Steady-state analysis of a three-term fuzzy controller

Abdelnour, G.; Cheung, J.Y.; Chang, Ching-Haur; Tinetti, Giovanna

doi:10.1109/21.229475

Cited by 21 publications

(6 citation statements)

References 4 publications

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“…1tX Jo with (i = ~(-1)) r(t )= X sin(rot) Xe Da,Da =[A;, AJ (Ai,AJe 9\~ and the assumption thatNL has asymmetric characteristic (i.e: NL(r) = NL(-r)). 42 Physically, replacing NL with LNL consists of neglecting higher harmonics. …”

Section: Stability and Robustness In Sjdf Sensementioning

confidence: 99%

Fuzzy Control Systems Stability: Time and Frequency Domain Criteria

Jamshidi¹,

Marín²,

Τitli³

1998

Intelligent Automation & Soft Computing

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Stability is the most important attribute of any system. A prerequisite for all stability criteria of control systems is the existence of a mathematical model. In contrast. fuzzy control systems are often designed based on heuristic human knowledge and without a mathematical model, hence, it has been a difficult task to determine stability of fuzzy control systems under such restrictions. This paper uses the Takagi/Sugeno type of fuzzy rules whose consequences are analytical, and singletons are used as a basis for a number of sufficiency conditions for stability. The schemes considered here are time-domain, but a brief survey which proceeds the main results considers frequency domain as well. Both Lyapunov and interval matrix criteria are presented with some proofs and numerical examples.

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Section: Stability and Robustness In Sjdf Sensementioning

confidence: 99%

Fuzzy Control Systems Stability: Time and Frequency Domain Criteria

Jamshidi¹,

Marín²,

Τitli³

1998

Intelligent Automation & Soft Computing

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“…HE steady state error is one of indexes for evaluating the performance of control systems, but the study of steady state error in fuzzy control systems [1], [2] is less than general control systems. In [1], the describing function is applied into analysis of steady error in fuzzy control systems.…”

Section: Introductionmentioning

confidence: 99%

“…In [1], the describing function is applied into analysis of steady error in fuzzy control systems. Because the nature of look-up table bases on the fuzzy addition, it enables us to decompose the fuzzy controller into three one-dimensional-multilevel relays.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Equilibrium Points in Static Fuzzy Control Systems with Reference Inputs and Adjustable Parameters

Perng

et al. 2006

2006 IEEE International Conference on Fuzzy Systems

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In this paper, the stability in static fuzzy control systems for linear systems with different fixed reference inputs and adjustable parameters are analyzed. Under certain conditions, the unique equilibriums of error in fuzzy control systems can be solved with fixed reference. Furthermore, when the unique equilibrium is stable, the steady state error can be obtained from this stable equilibrium. Under the adjustable parameters and reference inputs, the equilibriums may have stable and unstable transformations each other respect to absolutely stability. Additionally, the insight mechanism for oscillation of equilibrium is also given with a numerical example.

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“…Current approaches to the describing function method used in the stability analysis of FCSs deal with the following applications of this method: in the form of the exponential-input describing function technique to FCSs using the representations of the FCs as multidimensional-multilevel relays (Abdelnour, et al, 1993a(Abdelnour, et al, , 1993b; to FCSs based on Mamdani FCs without dynamics (Passino and Yurkovich, 1998); to multivariable Takagi-Sugeno FCSs (Cuesta, et al, 1999); to FCSs based on FCs with dynamics, by using the describing function of the saturation which occurs outside the input universes of the FCs (Aracil and Gordillo, 2000). All these approaches require the prediction of the limit cycles, specific to the describing function method (Kim, et al, 2000).…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Fuzzy Control Systems. Multivariable Point of View

Precup

Preitl

2005

IFAC Proceedings Volumes

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The paper proposes a new global stability analysis method dedicated to fuzzy control systems containing Mamdani fuzzy controllers with dynamics to control SISO linear / linearized plants. The method is expressed in terms of relatively simple steps based on the generalization of the describing function method to the MIMO case and on the application of the least squares method to approximate the describing functions. The method is applied to the stability analysis of a class of PI-fuzzy controlled servo systems and validated by a case study.

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Steady-state analysis of a three-term fuzzy controller

Cited by 21 publications

References 4 publications

Fuzzy Control Systems Stability: Time and Frequency Domain Criteria

Fuzzy Control Systems Stability: Time and Frequency Domain Criteria

Stability Analysis of Equilibrium Points in Static Fuzzy Control Systems with Reference Inputs and Adjustable Parameters

Stability Analysis of Fuzzy Control Systems. Multivariable Point of View

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