Model Complexity Requirements in Design of Half Car Active Suspension Controllers

Abstract

This paper investigates the appropriate level of model complexity when designing optimal vehicle active suspension controllers using the Linear Quadratic Regulator (LQR) method. The LQR method requires the formulation of a performance index with weighting factors to penalize the three competing objectives in suspension design: suspension travel (rattle space), sprung mass acceleration (ride quality) and tire deflection (road-holding). The optimal control gains are determined from the solution of a matrix Riccati equation with dimension equal to the number of state variables in the model. A quarter car model with four states thus poses a far less onerous formulation problem than a half or full car model with eight or more states. However, half and full car models are often assumed to be more accurate than quarter car models, and necessary for capturing and controlling degrees of freedom such as pitch and roll motion which are not directly available from a quarter car. The vertical acceleration, pitch acceleration and roadholding of a pitch plane vehicle are controlled in this paper using both quarter and half car-based controllers. First, optimal gains are calculated for each of the front and rear actuators assuming that the front and rear of the vehicle can be separately modeled as quarter cars with four states each. Then, half car-based optimal gains, based on feedback of eight states for the entire vehicle, are computed. Using quarter car-based controllers at the front and rear of a half car gives superior performance in reducing sprung mass inertial acceleration, and can effectively control pitch motion even when interactions between front and rear suspensions are not decoupled. Minimizing vertical motion of the front and rear ends indirectly regulates pitch motion. Improvements resulting from the additional complexity of the half car-based controller are seen only when the weighting factor for pitch suppression is very high in the performance index.