Differential equation approximation and enhancing control method for finding the PID gain of a quarter-car suspension model with state-dependent ODE

Abstract

Active suspension control strategy design in vehicle suspension systems has been a popular issue in road vehicle applications. In this paper, we consider a quarter-car suspension problem. A nonlinear objective function together with a system of state-dependent ODEs is involved in the model. A differential equation approximation method, together with the control parametrization enhancing transform (CPET), is used to find the optimal proportional-integral-derivative (PID) feedback gains of the above model. Hence, an approximated optimal control problem is obtained. Proofs of convergences of the state and the optimal control of the approximated problem to those of the original optimal control problem are provided. A numerical example is solved to illustrate the efficiency of our method.