Mathematical analysis of a simplified general type-2 fuzzy PID controller

Jianzhong Shi; Ying Song; Jianzhong Shi; Ying Song

doi:10.3934/mbe.2020406

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 7994-8036. doi: 10.3934/mbe.2020406

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Mathematical analysis of a simplified general type-2 fuzzy PID controller

Jianzhong Shi ^,,
Ying Song

School of Energy and Power Engineering, Nanjing Institute of Technology, Nanjing 211167, China

Received: 09 September 2020 Accepted: 28 October 2020 Published: 12 November 2020

For the type reduction of general type-2 fuzzy PID controller is time consuming and the mathematical expression of general type-2 fuzzy PID controller is difficult to derived. So, a simplified general type-2 fuzzy PID (SGT2-FPID) controller is studied in this article. The SGT2-FPID controller adopts triangular function as the primary and secondary membership function. Then the primary membership degree of apex for the secondary membership degree will be applied to get the output of SGT2-FPID controller, which can reduce the computation complexity of general type-2 fuzzy controller type reduction. Furthermore, the mathematical expressions of SGT2-FPID controller, type-1 fuzzy PID controller and interval type-2 fuzzy PID controller are discussed. Finally, 4 plants are applied to demonstrate the effectiveness and robustness of SGT2-FPID controller. The simulation results show that when the plants have uncertainty in model structure, measurement and external disturbance, the SGT2-FPID controller can achieve better control performances in contrast to compared controllers.
- type-2 fuzzy sets,
- type-2 fuzzy logic systems,
- type-2 fuzzy controller,
- type reduction,
- fuzzy controller structure analysis
Citation: Jianzhong Shi, Ying Song. Mathematical analysis of a simplified general type-2 fuzzy PID controller[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 7994-8036. doi: 10.3934/mbe.2020406

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Abstract

For the type reduction of general type-2 fuzzy PID controller is time consuming and the mathematical expression of general type-2 fuzzy PID controller is difficult to derived. So, a simplified general type-2 fuzzy PID (SGT2-FPID) controller is studied in this article. The SGT2-FPID controller adopts triangular function as the primary and secondary membership function. Then the primary membership degree of apex for the secondary membership degree will be applied to get the output of SGT2-FPID controller, which can reduce the computation complexity of general type-2 fuzzy controller type reduction. Furthermore, the mathematical expressions of SGT2-FPID controller, type-1 fuzzy PID controller and interval type-2 fuzzy PID controller are discussed. Finally, 4 plants are applied to demonstrate the effectiveness and robustness of SGT2-FPID controller. The simulation results show that when the plants have uncertainty in model structure, measurement and external disturbance, the SGT2-FPID controller can achieve better control performances in contrast to compared controllers.

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