Global minimum-variance PID control

In this paper we address the problem of finding the parameters of a PID controller in order to achieve the minimum variance performance. In particular, a global optimal solution is found by exploiting the analytic expression for the output variance as an explicit function of PID settings, and by using the DIviding RECTangles (DIRECT) algorithm, which is a modification of the standard Lipschitzian approach that eliminates the need to specify a Lipschitz constant. Illustrative examples show the effectiveness of the method.