Studies on the output of fuzzy controller with multiple inputs

Wong, Ching‐Chang; Chou, Chih-Hsun; Mon, Don‐Lin

doi:10.1016/0165-0114(93)90154-a

Cited by 43 publications

(6 citation statements)

References 18 publications

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“…In 1990, we developed the first technique in the literature to cover Zadeh AND operator and a particular class of symmetric trapezoidal (or triangular) input fuzzy sets [19]. Our method has been widely used (e.g., [2], [3], [6], [10], [11], [14], and [16]). Recently, we have generalized it to cover arbitrary trapezoidal/triangular fuzzy sets [28].…”

mentioning

confidence: 99%

Deriving Analytical Input–Output Relationship for Fuzzy Controllers Using Arbitrary Input Fuzzy Sets and Zadeh Fuzzy AND Operator

Ying

2006

IEEE Trans. Fuzzy Syst.

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Abstract-A fuzzy controller uses either Zadeh or product fuzzy AND operator, with the former being more frequently used than the latter. We have recently published a novel technique for deriving analytical input-output relation for the fuzzy controllers that use Zadeh AND operator and arbitrary trapezoidal input fuzzy sets, including triangular ones as special cases. In this paper, we have developed a general technique based on that technique to cover arbitrary types of input fuzzy sets. Moreover, we have established some necessary and sufficient conditions to characterize general relationship between shape of input fuzzy sets and shape of input space divisions, an important and integral issue because analytical relationship differs in different regions of input space. The new technique and the shape relations are applicable to any type of fuzzy controllers (e.g., Mamdani type or Takagi-Sugeno type). The analytical structures that we have derived provide an unprecedented opportunity to insightfully and rigorously examine the advantages and shortcomings of different design choices available for various components of the fuzzy controllers. We have focused on type selection for input fuzzy sets of Mamdani fuzzy controllers. Our preliminary analysis indicates that the fuzzy controllers using trapezoidal fuzzy sets may be understood (and possibly analyzed and designed) more sensibly and easily in the context of conventional control theory than the fuzzy controllers using any other types of fuzzy sets. Our proposition is that trapezoidal fuzzy sets should be the first choice and used most of time. Possible implication for automatic learning of input fuzzy sets via neural networks or genetic algorithms is briefly discussed.

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confidence: 99%

Deriving Analytical Input–Output Relationship for Fuzzy Controllers Using Arbitrary Input Fuzzy Sets and Zadeh Fuzzy AND Operator

Ying

2006

IEEE Trans. Fuzzy Syst.

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“…If the number of linear fuzzy rules is sufficiently large, it can be shown that in the limit the defuzzified output can be approximated by a linear function of the controller input [22]. This result can also be extended to fuzzy controllers with multi-input [23].…”

Section: Properties Of the Neurofuzzy Controllermentioning

confidence: 91%

Model-Reference Adaptive Control Based on Neurofuzzy Networks

Liu

Lara-Rosano

Chan³

2004

IEEE Trans. Syst., Man, Cybern. C

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Model reference adaptive control (MRAC) is a popular approach to control linear systems, as it is relatively simple to implement. However, the performance of the linear MRAC deteriorates rapidly when the system becomes nonlinear. In this paper, a nonlinear MRAC based on neurofuzzy networks is derived. Neurofuzzy networks are chosen not only because they can approximate nonlinear functions with arbitrary accuracy, but also they are compact in their supports, and the weights of the network can be readily updated on-line. The implementation of the neurofuzzy network-based MRAC is discussed, and the local stability of the system controlled by the proposed controller is established. The performance of the neurofuzzy network-based MRAC is illustrated by examples involving both linear and nonlinear systems.

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“…They all used linear fuzzy sets to fuzzify input variables. The variable gains enabled the fuzzy controllers to outperform their linear counterparts when controlling nonlinear or timedelay systems [9][10][11][12]. However, since the relationship between adjustment of the consequents of the rules and properties of controllers is not explicit, big trouble is caused to adjust controller parameters.…”

Section: Introductionmentioning

confidence: 99%

Application of a New Membership Function in Nonlinear Fuzzy PID Controllers with Variable Gains

Zhang

Bao

et al. 2014

Journal of Applied Mathematics

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This paper proposes a nonlinear fuzzy PID control algorithm, whose membership function (MF) is adjustable, is universal, and has a wide adjustable range. Appling this function to fuzzy control theory will increase system’s tunability. The continuity of this function is proved. This method was employed in the simulation and HIL experiments. Effectiveness and feasibility of this function are demonstrated in the results.

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Studies on the output of fuzzy controller with multiple inputs

Cited by 43 publications

References 18 publications

Deriving Analytical Input–Output Relationship for Fuzzy Controllers Using Arbitrary Input Fuzzy Sets and Zadeh Fuzzy AND Operator

Deriving Analytical Input–Output Relationship for Fuzzy Controllers Using Arbitrary Input Fuzzy Sets and Zadeh Fuzzy AND Operator

Model-Reference Adaptive Control Based on Neurofuzzy Networks

Application of a New Membership Function in Nonlinear Fuzzy PID Controllers with Variable Gains

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