Design of an Optimal PID Controller Based on Lyapunov Approach

This paper addresses on design of an optimal proportional integral derivative (PID) controller by applying Lyapunov approach. The optimal PID controller is acquired through minimizing an augmented integral squared error (AISE) performance index that contains control error and at least first order error derivative, and even may contain n orders error derivative. The order of error derivative is determined by the controlled plant's model order. The optimal control problem is transformed into a nonlinear constraint optimization (NLCO) problem. The optimal parameters are obtained from solving the NLCO problem. The performances of different tuning methods are compared. The effects of control weight on optimal controller and control system's performance are analyzed as well. The computer simulation results are presented to demonstrate the effectiveness of the proposed method and optimal PID controller.