Design of distributed PID-type dynamic matrix controller for fractional-order systems

ABSTRACT

With the continuous requirements for product quality and safety operation in industrial production, it is difficult to describe the complex large-scale processes with integer-order differential equations. However, the fractional differential equations may precisely represent the intrinsic characteristics of such systems. In this paper, a distributed PID-type dynamic matrix control method based on fractional-order systems is proposed. First, the high-order approximate model of integer order is obtained by utilising the Oustaloup method. Then, the step response model vectors of the plant is obtained on the basis of the high-order model, and the online optimisation for multivariable processes is transformed into the optimisation of each small-scale subsystem that is regarded as a sub-plant controlled in the distributed framework. Furthermore, the PID operator is introduced into the performance index of each subsystem and the fractional-order PID-type dynamic matrix controller is designed based on Nash optimisation strategy. The information exchange among the subsystems is realised through the distributed control structure so as to complete the optimisation task of the whole large-scale system. Finally, the control performance of the designed controller in this paper is verified by an example.

KEYWORDS:

• Fractional-order systems
• distributed dynamic matrix control
• PID control
• Oustaloup approximation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Zhejiang Provincial Natural Science Foundation of China [grant number LR16F030004] and the National Natural Science Foundation of China [grant number 61673147].

Notes on contributors

Dawei Wang

Dawei Wang is currently a master student with the Institute of Information and Control, Hangzhou Dianzi University, Hangzhou. His research interests include model predictive control, distributed control and nonlinear systems.

Ridong Zhang

Ridong Zhang received the Ph.D. degree in control science and engineering from Zhejiang University, Hangzhou, China, in 2007. He is currently a Professor with the Institute of Information and Control, Hangzhou Dianzi University, Hangzhou. His research interests include process modeling, process control and nonlinear systems.