Optimization and finite-frequency H_∞ control of active suspensions in in-wheel motor driven electric ground vehicles

Abstract

In this paper, the parameter optimization and $H_{\infty }$ control problem of active suspensions equipped in in-wheel motor driven electric ground vehicles are investigated. In order to better isolate the force transmitted to motor bearing, dynamic vibration absorber (DVA) is installed in the active suspension. Parameters of the vibration isolation modules are also optimized in order to achieve better suspension performances. As the human body is much sensitive to vibrations between 4 and 8 Hz, a finite-frequency state-feedback $H_{\infty }$ controller is designed to achieve the targeted disturbance attenuation in the concerned frequency range while other performances such as road holding capability and small suspension deflection are also maintained. The performance of the proposed finite-frequency $H_{\infty }$ controller is compared with that of an entire frequency one, simulation results prove the effectiveness of the proposed control method.

Introduction

Electric vehicles have several advantages such as energy efficiency and environmental friendliness [1]. Compared to the conventional electric vehicle architectures, the in-wheel (or hub) driven electric vehicles enjoy various additional control and functional merits [2]. For example, as each of the wheels in an in-wheel motor driven electric vehicle is independently and directly actuated, the actuation flexibility together with the fast torque responses of electric motors enhances the performance of existing vehicle motion/stability control systems such as traction control system and direct yaw-moment control [3]. In addition, the usage of in-wheel motors enables a roomy interior and makes it possible to place the batteries in the vehicle for best weight distribution and design the vehicle body for best aerodynamics and handling [4], [5].

In an in-wheel motors driven electric vehicle, the propulsion system is removed from the vehicle body to the wheels, so the ratio between unsprung and sprung masses is increased. Note that the increased ratio between unsprung and sprung masses may severely deteriorate vehicle ride comfort and road-holding performance, this is one of the reasons that in-wheel motors have not been widely used even though in-wheel motors driven electric vehicles have many aforementioned advantages over the conventional vehicle architectures. Besides the increased unsprung mass, motor bearing wear is another critical problem that must be resolved in the in-wheel motor driven electric vehicles. The motor bearings, which now also become the wheel bearings, must carry the weight of the car. However, as large gap between the motor rotor and the stator can significantly reduce the motor torque and power, the gap must be precisely controlled and restricted to be as small as possible, making the bearings easy to wear and fail due to the fast change of road conditions and heavy load [6]. Many researches have been carried out on suspension systems for improving the ride quality and vehicle handling [7], [8], [9], [10], [11], [12], [13], [14]. For example, in order to achieve cost reduction and augmented reliability, a single accelerometer based control strategy for a semi-active suspension is presented in [10]. To solve the problem of multi-objective control for vehicle active suspension, a load-dependent controller design based on the state-feedback strategy is presented in [11]. In order to attenuate the disturbance, a robust $H_{\infty }$ state-feedback control for an active suspension is designed in [12], the constraints required in the vehicle suspension control are also considered in this paper. Controller design for active suspension considering actuator input delay is considered in [13], [14]. Moreover, the problem of $H_{\infty }$ control with time domain constraints for active vehicle suspension systems in finite frequency-domain is studied in [16], simulation results show that the ride comfort can be significantly improved within the frequency band concerned, while the time-domain constraints are also guaranteed. However, most of the existing suspension control methods are designed for the conventional vehicle architectures, not for the suspensions increased unsprung mass or specifically for the in-wheel motor driven electric vehicles.

In this study, the $H_{\infty }$ control problem of active suspensions equipped in electric vehicles with in-wheel motors is investigated. The quarter-car model of the active suspension is employed as the object of research. The main contributions of this paper lie in the following aspects. First, in order to minimize the in-wheel motor stator vibration and reduce the dynamic load applied on the in-wheel motor bearing, a dynamic vibration absorber (DVA) is installed in the suspension. Optimization on the parameters of the DVA is also performed such that the new suspension system can still give acceptable performance even if the suspension is not actively controlled. Second, in view of the fact that human body is much sensitive to vibrations between 4 and 8 Hz in the vertical direction, a finite-frequency state-feedback $H_{\infty }$ controller based on the generalized Kalman–Yakubovich–Popov (KYP) lemma [15] is used to achieve the targeted disturbance attenuation in the specific frequency. In addition, other performance requirements of vehicle active suspension such as road holding, suspension stroke, and actuator limitation are all considered in the controller design.

The rest of this paper is organized as follows. The quarter-car model of an active suspension equipped with vibration isolation module is briefly described in Section 2. An optimization algorithm for designing the parameters of the vibration isolation module is presented in Section 3. The proposed finite-frequency $H_{\infty }$ controller is described in Section 4. Simulation results are presented in Section 5 followed by conclusive remarks.