This chapter presents two sliding mode controllers of semi-active suspension systems with magnetorheological dampers, which have undesirable nonlinear properties. One sliding mode controller is based on the theory of model-following control. In the model-following controller, a desired semi-active suspension system is chosen as the reference model to be followed, and the control law is determined so that an asymptotically stable sliding mode occurs in the error dynamics between the plant and the reference model states. The advantages of this controller are as follows: (1) measurement of the damping force is not required, (2) the reference model specifies the desired performance considering the passivity constraint of the damper, and (3) it is entirely possible to maintain the sliding mode and achieve high robustness against the nonlinear properties of the damper. The other sliding mode controller is designed by the describing function method so that a switching function is enforced into a desired limit cycle instead of a perfect sliding mode. Although the proposed sliding mode controller cannot generate the limit cycle as desired because of the passivity constraint of controllable dampers, restricting the switching function in the vicinity of the origin can suppress the deterioration due to the passivity constraint, such as increase in jerk of the sprung mass. Moreover, a method for designing an observer is introduced for semi-active suspension systems using variable structure system theory, which provides a highly robust property against modeling errors and disturbances in the context of the matching conditions. The structure of the introduced observer is designed to be robust against road variations, which can be seen as nonstationary system disturbances. Although this structure basically requires the actual damping force to be measured, it is estimated using a model of the damper. Thus, the effect of the estimation errors of the damping force on the state estimation is discussed in detail, and the sufficient conditions for stability of the observer are given using Lyapunov's theory. As a result, both the structure and the design process of the proposed observer are simplified in comparison with existing ones.

Chapter Contents:

• Abstract
• 9.1 Introduction
• 9.2 Control of semi-active suspension systems with MR dampers
• 9.2.1 Variable orifice damper
• 9.2.2 MR damper
• 9.3 Model-following sliding mode controller for semi-active suspension systems
• 9.3.1 System model and problems
• 9.3.2 Sliding mode controller
• 9.3.3 Simulation results
• 9.4 Sliding mode controller with describing function method
• 9.4.1 Problem formulation
• 9.4.2 Integral sliding mode control
• 9.4.3 Redesign of relay input with describing function method
• 9.4.4 Simulation conditions
• 9.4.5 Accuracy of limit cycle of switching function
• 9.4.6 Improvement of deterioration caused by passivity constraint
• 9.4.7 Verification of robustness against parameter variation
• 9.5 VSS observer of semi-active suspension systems
• 9.5.1 Plant
• 9.5.2 Problem formulation
• 9.5.3 Design of VSS observer
• 9.5.4 Numerical simulations
• References

Inspec keywords: Lyapunov methods; variable structure systems; suspensions (mechanical components); limit cycles; control system synthesis; asymptotic stability; automotive components; magnetorheology; observers; nonlinear control systems

Other keywords: reference model; magnetorheological dampers; error dynamics; damping force estimation errors; describing function method; semiactive suspension systems; nonstationary system disturbances; sliding mode controller design; switching function; nonlinear properties; model-following control; asymptotic stability; Lyapunov theory; damper passivity constraint; variable structure system theory; observer design; state estimation

Subjects: Automobile industry; Multivariable control systems; Road-traffic system control; Nonlinear control systems; Mechanical components; Stability in control theory; Control system analysis and synthesis methods