Optimal PID tuning for discrete-time systems with stochastic disturbance

It is difficult for the traditional deterministic method to deal with the variance-optimal PID tuning problem when there exist some stochastic parameters in the disturbance model. In the presence of a stochastic parameter in the disturbance model, this paper proposes a novel PID tuning technique based on an randomized algorithm so as to minimize the mean value of output variance in the sense of probability. Compared with the traditional deterministic PID tuning method, the proposed technique shows obvious improved performance. Finally, numerical examples are used to demonstrate the effectiveness of the proposed one.