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**Design and analysis of a fuzzy proportional-integral-derivative controller.**
*(English)*
Zbl 0872.93049

Summary: This paper describes the design principle, tracking performance and stability analysis of a fuzzy proportional-integral (PI) plus a derivative (D) controller. First, the fuzzy PID controller is derived from the conventional continuous-time linear PID controller. Then, the fuzzification, control-rule base, and defuzzification in the design of the fuzzy controller are discussed in detail. The resulting controller is a discrete-time fuzzy version of the conventional PID controller, which has the same linear structure in the proportional, integral and derivative parts but has nonconstant gains: the proportional, integral and derivative gains are nonlinear functions of the input signals. The new fuzzy PID controller thus preserves the simple linear structure of its conventional counterpart yet enhances the self-tuning control capability. Computer simulation results have demonstrated the advantages of the fuzzy controller, particularly when the process to be controlled is nonlinear. After a brief stability analysis, where a simple and realistic sufficient condition for the bounded-input/bounded-output stability of the overall feedback control system was derived, several computer simulation results are shown to compare with the conventional PID controller. Computer simulation results have shown the new fuzzy controller indeed has satisfactory tracking performance.

### MSC:

93C42 | Fuzzy control/observation systems |

### Keywords:

fuzzy proportional-integral derivative controller; computer simulation; design; tracking; stability
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\textit{D. Misir} et al., Fuzzy Sets Syst. 79, No. 3, 297--314 (1996; Zbl 0872.93049)

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### References:

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