An H2 Formulation for the Design of a Passive Vibration-Isolation System for Cars

Optimal design of an active suspension system for road vehicles can be solved using LQR techniques. Such a problem is equivalent, in the frequency domain, to determine the state feedback gain matrix that minimizes the H₂ norm of a suitable transfer matrix.

A passive suspension system can be seen as the physical realization of a suitable state feedback law whose gains are function of the system parameters. This law, and thus the characteristic elements of the passive suspension, can be determined as an approximation of the H₂ optimal solution. This methodology allows one to choose the best controller from a constrained subset (i.e., all possible passive suspensions of a particular form) of all possible controllers.     

Design of a Predictive Semiactive Suspension System

In this paper we present an original design procedure for semiactive suspension systems. Firstly, we consider a target active control law that takes the form of a feedback control law. Secondly, we approximate the target law by controlling the damper coefficient f of the semiactive suspension. In particular, we examine two different kinds of shock absorbers: the first one uses magneto-rheological fluid instead of oil, while the second one is a solenoid valve damper. In both cases the nonlinear characteristics force-velocity of the damper are used to approximate the target law. To improve the efficiency of the proposed system, we take into account the updating frequency of the coefficient f and compute the expected value of f using a predictive procedure. We also address the problem of designing an asymptotic state observer that can be used not only to estimate the current state but also to predict the value that the state will take at the next sampling time.     

Semiactive Suspension Design with an Optimal Gain Switching Target

The paper presents a two-phase design technique for semiactive suspensions. In the first phase, we use a procedure proposed by Yoshida et al. to compute a target active control law that can be implemented by Optimal Gain Switching. This control law is such that the force generated by the suspension system is bounded within a set U . In the second phase, we approximate this target by controlling the damper coefficient of the semiactive suspension. We also compute the region of the state space in which the force generated by the semiactive suspension is still within the set U . The results of several simulations show that the use of a semiactive suspension leads to minimal loss with respect to optimal performance of an active suspension.