Design of modified 2-degree-of-freedom proportional–integral–derivative controller for unstable processes

Ziwei Li,Hongbo Zou,Furong Gao,Zheng Xu,Ridong Zhang

doi:10.1177/0020294020944954

Abstract

Concerning first-order unstable processes with time delays that are typical in chemical processes, a modified 2-degree-of-freedom proportional–integral–derivative control method is put forward. The system presents a two-loop structure: inner loop and outer loop. The inner loop is in a classical feedback control structure with a proportional controller intended for implementing stable control of the unstable process; the outer loop is in a 2-degree-of-freedom structure with feedforward control of set points, where the system’s tracking response of set points is separated from its disturbance response. To be specific, the system has a feedforward controller that is designed based on the controlled object models and mainly used for regulating the system’s set point tracking characteristics; besides, it has a feedback controller that is designed on the ground of direct synthesis of disturbance suppression characteristics to improve the system’s disturbance rejection. To verify the effectiveness, the system is put into a theoretical analysis and simulated comparison with other methods. Simulation results show that the system has good set point tracking characteristics and disturbance suppression characteristics.

Highlights

Proportional–integral–derivative (PID) controller remains one of the most universal control methods used in current industrial production due to its advantages of a simple control structure, sound robustness, and reliability among others.[1,2,3] it is challenging to make effective control in the traditional PID method for unstable processes with time delays
It is challenging to make effective control in the traditional PID method for unstable processes with time delays. To cope with such unstable processes with time delays, De Paor and O’Malley[4] proposed a Z-N-structure PID controller tuning method; Shafiei and Shenton[5] raised a graphical method by PID controller using D-divide method; and some advanced methods are targeted at common unstable integral processes and first-order processes with time delays,[6,7] but such methods do not suffice regarding the control of system performance
To design a controller for practical industrial control processes, in addition to stable control of the unstable processes, focus should be given to optimization of system performance indicators, among which set point tracking characteristics and disturbance suppression characteristics dominate

Summary

Introduction

Proportional–integral–derivative (PID) controller remains one of the most universal control methods used in current industrial production due to its advantages of a simple control structure, sound robustness, and reliability among others.[1,2,3] it is challenging to make effective control in the traditional PID method for unstable processes with time delays. Based on the 1-degree-of-freedom-to-2-degree-of-freedom span, a double 2-degreeof-freedom control method[21,22] is put forward, where four independent controllers are designed for stabilizing the open-loop unstable or integral processes with delay, improving set point response tracking performance and enhancing the system’s disturbance suppression characteristics. In practical industrial process control, many factors need to be simultaneously considered in terms of control performance to meet the expected control requirement To this end, 2-degree-of-freedom control is an appropriate design method, where two independent controllers with independent parameters are designed to optimize the system’s disturbance suppression performance and set point tracking performance at the same time. Through an analysis on equations (1)–(3), any one closed-loop transfer function can be used to derive the other two functions This system is a 1degree-of-freedom control system that cannot give a consideration to both set point tracking performance and disturbance suppression performance at the same time.

Design of controllers Stability controller

Conclusion