tested a three-phase photo-voltaic fault-tolerant control scheme with the PIL method [46]. However, according to the author’s review, research on the design and implementation of SASS with PIL verification for control algorithm validation is still missing in the literature.

As mentioned before, road holding and ride comfort are trade-off parameters for suspension systems. Improving both parameters together is the main objective of SASS control. The motivation of this study is to optimize the controller parameters to minimize this conflicting behavior of the SASS. In this study, the characteristics of the MR damper in the shock absorber test device were modeled by training a feedforward ANN. Current, velocity, and displacement for the MR damper are the inputs of this ANN model. Furthermore, a classical controller with a robust optimization algorithm was employed on an experimental quarter car suspension system setup and obtained highly satisfying results. The verification of the controller algorithm was realized with the PIL approach on a real-time processor. The main contribution of this study is to implement a PSO-optimized and then PIL-verified PID controller on a real MR damper-based SASS. Three different bump inputs were applied to analyze the MR damper dynamic response. The performance parameters analyzed in this study are RMS values of sprung mass acceleration, sprung mass displacement, and suspension deflection for the experimental tests. Additionally, the dynamic load coefficient (DLC) is calculated for the simulation study with the random Type-C road profile. A significant improvement was achieved in all performance parameters. Consequently, the proposed controller could supply an enhancement of the conflict behavior of road holding and ride comfort.

2. Materials and Methods

2.1. Semi-Active Suspension System Model

SASS was modeled as a quarter-car suspension system as given in Figure 1. The SASS model comprises an unsprung mass, sprung mass, and suspension components on a structure designed as a model for a quarter car. The suspension components are an MR damper and a linear spring. The tire was represented solely by a linear spring, neglecting the damping element. The equation of motion for sprung and unsprung masses are given in Equation (1), which were obtained by Newton’s laws of motion. Quarter car suspension system parameters are given in

Table 1. Quarter car SASS model parameters.

Parameter	Definition	Value
$m_s$	Sprung Mass (kg)	95
$m_u$	Unsprung Mass (kg)	22.2
$k_s$	Suspension spring stiffness (N/m)	14,950
$k_u$	Tire stiffness (N/m)	156,960

. These parameters are for the experimental test setup placed in our laboratory. Therefore, these parameters are different from the real quarter car model parameters.

$$\begin{array}{cc}\hfill m_u\ddot{z_u}& =k_u(z_r-z_u)-k_s(z_u-z_s)-F_{MR}\hfill \\ \hfill m_s\ddot{z_s}& =k_s(z_u-z_s)+F_{MR}\hfill \end{array}$$

(1)

The system was modeled as a state-space model. The displacements and velocities of sprung and unsprung masses were chosen as state variables of the system. According to the state-space model, the MR damper force is a control input, the road input is a disturbance, and system outputs are the displacements of sprung and unsprung masses. The model parameters are shown in

Table 2. State-space model parameters of SASS.

State Variables		Outputs		Inputs
Variables	Description	Variables	Description	Variables	Description
$x_1=z_s$	Sprung mass displacement	$y_1=z_s$	Sprung mass displacement	$u=F_{MR}$	MR damper force
$z_2={\dot{z}}_s$	Sprung mass velocity	$z_2={\dot{z}}_s$	Sprung mass velocity	$d=z_r$	Road input (as disturbance)
$x_3=z_u$	Unsprung mass displacement	$y_3=z_u$	Unsprung mass displacement
$x_4={\dot{z}}_u$	Unsprung mass velocity	$y_4={\dot{z}}_u$	Unsprung mass velocity

. The state-space mathematical expressions are in Equation (2). $A,B,C,D$ and E are the coefficient matrices as in Equation (3). State vector (x), input (u), and disturbance input (d) are in Equation (4):

$$\begin{array}{cc}\hfill \dot{x}& =Ax+Bu+Ed\hfill \\ \hfill y& =Cx+Du\hfill \end{array}$$

(2)

$$A=\left[\begin{array}{cccc}0& 1& 0& 0\\ -\frac{k_s}{m_s}& 0& \frac{k_s}{m_s}& 0\\ 0& 0& 0& 1\\ \frac{k_s}{m_u}& 0& -\frac{k_s+k_u}{m_u}& 0\end{array}\right],B=\left[\begin{array}{c}0\\ \frac{1}{m_s}\\ 0\\ -\frac{1}{m_u}\end{array}\right],C=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right],D=0,E=\left[\begin{array}{c}0\\ 0\\ 0\\ \frac{k_u}{m_u}\end{array}\right]$$

(3)

$$x=\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\\ x_4\end{array}\right],u=F_{MR},d=z_r$$

(4)

2.2. Characterization and Modeling of the MR Damper

MR fluids are magnetic field-dependent fluids used in a semi-active damping system. MR fluids usually consist of magnetic particles dispersed in a carrier fluid. In this study, we used the MR damper, which was developed and described in [47]. The structure and prototype of the MR damper are shown in Figure 2, and the technical specifications are given in

Table 3. State-space model parameters of SASS.

Component and Specification	Value
Stroke	180 mm
MR fluid type	Carbonyl iron-based
Coil inductance	5.74 mH
Coil resistance	34.45 $\Omega$
MR fluid gap	1 mm

.

A series of tests were performed to identify the MR damper’s damping characteristics under harmonic excitation on the Roehrig 20VS shock absorber test device as shown in Figure 3. For damping force measurement, tests were carried out by applying 3.18 Hz sinusoidal excitation and ±25 mm displacement, taking into account the JASO C602:2001 standard. Tests were repeated for coil currents of 0 A, 0.2 A, 0.8 A, 1.4 A, and 2 A. The force–displacement F(X) and the force–velocity F(V) were achieved from the damping tests and can be investigated in detail in [47].

Non-parametric modeling uses a black box to determine the damper dynamics based on experience and measurable data, eliminating the need for a damper structure. This non-parametric approach is thought to map the relationship between the tested damper’s inputs and output data. A non-parametric MR damper model was developed by training a feedforward ANN for five different currents.

The inputs for this network included the coil current, velocity, and displacement of the MR damper. The damping force of the MR damper was chosen as the output of the network. The characterization tests of the MR damper were performed for five different current values, and a total of 6078 data were obtained for the non-parametric model. These data were used for obtaining the ANN model with the MATLAB Neural Network Toolbox. The test data were divided into three sections randomly. Then, 70% of the test data was for training, 15% of the data was for testing, and 15% was for validation of the network. The network was trained with the Levenberg–Marquardt algorithm, which evaluates performance by optimizing the weight and bias parameters, aiming to minimize training errors in order to attain the desired output. The best performance was obtained with a network structure of a single hidden layer containing 15 neurons with a tangent sigmoid activation function. A linear activation function was chosen for the output layer. The selection of the number of hidden layers, the number of neurons within these hidden layers, training epochs, and the choice of activation functions were determined through an empirical trial-and-error process. The network structure for the MR damper is shown in Figure 4. Regression results and training performance for the ANN are given in Figure 5 and Figure 6, respectively.

$R^2$ measures the variation rate of the dependent variable according to the independent variables in the model and indicates how well the data match the regression model. In Figure 5, when examining the $R^2$ results presented in the graphs, it can be observed that the actual data align effectively with the predicted data. The correlation coefficients of the network for training, testing, and validation are calculated as 0.99987%. To evaluate the performance of the model, loss functions are employed. The mean squared error was chosen as the loss function and can be seen from Figure 6. While the error is almost ${10}^5$ at the beginning, it decreases gradually with the number of epochs. As expected, this resulted in a high rate in the first 50 epochs and then reached the best result in 482 epochs.

Test results for the MR damper characterization and predicted values with ANN are given in Figure 7a and Figure 7b, respectively.

2.3. Test Setup

Experimental studies were carried out on the Thepra suspension test system. The system consists of quarter car suspension components and allows to apply bump input manually. Two position sensors located on the system are for measuring the displacements of sprung and unsprung masses. The visualization and data acquisition of test results were obtained with the Rigol oscilloscope. The whole experimental test setup is given in Figure 8.

2.4. Controller Design and Optimization

The PID controller is preferred due to the reasons mentioned before for the MR damper control. The basic control diagram for the SASS is shown in Figure 9. Three control terms can be explained: the proportional expression (P) is in relation to the current error, the integral expression (I) is contingent upon the cumulative past errors, and the derivative expression (D) entails a prognostication of future errors. The controller output is regulated to maintain zero error condition. The error used for the controller is as follows:

$$e\left(t\right)=0-ba$$

(5)

where $ba$ is the sprung mass acceleration for a ride comfort index. The PID controller fundamental equation is

$$u\left(t\right)=K_{p}e\left(t\right)+K_i\int e\left(t\right)dt+K_d\frac{de\left(t\right)}{dt}$$

(6)

The control signal $u\left(t\right)$ is the current for the MR damper. These coefficients were determined with the optimization method. A stochastic optimization algorithm, PSO, developed by Kennedy and Eberhart [48], is based on the behavior of searching for potential food in a specific area of bird or fish swarms’ particles. This algorithm is commonly utilized in problems that involve determining optimal particle placement within a given search space.

In the context of SASS, the PSO algorithm employs an objective function that encompasses conflicting performance measures, such as ride comfort, road holding, and suspension deflection. The primary aim of employing an optimization algorithm is to optimize the system’s performance metrics by minimizing or maximizing them. By considering the particles’ position and velocity, the swarm collaboratively identifies the target location, resembling the search for the global best. Through multiple iterations, the PSO algorithm strives to achieve the optimal value for the swarm of particles, resulting in enhanced system performance. When applied to a PID controller, the tuning parameters ($K_p$, $K_i$, and $K_d$) represent the particles within the swarm, while the performance criteria serve as the objective function for the algorithm.

In suspension design, three key performance criteria are essential: ride comfort, road holding, and handling. When designing the controller, the primary requirement lies in ride comfort, which is assessed through sprung mass acceleration. Providing comfort requires dampening the vibrations to which passengers are subjected [49]. External factors, such as road disturbances, can cause a lack of contact between the tires and the road. Therefore, minimizing tire deflection, which affects road holding, is crucial. Additionally, the reduction in suspension deflection is vital, particularly concerning the structural characteristics of the vehicle. Failure to adhere to this value results in a decline in ride comfort, road holding, handling and an increase in suspension system wear and fatigue.

The aim is to minimize the cost function for optimization when taking into account the quarter car model given in Figure 1 and Equation (1), model variables in Table 2. The optimization is handled to supply control objectives, to minimize sprung mass acceleration for ride comfort, tire deflection for road holding, and suspension deflection for vehicle wear and handling. The cost function to be minimized is written to supply suspension system performance as

$$J=w_1{\int }_0^t{\ddot{z}}_s^{2}dt+w_2{\int }_0^t{t}_d^2+w_3{\int }_0^t{s}_d^2$$

(7)

where the optimization period $\left[0,t\right]$ refers to the road disturbance period. The first term of Equation (7) is sprung mass acceleration (${\ddot{z}}_s$), mentioned as a state variable ${\ddot{x}}_1$. The second term is tire deflection ($t_d$), which is about the road holding capability and is calculated as

$$t_d=z_u-z_r=x_3-z_r$$

(8)

The last term is suspension deflection and is calculated as

$$s_d=z_s-z_u=x_1-x_3$$

(9)

Another key parameter for the suspension system is the dynamic load coefficient (DLC). It is used to assess vehicle response to ride safety, road holding, and driving stability [50,51]. The DLC reveals variations in the vertical tire force when compared to its static force and is calculated as

$$DLC=\frac{F_{Z,dyn}}{F_{stat}}$$

(10)

where $F_{Z,dyn}\left(t\right)$ is the vertical dynamic tire force in the time variable, and $F_{stat}$ stands for the static force. They are calculated, respectively, as

$$F_{Z,dyn}\left(t\right)=k_u(z_u-z_r)$$

(11)

$$F_{stat}=k_u(z_u-z_r)$$

(12)

where g is the gravitational acceleration (g = 9.81 m/s${}^2$).

Lyapunov stability analysis and phase plane analysis are essential tools for studying the stability of dynamical systems. Lyapunov stability analysis determines the stability of a system mathematically by examining the behavior of trajectories around an equilibrium point. However, phase plane analysis provides a visual representation of the system’s dynamics. The system trajectories converge to the equilibrium point, and this determines the system as asymptotically stable. Through the graphical representation of the system’s state variables in relation to one another, the phase plane analysis offers valuable insights into the system’s behavior in the presence of equilibrium points, limit cycles, and transient trajectories [5]. Figure 10 presents the passive suspension system and SASS with the proposed controller phase planes. These phase planes illustrate the trajectories obtained by subjecting these systems to a bump input. The observed trajectories in Figure 10 demonstrate a convergence towards the equilibrium point. Furthermore, the trajectories indicate that the SASS with the proposed controller exhibits superior energy dissipation capability. Analyzing the phase planes reveals that the SASS achieves asymptotic stability in the sense of Lyapunov.

2.5. PIL Verification

Through the utilization of rapid prototyping methods in design and testing procedures, the inherent difficulties faced during the design phase can be efficiently and economically resolved [33]. The classification of these methods from simple to complex is seen in Figure 11. In the MIL, the system model is first obtained. Then, it is tested in a simulation environment. In the software-in-the-loop (SIL), a code is generated in the same way as it is generated in the embedded system. The generated code is run in a simulation environment, and the whole system is tested. In the PIL, the generated code is tested in real-time by running on a processor. In the hardware-in-the-loop (HIL), the generated code is tested together with a real system response.

Although MIL and SIL methods can produce definite results, the results may differ from MIL and SIL, regarding real-time implementation of the algorithm [52]. For this reason, it is crucial to validate the control algorithm with PIL to obtain results close to the real application. The controller used in the SASS was verified by preparing a PIL simulation in a MATLAB/Simulink environment. Moreover, performance improvements were supplied through PIL simulation.

In PIL simulation, the code obtained from the designed controller model was run on a real microprocessor. The STM32H743ZI2 microprocessor was used for this purpose. The used PIL architecture is shown in Figure 12. In general, the PIL comprises a model of the system where the control algorithm is applied, a two-way communication line that will provide communication between the simulation environment and the processor and a microprocessor where the control algorithm will execute. In PIL simulation, the system model generates a response in accordance with the applied control signal and then transmits this signal to the microprocessor through a communication line. In response to the transmitted signal, the control algorithm is re-executed. While the microprocessor is running, the system model waits in a halt mode, and similarly, when the system model is running, the microprocessor waits in a halt mode. On the other hand, when preparing a PIL simulation, its limitations should be taken into account [52]. Due to the discrete-time behavior of the microprocessor, the simulation environment in which the model is prepared should be suitable for discrete-time operation. The variables to be used both in the simulation and in the microprocessor should be the same type. The simulation speed is affected by the communication line operation speed. Therefore, both the speed of the communication line and the running time of the simulation should be set appropriately. The oscillator frequency of the microprocessor should also be considered as another limitation of a PIL simulation. Consequently, the oscillator frequency of the microprocessor should also be considered when determining how long the simulation will take.

3. Results

3.1. Simulation Results

The passive suspension system and the SASS were analyzed to reveal the superiority of the controller for the simulations. The simulation studies were conducted utilizing a random Type-C road profile in accordance with ISO 8608 standard for a quarter car model. The road spanned a length of 100 m, while the vehicle was traveling at a speed of 20 m/s. The results of the SASS were evaluated and compared with the passive suspension system results concerning sprung mass acceleration, displacement, suspension deflection, and DLC.

The Type-C road input is shown in Figure 13. The sprung mass displacements and the accelerations of the passive and the SASS are shown in Figure 14 and Figure 15, respectively. The other evaluation parameter is suspension deflection, and it can be seen from Figure 16. According to Equation (10), the DLC values for SASS and passive suspension system were calculated as 0.7401 and 1.069 respectively. As seen from these results, the DLC was improved by 30.77%. When all these results are analyzed, the SASS parameters are highly improved compared to the passive system. This shows that the developed controller has good performance for the random input.

For the verification of the control algorithm, a quarter car model was used to test the SASS in PIL simulation. The test scenario was a bump to the model 20 ms after the simulation started as seen from Figure 17. The sprung mass displacement of the passive and the SASS obtained from this scenario is shown in Figure 18. In the SASS, it was observed that the sprung mass displacement moved about 23% less. In addition, the acceleration caused by the displacement of the sprung mass after the bump was applied is shown in Figure 19. Similar to Figure 18, the SASS had about 23% less acceleration at the first moment of bump application. The other parameter of the quarter car model, suspension deflection, is shown in Figure 20. It can be seen that the suspension deflection is similar. The control algorithm of the system was validated by obtaining zero error for the difference between model-in-the-loop (MIL) and processor-in-the-loop (PIL).

3.2. Experimental Test Results

The ride comfort and road holding characteristics of SASS with MR damper were investigated in the experimental test setup as shown in Figure 8. Three different half-sine bumps of 25 mm, 15 mm, and 10 mm amplitudes were used as road input in the system. The system response to the road disturbance was examined by observing three suspension system parameters. These parameters are sprung mass displacement, sprung mass acceleration, and unsprung mass displacement. Although unsprung mass displacement is not meaningful on its own, it plays a significant role in achieving suspension deflection.

Sprung mass displacement and sprung mass acceleration are related to ride comfort. Suspension deflection is the parameter that is effective in evaluating the ride comfort and the road holding characteristics implicitly. The test results were obtained from the oscilloscope and are presented in Figure 21, Figure 22 and Figure 23 as oscilloscope images for the three different bumps. These results were obtained for both the passive system and the SASS.

4. Discussion

The test results for the highest bump for the passive system and the SASS are in Figure 21. Considering the passive system’s response (Figure 21a), the sprung mass displacement was completed in about 3.5 cycles. For the same bump, the sprung mass displacement of SASS in Figure 21b was damped in about 1 cycle. A similar result was observed for the sprung mass acceleration between the passive system and the SASS. In the passive system (Figure 21a), the body oscillations took 2.5 s after the application of the bump input, while it took only 1 s for the SASS (Figure 21b). In addition, the unsprung mass oscillations of the passive system took longer to reach equilibrium compared to the SASS. In the passive system, the tire oscillations took 2 s after applying the bump input, while in the SASS, it took only 0.6 s.

The test results for the medium bump comparing the passive system and the SASS are shown in Figure 22. Regarding the passive system’s response (Figure 22a), the sprung mass displacement was completed within approximately 1.5 cycles. Furthermore, the SASS (Figure 22b) ensured a damped sprung mass displacement in just a 0.75 cycle for the same bump. A similar trend was observed in terms of the sprung mass acceleration between the passive system and the SASS. In the case of the passive system (Figure 22a), it took 1 s for the body oscillations to settle after the application of the bump input, whereas the SASS accomplished this within 0.7 s (Figure 22b). Additionally, the unsprung mass oscillations of the passive system required more time to reach equilibrium compared to those of the SASS. The tire oscillations in the passive system took 0.5 s to stabilize following the bump input, whereas the SASS achieved this in 0.4 s.

The comparative test results for the lowest bump between the passive system and the SASS are presented in Figure 23. When examining the response of the passive system (Figure 23a), it can be detected that the sprung mass displacement was completed within approximately 1.5 cycles. In contrast, the SASS (Figure 23b) achieved a damped sprung mass displacement for the same bump in just 0.5 cycles. The periods of the parameters obtained from the lowest bump were nearly equal to the medium bump results, while their amplitudes were reduced. A similar case occurred when considering the sprung mass acceleration in the passive system and the SASS. In the passive system (Figure 23a), it took 1 s for the body oscillations to settle following the application of the bump input, while the SASS accomplished this within 0.5 s (Figure 23b). Furthermore, compared to the SASS, the passive system required more time for the unsprung mass oscillations to reach equilibrium. The tire oscillations in the passive system took 0.4 s, while the SASS achieved this in 0.35 s.

The RMS values of three critical parameters for both the passive and the SASS were calculated by using the data from the test results obtained with the oscilloscope. These values were obtained for all three different bumps and can be seen in

Table 4. RMS values of suspension system parameters for different bump inputs.

Parameter	Highest Bump			Medium Bump			Lowest Bump
	Passive	SASS	Improvement (%)	Passive	SASS	Improvement (%)	Passive	SASS	Improvement (%)
Sprung Mass Disp.	0.2237	0.0915	59.1	0.0626	0.0501	19.96	0.0434	0.0361	16.82
Sprung Mass Acc.	0.2490	0.0910	63.45	0.0637	0.0437	31.39	0.0436	0.0356	18.35
Suspension Def.	0.266	0.1256	52.78	0.0989	0.0830	16.07	0.0736	0.0620	15.76

. The sprung mass displacement was improved by 59.10% for the highest bump, 19.96% for the medium bump, and 16.8% for the lowest bump with SASS. The improvement rates for the sprung mass acceleration in the SASS were 63.45% for the highest bump, 31.39% for the medium bump, and 18.35% for the lowest bump. Finally, the suspension deflection in the SASS was enhanced with improvement rates of 52.78% for the highest bump, 16.07% for the medium bump, and 15.76% for the lowest bump.

Considering the aforementioned results, the best improvement was achieved in sprung mass acceleration for all the bumps. This means that ride comfort was notably enhanced with the proposed controller. This is the result of determining the weight coefficient larger than the other terms for the sprung mass acceleration in the objective function. Furthermore, suspension deflection was improved for all of the bumps. This shows that road holding was improved, and suspension wear and fatigue were decreased. The most significant improvement among all suspension parameters was observed at the highest bump. This observation proves that the controller demonstrates superior control efficacy at elevated magnitudes of bump as indicated by the substantial enhancement in all suspension parameters.

5. Conclusions

This paper presents an improvement in ride comfort and road holding simultaneously on a real SASS with MR damper experimental setup. The MR damper model was obtained with ANN, and correlation coefficients of the network for training, test, and validation were calculated as 0.99987%. Before application, the control algorithm was validated by using PIL verification. PID controller coefficients were optimized with PSO. Although the classical controller was used, optimizing the controller coefficients contributed significantly to the results. The optimized controller performance was compared to the passive suspension system performance. The passive mode was obtained by not applying current to the MR damper. A current in the range of 0– 2A was supplied to the MR damper for the semi-active mode. The proposed controller reduced sprung mass displacement by 59.1%, sprung mass acceleration by 63.45%, and suspension deflection by 52.78%, respectively, for the highest bump disturbance. In the analysis of test results, it was observed on a real test setup that all parameters of ride comfort and road holding, which have a trade-off characteristic, were significantly improved simultaneously. This observation forms the inspiration point for this study. The test setup developed to control a real quarter car SASS contributes to the existing literature. Additionally, the utilization of PIL verification for the first time in the validation of a suspension system provides another contribution to the literature. As an important conclusion, the proposed controller can be used effectively on the SASS with the MR damper.