Three-time scale multi-objective optimal PID control with filter design

This paper presents the design of a multi-objective PID (proportional, integral, and derivative) controller in three time scales for a system with load disturbances and sensor noise. The key to this design method is to divide the problem into three time scales by following a singular perturbation approach, which allows for the optimization of fewer parameters in each time scale instead of all the three PID gains at once, hence less computation and design effort. The optimization objectives are the minimization of the overshoot and peak time and the maximization of the closed-loop system's ability to reject noise and load disturbances. The impact of the integral action and filter on the optimal results is investigated by tuning the singular perturbation parameters. The obtained results show that the performance of the closed-loop system recovers the optimal solution, which is based on the fast subsystem, as the singular perturbation parameters get sufficiently small.