Research on Satisfactory PID Control for Stochastic Systems with Opportunity-Awaiting Control Characteristic Indices Constraints

The problem of satisfactory PID control for a class of stochastic systems with constraints on desired opportunity-awaiting control characteristic indices and decay ratio index is considered. First, on the basis of the boundary cross theorem, an approach of determining all stabilizing PID controllers and the set of PID controller satisfying the desired decay ratio index is proposed. Second, according to the opportunity-awaiting control theory, the expressions of characterization of the set of PID controller satisfying the desired opportunity-awaiting characteristic indices, such as average residence time and average waiting time, are derived. Then, using the idea of satisfactory control, the consistency of the above three indices is analyzed. Moreover, an efficient algorithm of determining the range of consistent indices is also presented. Finally, a method of calculating the set of PID controller when the indices are consistent is given. A numerical example shows the validity and feasibility of the proposed method.