Optimal PID Tuning for Plants with Random Parameters

In this paper, the randomized algorithm is established to solve the variance-optimal tuning problem of PID controller for plants with random parameters. The tuning problem of the PID controller is reduced to an optimization problem to minimize the expected value of output variance in the sense of probability based on the established randomized algorithm, in which the Newton's iterative method is employed to find the optimal solution viz. the tuning parameter of PID controller. The validity of the proposed approach and randomized algorithms will be verified through case studies.