Extending the LQR to the design of PID type‐ii and type‐iii control loops

Abstract

AbstractThis paper concerns the improvement on Proportional‐Integration‐Derivative (PID) control for standard second‐order plus time‐delay systems (SOPTD). To achieve higher tracking precision and stronger disturbance rejection, a PID type‐ii and type‐iii control‐loops design method based on the combination of the linear quadratic regulator (LQR) and dominant pole configuration technology is proposed in this paper. The PID type‐ii control loop is capable of achieving perfect tracking of step and ramp reference signals with zero steady‐state position and velocity error. The PID type‐iii control loop is capable of achieving perfect tracking of step, ramp and parabolic reference signals with zero steady‐state position, velocity and acceleration error. The effectiveness of the proposed PID type‐ii and type‐iii controller parameters tuning rules has been demonstrated via simulation of over‐damped, critical‐damped and under‐damped systems. To be specific, compared with the PID type‐i control loop, rise time, settling time and disturbance rejection property of the system have been significantly improved while realizing faster reference signal tracking. Finally, the effects of non‐dominant pole on the stability and robustness of PID type‐ii and PID type‐iii closed loop systems have also been discussed.