1. Introduction
The advancements in the design of vehicle geometry to enhance vehicle ride comfort and road-holding capability over the past few decades have significantly contributed to the automotive industry [
1,
2,
3,
4]. The uncomfortable vibrations that the vehicle body transmits to the passengers have an impact on ride comfort. To improve the tire’s traction on the road, road holding refers to lowering oscillations in the typical wheel load. Though these two are the essential components of vehicle ride performance, there is always a trade-off between ride comfort and road-holding capability. Therefore, an appropriate control system framework that can easily address this aspect is essential to enhance ride performance. In [
5], a hybrid fuzzy controller was used to reduce the trade-off between ride comfort and road holding. In [
6], an optimal trade-off was achieved using a passive–active-based control approach. As reported in [
7], we have used an active suspension control strategy integrated with an active seat to improve ride comfort and road-holding capability. The researchers in [
8] reported a substantial improvement in ride comfort and road-holding capability considering various road conditions. In [
9], an approximation-free control for active suspension system was used to improve the ride comfort. To address the trade-off between these two components of ride performance, this research was mostly based on active suspension or semi-active suspension systems; however, recent research on the applications of aerodynamic-surface-based control strategies has gained significant impetus to improve vehicle performance.
Active aerodynamic-surface-based control strategies can significantly increase negative lift force with increased vehicle speed, effectively improving ride performance. Therefore, applications of active aerodynamic surfaces (AASs) installed on the vehicle sprung mass has attracted many researchers’ interest. For example, Savkoor [
10,
11,
12] published early primary research on the applications of AAS, using several control strategies to reduce the heave and pitch angle of a truck cabin. Active aerodynamic control (AAC) strategies are also effective in improving the lateral performance of a road vehicle. In [
13], Doniselli et al. investigated how aerodynamics affected a high-speed car’s ride quality on a randomly contoured route. The recent research on sports cars by [
14,
15,
16,
17,
18] used various control approaches to investigate the applications of AAS to improve ride comfort. To improve the vehicle’s handling, AACs have been used to adjust aerodynamic surfaces and provide a range of negative lift forces [
19,
20,
21]. In our earlier research [
22,
23], we examined how aerodynamic surfaces could produce a negative lift force to enhance a vehicle’s ride quality while considering pitch and roll dynamics. Though these pieces of research effectively improve ride performance, their performance depends on AAS’s idealistic independent operation. The major challenge with vehicles equipped with AAS is the realistic motion of aerodynamic surfaces installed on the unsprung mass. Due to high speed, the sharp movement of aerodynamic surfaces will result in high vehicle body jerk and acceleration, severely affecting passenger ride comfort. Therefore, an appropriate solution to reduce the adverse impact of vehicle body jerk on passengers to ensure better ride comfort and road-holding capability is aimed toward an anti-jerk control strategy.
As discussed by [
24], the term “jerk” is considered a better performance parameter for measuring ride comfort than acceleration and is widely used in engineering applications. For example, it has been considered as a ride comfort parameter for amusement rides [
25,
26,
27], elevators [
28], ships [
29], and buses [
30]. Jerk is considered an important passenger ride discomfort parameter in vehicles and is extensively discussed in automotive engineering. Anti-jerk controllers have been commonly employed in electric vehicles to reduce longitudinal jerk to enhance ride comfort and drivability [
31,
32]. Hence, anti-jerk control strategies have inspired many researchers to enhance ride comfort by reducing longitudinal jerk produced during the starting of electric vehicles. A non-linear predictive-based anti-jerk cruise controller model was developed in [
33] for electric vehicles to reduce longitudinal jerk and improve passenger ride comfort. In [
34], a predictive anti-jerk controller model was developed to overcome the trade-off between ride comfort and vehicle handling. In [
35], an anti-jerk controller was developed for a hybrid electric vehicle to reduce the jerk produced during clutch start. To track the intended velocity with the least jerk and improved road safety, ref. [
36] employed a linear-quadratic-based anti-jerk controller. Ref. [
37] utilized a low-jerk suspension control technology to improve ride comfort. A backlash-based anti-jerk controller was employed in [
38] to reduce jerk during clutch engagement. However, these anti-jerk control strategies minimize longitudinal jerk to improve ride comfort, while the research on improving vehicle performance during lateral or vertical motion is very limited, and early efforts by Hrovat and Hubbard [
39,
40] implemented an anti-jerk control strategy to enhance ride comfort during vertical motion of a quarter-car model. Where an augmented performance index was introduced to include the jerk rms term in addition to other outputs to improve ride comfort, their results for the one-degree-of-freedom (DOF) quarter-car model showed a reduction in rms jerk at the cost of an increase in the rms of heaving acceleration, tire deflection, and rattle space. In [
41], they further investigated the application of an optimal anti-jerk controller for a two-DOF quarter-car model. They predicted that a maximum reduction in rms jerk can be obtained at a cost of a modest increase of 23% in rattle space and a significant increase of 127% in tire deflection. Hence, such significant improvements in ride quality can be achievable at the penalty of vehicle handling. In [
42], using a semi-active suspension system, we have implemented a preview-based anti-jerk control strategy to improve ride comfort without degrading the road-holding capability under different road conditions. Despite the exciting results, to the researcher’s knowledge, the previous anti-jerk methodologies only focus on enhancing ride comfort using conventional active or semi-active suspension systems. Moreover, the high speed of vehicles can also limit the application of these conventional methodologies. Therefore, in [
43], we have implemented an active aerodynamic-based anti-jerk control strategy on a half-car model to improve the vehicle performance under different road conditions, i.e., bump inputs and asphalt roads. However, load transfer effects during lateral motion are not considered, which greatly impacts passengers’ ride comfort during cornering, braking, or forward acceleration.
Leaning the vehicle body against the vehicle body forces during lateral or longitudinal motion is very useful to mitigate the load transfer effects to enhance ride comfort. For example, the authors of [
44,
45] used an anti-roll bar methodology to reduce the impact of load transfer during cornering. In [
46,
47], tilting control systems were developed to improve vehicle safety during cornering. In [
48], we have designed a preview-based attitude controller to reduce the load transfer effect and track the desired roll and pitch position during cornering or forward acceleration to enhance ride quality. Similarly, in [
7], using a conventional active suspension system, an attitude motion controller was developed for vehicles with active passenger seat systems to improve ride comfort and vehicle handling. In [
23], we implemented an AAC strategy to tilt the vehicle body against centrifugal or inertial forces to track the desired roll or pitch position to enhance ride performance. This performance was achieved by the independent operation AAS, which is an idealistic approach. AASs are directly installed on the sprung mass of the vehicle; therefore, their movement also has a direct impact on vehicle body jerk, which is an important ride comfort parameter. This is because negative lift force or downforce generated by aerodynamic surfaces strictly depends upon vehicle speed and the angle of attack. Therefore, it is important to achieve realistic motion of aerodynamic surfaces to reduce vehicle body jerk during attitude motion.
Motivated by these perceptions, in this paper, a four-degrees-of-freedom half-car model equipped with aerodynamic surfaces is considered to explore the applications of aerodynamic-based anti-jerk optimal control strategy, which comprises a feed-forward control strategy in addition to a state feedback controller. The feed-forward control can anticipate the force required to track the desired attitude angle. The state feedback controller can adjust the force to minimize the tracking error. Our main goal is to achieve the realistic motion of aerodynamic surfaces to minimize vehicle body jerks without degrading the road-holding capability. Anti-jerk optimal control with known predicted information regarding the future road maneuver is proposed to enhance the ride comfort during cornering, braking, or accelerating. The difference between braking and cornering is that braking performance is dependent only on the vehicle’s speed, while cornering performance is dependent on the speed of the vehicle as well as the radius of the curvature. The proposed optimal predictive control strategy can generate anticipating actions against future road maneuvers. The following are the distinguished features that contribute to this work:
A ubiquitous four-DOF half car equipped with AAS is presented as a case study.
Information about future road maneuvers can be obtained by direct detection using sensors attached to the vehicle with a 0.3 s preview time.
The desired roll or pitch angles are computed using vehicle speed, future road maneuvers, and the disturbance forces acting on the vehicle body.
The proposed control scheme aims to improve ride performance by canceling external jerks.
The simulation results are carried out using MATLAB to validate the effectiveness of the proposed anti-jerk predictive control strategy in terms of reducing the controlling jerk to achieve the smooth movement of AAS, to overcome the trade-off between ride comfort and road-holding at the cost of slow tracking.
The rest of the paper is organized as follows: In
Section 2, the problem formulation is presented.
Section 3 represents the proposed optimal anti-jerk control strategy, while
Section 4 discusses the simulation results, followed by a conclusion with future recommendations.