Quadratic Synthesis of Active Controls for a Quarter-Car Model

Abstract

The design of active vehicle suspensions with integral constraints to control the response of a vehicle traversing a road is considered. The problem is initially formulated in the linear quadratic regulator (LQR) framework with full-state feedback. Alternate formulations based on optimal output feedback (OOFB) and the minimum norm criterion (MNC) approach in the absence of complete state information are then presented. A general expression for the required optimal value of the control force based on easily measurable feedback quantities is developed. To reduce the effect of the body jerk, the high rate of change of actuator control force is penalized by adding a roll-off prefilter to the control. Results based on LQR, OOFB, and MNC are compared, and it is shown that the OOFB and MNC give performances as effective as the full-state feedback without the need to measure the tire deflection. The effectiveness of the roll-off prefilter in reducing the body jerk is demonstrated in an example problem.