A design method of optimal PI controller with saturation characteristic for second-order processes

In this paper, a design method of optimal proportional-integral (PI) controller with saturation characteristic is presented for second-order processes. Closed-loop system can be seen as the nonlinear control system because of PI controller's saturation characteristic. The closed-loop feedback system is equivalently transformed into linear switch system (LSS) or autonomous switch system (ASS). The optimal control problem is equivalently transformed into nonlinear constraint optimization (NLCO) problem via the common Lyapunov functions (CLF) theorem and Lyapunov theorems. Therefore, optimal PI controller parameters can be obtained from solving the NLCO problem. Simulation results show effectiveness and usefulness of the proposed design method.