Implementation of Simplified Fractional-Order PID Controller Based on Modified Oustaloup's Recursive Filter

doi:10.1007/s12204-019-2139-6

Abstract

Abstract: The aim of this paper is to simplify the design of fractional-order PID controllers. Because the analyt- ical expressions and operations of fractional-order systems are complex, numerical approximation tool is needed for the simulation analysis and engineering practice of fractional-order control systems. The key to numerical approximation tool is the exact approximation of the fractional calculus operator. A commonly used method is to approximate the fractional calculus operator with an improved Oustaloup's recursive filter. Based on the modified Oustaloup's recursive filter, a mathematical simplification method is proposed in this paper, and a sim- plified fractional-order PID controller (SFOC) is designed. The controller parameters are tuned by using genetic algorithm (GA). Effectiveness of the proposed control scheme is verified by simulation. The performance of SFOC has been compared with that of the integer-order PID controller and conventional fractional-order PID controller (CFOC). It is observed that SFOC requires smaller effort as compared with its integer and conventional fractional counterpart to achieve the same system performance.

Key words: fractional calculus| Oustaloup's recursive filter| simplified fractional-order PID controller (SFOC)| genetic algorithm (GA)| controller tuning

摘要： The aim of this paper is to simplify the design of fractional-order PID controllers. Because the analyt- ical expressions and operations of fractional-order systems are complex, numerical approximation tool is needed for the simulation analysis and engineering practice of fractional-order control systems. The key to numerical approximation tool is the exact approximation of the fractional calculus operator. A commonly used method is to approximate the fractional calculus operator with an improved Oustaloup's recursive filter. Based on the modified Oustaloup's recursive filter, a mathematical simplification method is proposed in this paper, and a sim- plified fractional-order PID controller (SFOC) is designed. The controller parameters are tuned by using genetic algorithm (GA). Effectiveness of the proposed control scheme is verified by simulation. The performance of SFOC has been compared with that of the integer-order PID controller and conventional fractional-order PID controller (CFOC). It is observed that SFOC requires smaller effort as compared with its integer and conventional fractional counterpart to achieve the same system performance.

关键词: fractional calculus| Oustaloup's recursive filter| simplified fractional-order PID controller (SFOC)| genetic algorithm (GA)| controller tuning

CLC Number:

TP 273

LI Jie (李杰), LIU Yongzhi (刘勇智), SHAN Chenglong (鄯成龙), DAI Cong (戴聪). Implementation of Simplified Fractional-Order PID Controller Based on Modified Oustaloup's Recursive Filter[J]. Journal of Shanghai Jiao Tong University (Science), 2020, 25(1): 44-50.

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