Design of robust optimal proportional–integral–derivative controller based on new interval polynomial stability criterion and Lyapunov theorem in the multiple parameters' perturbations circumstance

Abstract

Based on the new interval polynomial stability criterion and Lyapunov theorem, a robust optimal proportional -integral -derivative (PID) controller is proposed here to design for different plants that contain the perturbations of multiple parameters. A new stability criterion of the interval polynomial is presented to determine whether the interval polynomial belongs to Hurwitz polynomial. The robust optimal PID controller is acquired through minimising an augmented integral squared error (AISE) performance index. The robust optimal control problem is transformed into a non-linear constraint optimisation (NLCO) problem by applying new polynomial stability criterion and Lyapunov approach. The robust optimal PID parameters are obtained from solving the NLCO problem. The robustness and performances of the proposed method and other different tuning methods are compared. The ability of the proposed PID tuning method and other tuning methods to reject disturbances is discussed as well. The simulation results are presented to demonstrate the effectiveness of the proposed method and show better robustness of the robust optimal PID controller.

Optimal Design Method of Pi Controller for Multiple Processes and Coupled Liquid Level System

“…The integral squared error, integral absolute error, integral time absolute error, integral of squared time and error and integral time squared error performance index are often used to design optimal PI/PID controller. In this paper, AISE performance index in [7], [12] is used to design the optimal controller. So, optimal PI controller of the proposed method should satisfy basic requirement: (i) it can minimize performance index; (ii) it can stabilize feedback system.…”

“…In [11], non-convex optimization method is proposed to design optimal PI controller in frequency domain. In [12], a method is proposed to design robust optimal PID controller via new interval polynomial stable criterions. In [13], a design method of fuzzy optimal PI controller is presented for a heat exchanger via solving a non-constraint optimization problem.…”

A New Design Method of Optimal Pid Controller With Dynamic Performances Constrained

“…Precision and steady-state characteristic of control system are directly reflected by control error. In this paper, the AISE [21], [22] and AISE-HDPI performance index are proposed to design the optimal PID controller. Hence, the optimal PID controller not only stabilizes the control system but also satisfies the dynamic performance requirement of the control system.…”

Identification and robust controller design for an electromechanical actuator with time delay

“…A graphical design method based on the Kharitonov theorem for characterizing all PI and PD controllers is developed in Tan (2009) and all the PID controllers in Huang and Wang (2000), which achieve pre-specified gain and phase margins for uncertain plant, but without introducing the bandwidth condition. A design approach for systems without time delay was presented in Li et al (2010) and Rigatos and Siano (2011). An H N theory-based controller was designed to obtain a faster and more accurate EMA system in Yoo et al (2004) and to improve the tracking and resolution of a servo positioning system in Raafat et al (2012).…”