A Design Method of Saturated Optimal PID Controller for the Low-order Controlled Processes with Time Delay

In actual control systems,the controller's output signal is bounded,which is the controller's output saturated problem. This paper presents a design method of saturated optimal proportional integral derivative (PID) controller for low-order processes with time delay. The controller error,first-order error derivative,second-order error derivative,third-order error derivative,and their cross-items are used to calculate performance index. Subsequently,a nonlinear optimal control problem with the state constraint,and stability and algebraic constraint is proposed. The constraint optimal control problem is transformed into the nonlinear constraint optimization problem using common Lyapunov functions and Lyapunov theorems. Thus,the saturated optimal PID controller can be obtained by solving the nonlinear constraint optimization problem. The simulation results illustrate effectiveness and usefulness of the proposed design method.