Optimal active suspension structures for quarter-car vehicle models

Abstract

The preliminary design of active vehicle suspensions can be naturally cast into an equivalent linear-quadratic Gaussian (LQG)-optimization problem, where the performance index is an appropriate combination of ride comfort, vehicle handling and suspension design constraints. The vehicle models vary in complexity with the simplest one being the one degree-of-freedom (DOF) quarter-car model which neglects wheel dynamics. The present paper explores the connections between LQG-optimal one DOF and two DOF models. In a recent study (Hrovat, 1987), it was shown that for the optimal two DOF systems, both ride and handling can be improved by reducing the unsprung mass. The limiting one DOF case of zero unsprung mass then represented the maximum possible improvement within the constraint of a single active actuator. It is shown in the present paper that in practice these limiting benefits can be approached via passive dynamic absorbers attached to the unsprung mass. Moreover, the structural constraint of a single active actuator has been relaxed to allow for both secondary suspension and unsprung mass active actuators. Here the maximum possible ride and handling improvements for two DOF systems are obtained in the limiting case of singular control with zero penalty on unsprung actuator force. This absolutely optimal structure turns out to be yet another special one DOF system, which in practice could be approached with the help of active dynamic absorbers.