Linear Quadratic Regulator Time-Delay Controller for Hydraulic Actuator

A novel algorithm based on LQR approach is presented to optimally tune the gains of a PI controller of a first order plus time-delay system. In this algorithm the weighting matrices Q and R of the cost function are adjusted by the natural frequency and damping ratio of the closed–loop system. In order to prove the optimality of this algorithm, it is applied to a servo-hydraulic actuator with nonlinear dynamics. In this case, in order to apply the algorithm to the system and obtain the PI tuning gains, the nonlinear governing system equations should be replaced by simplified alternative equations which are realistic as well. In the other word, high-order equations should be simplified. Then the simulation results of the nonlinear plant are compared to those of the related simplified model.