Systematic design and stability analysis of a fuzzy logic controller

Limit-cycle is the phenomenon that can be observed in the systems composed of nonlinear elements. The phenomenon is of fundamental importance in nonlinear systems and, as far as the design of a nonlinear system is concerned, it should be considered along with the stability analysis. In this paper, the limit-cycle of a system controlled by a fuzzy logic controller (FLC) is addressed via some of the classical control techniques used to analyze nonlinear systems in the frequency domain. First, reasonable assumptions are made on the structure of the FLC by using fuzzy basis functions (FBF's) and the describing function of the FLC is derived to analyze and predict the existence of the limit-cycle of the closed-loop system including the FLC. Finally, computer simulation is performed to show how the analysis given in the paper is used to predict the existence of the limit-cycle of the fuzzy control system.

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“…Especially, the fuzzy sliding mode controllers (FSMC) satisfy the above skew-symmetric condition [20]- [22] D3)…”

Section: For the Dynamic Casementioning

confidence: 99%

Limit-cycle prediction of a fuzzy control system based on describing function method

Kim

Lee

Park

2000

IEEE Trans. Fuzzy Syst.

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“…We can conclude that is the least robust rule for positive Similarly, if is negative, we can also use condition (13) to conclude that is the least robust rule. In conclusion, either the rule corresponding to or is the least robust rule.…”

Section: B Robustness Of the Flcmentioning

confidence: 99%

“…Following the same analysis procedures, condition (14) can be obtained by replacing with 3) If similar to the second case, condition (8) is replaced by (15), and condition (14) can also be obtained by replacing with Consequently, the new system is stable ISL after adding the new rule. Moreover, unlike that in [11]- [13], the new rule is not restricted in terms of the shape, symmetry, and distribution of the input membership functions.…”

Section: A Adding Of Rulesmentioning

confidence: 99%

“…This common Lyapunov function is easier to be found than that in [2] because the number of fuzzy subsystems involved is only the number of rules instead of Moreover, by using this design approach, the adding of a new fuzzy rule becomes very easy. Unlike the state-space partitioning approaches [11]- [13], [17], no restriction on the shape and distribution of input membership functions is needed. An example on designing a heuristic FLC will be given to illustrate the proposed stability design approach.…”

mentioning

confidence: 99%

“…Besides the fuzzy-model-based approaches, some other approaches [11]- [13], [17] involve partitioning of the state space into small parts, and each part is analyzed for closedloop stability. However, if the number of rules is large, the number of partitions will become large and the analysis will be very time consuming.…”

mentioning

confidence: 99%

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Lyapunov-function-based design of fuzzy logic controllers and its application on combining controllers

Wong

Leung

Tam

1998

IEEE Trans. Ind. Electron.

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Abstract-This paper presents the design of fuzzy logic controllers (FLC's) for nonlinear systems with guaranteed closedloop stability and its application on combining controllers. The design is based on heuristic fuzzy rules. Although each rule in the FLC refers to a stable closed-loop subsystem, the overall system stability cannot be guaranteed when all these rules are applied together. In this paper, it is proved that if each subsystem is stable in the sense of Lyapunov (ISL) under a common Lyapunov function, the overall system is also stable ISL. Since no fuzzy plant model is involved, the number of subsystems generated is relatively small, and the common Lyapunov function can be found more easily. To probe further, an application of this design approach to an inverted pendulum system that combines a sliding-mode controller (SMC) and a state feedback controller (SFC) is to be reported. Each rule in this FLC has an SMC or an SFC in the consequent part. The role of the FLC is to schedule the final control under different antecedents. The stability of the whole system is guaranteed by the proposed design approach. More importantly, the controller thus designed can keep the advantages and remove the disadvantages of the two conventional controllers.

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Systematic design and stability analysis of a fuzzy logic controller

Cited by 31 publications

References 3 publications

Limit-cycle prediction of a fuzzy control system based on describing function method

Limit-cycle prediction of a fuzzy control system based on describing function method

Lyapunov-function-based design of fuzzy logic controllers and its application on combining controllers

Fuzzy Reasoning

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