Feasible Region Optimization of PI Control Parameters for Robust Tracking of First-Order Nonlinear Stochastic Time-Delay Systems

Abstract

This paper discusses the feasible region of PI control parameters for first-order nonlinear stochastic time-delay systems. The system can robust asymptotically track a set-point under any PI control parameters within the feasible region. First, the first-order nonlinear stochastic time-delay systems is transformed into a linear stochastic time-delay systems with the uncertainty. Second, for the fixed PI control parameters, the maximal allowable time delay under PI control is obtained by using the genetic algorithm (GA) and the generalized eigenvalue problem. Third, a new algorithm is proposed to compute the feasible region of PI control parameters for a fixed allowable time delay. Moreover, the improved algorithm is also proposed to reduce the time complexity. In particular, the stochastic disturbance and time delay disappear, the feasible region of PI control parameters obtained by the algorithm is consistent with the previous work. Finally, two simulation examples show the feasibility and effectiveness of the proposed two algorithms, respectively.