Tracking Control of Servo Systems With Disturbances and Time Delays

ABSTRACT This paper proposes a servo system tracking control strategy subject to both time‐varying input delay and disturbances. Due to the existence of external disturbances and time delays, the performance of the servo system can degrade, which may also induce phase lag and even instability. In this paper, a tracking control synthesis method is developed that addresses the aforementioned issues. Firstly, the tracking error dynamic system is derived based on the control objective, and a tracking control law is presented to achieve trajectory tracking of the servo motor. Considering the underlying time‐varying delay in the closed loop, the stability of the resulting servo system is established by a Lyapunov–Krasovskii functional method. A linear matrix inequality (LMI)‐based condition is developed, which can be efficiently checked using numerical algorithms. It also shows that this condition can ensure robustness despite disturbances with bounded norms. Besides stability analysis, the result is then extended to adapt to the synthesis of tracking control gains. Again, the extended condition is in the form of LMIs, thus able to be implemented efficiently. The effectiveness of the proposed method in servo motor tracking control is verified both by simulation and real experiments.