Multi-Objective Control of Semi-Active Suspension Systems

Abstract

Automotive industry pays a great attention on the study and implementation of active and semi-active suspension systems in commercial cars. This paper focuses on the control of a semi-active damper in order to achieve the improvement of ride comfort without a significant degra- dation of vehicle handling. The system under investigation is represented by the vertical dynamics of the whole vehicle, which can be studied by using the reduced quarter car and half car models. The actuation system dynamics and nonlinearities are taken into account for the derivation of the controllers. The control design is based on multi-objectives performance indices in order to fulfill both the control targets. Two controller architectures are discussed in this paper: the first is based on H∞ optimization; the second is a nonlinear controller based on an extension of the sky-hook strategy. Simulations in various conditions are used to show the effectiveness of the controllers proposed with respect to standard control strategies. I. INTRODUCTION The increasing presence of mechatronic devices in modern cars is determined by two main targets: the improvement of the safety characteristics of the car and of the travel comfort. In this context, active suspension sys- tems represent an important tool for the possibility of im- proving vehicle performances, from both the viewpoints, as their first applications in Formula 1 have shown in the 70's. Generally speaking, the suspensions are requested to attenuate the effects of the road and of the driving maneuvers on the car body; moreover, they are designed in order to keep an optimal contact between the tire and the road (handling) and to compensate for force unbalance depending on the dynamic behavior of the vehicle, i.e. the cases of acceleration/braking maneuvers, lane changes and turns. Comfort and handling are conflicting objectives for the design of a passive suspension system, which is based on a trade-off between these targets: active and semi-active suspensions can overcome this strong limitation and provide the vehicle a better behavior from both the perspectives. Today, active and semi-active suspensions are more and more adopted in high-level cars, granting a remarkable improvement in ride comfort, vehicle stability and road holding in various driving conditions, if compared with passive suspensions. The most largely used architecture is based on a passive spring in parallel with a force actuator in the active case or with a controllable damper in the semi-active one. The latter solution is very attractive for car industry because it is cheaper in terms of costs, weights and complexity with respect to the former: the balance between performances and costs is more favorable for semi-active systems. Besides the significant rising in performances, the emerging technologies of controllable dampers determine non-trivial control problems which can be addressed in the framework of robust control. In the case presented, the control action consists in the con- tinuous variation of the suspension damping coefficient: the results obtained by this approach are near to those of active suspensions, but the complexity of the system is smaller. The first contributions on semi-active suspensions con- trol focused on the sky-hook strategy, which is based on the idea of designing a control law for the damping force equivalent to that obtained by a damper placed between the car body and the sky (1). In this way, the damping force is proportional to the chassis vertical velocity and a complete decoupling of the chassis dynamics from road irregularities can be obtained. Sky-hook has become a reference model for inner loops because of its simplicity and good performances. H∞ and H2 controllers based on state space and LMI optimization, combined with nonlinear control and genetic search algorithms have been proposed for comfort improvement (2)-(4). This paper deals with the modelling and control of a semi-active suspension system of a high class-sport car, characterized by a mechanical design of the suspension mainly focused on handling performances: due to the in- trinsic limitations of the passive design, this leads to poor comfort performances. Therefore, the primary objective of control is the ride comfort, but a particular attention is paid in keeping handling and drive safety on satisfactory levels. Two control architectures are proposed. In the first one, a multi-objective H∞ controller is designed neglecting the nonlinearities of the semi-active damper; then, the optimal damping force is converted into an admissible control for the semi-active damper. The second controller is based on the nonlinear model of the system and tries to achieve both comfort and handling objectives by a proper modification of the sky-hook strategy. The proposed controllers are simulated with respect to normal driving conditions and their performances are compared with that of a passive system. The comfort and handling are evaluated with respect to standard indices and a frequency analysis of the closed loop systems is used in order to enlighten the features of the controllers.