Using circle criteria for verifying asymptotic stability in PI-like fuzzy control systems: application to the milling process

Schmitt-Braess, G.; Haber, Rodolfo E.; Alique, A.; Alique, José R.

doi:10.1049/ip-cta:20030795

Cited by 33 publications

(9 citation statements)

References 11 publications

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“…The famous circle criterion and its graphical interpretation are applied in [16] for stability analysis of the SISO and MIMO Mamdani fuzzy control systems. Similar research findings are reported in both [3,8]. In [17], the L 2 -stability analysis of SISO Mamdani fuzzy control systems is performed using the circle criterion in the frequency domain.…”

Section: Introductionsupporting

confidence: 54%

Stability analysis of the simplest Takagi–Sugeno fuzzy control system using circle criterion

Ban

Gao

Huang

et al. 2007

Information Sciences

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Section: Introductionsupporting

confidence: 54%

Stability analysis of the simplest Takagi–Sugeno fuzzy control system using circle criterion

Ban

Gao

Huang

et al. 2007

Information Sciences

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“…(25), cannot guarantee the stability of the milling process, and minimization of SLE and maximization of spindle speed cannot be achieved. In previous studies [26,27], uncertainties in the milling process were compensated by designing controllers for known process effects and accounted for the nonlinearity and uncertainties inherent in milling operations. However, the controller design is time-consuming and the expected performance can be alternatively achieved easily by using the cutting parameters optimization.…”

Section: Robust Cutting Parameters Optimizationmentioning

confidence: 99%

Numerical robust optimization of spindle speed for milling process with uncertainties

Zhang

Zhu

Zhang

et al. 2012

International Journal of Machine Tools and Manufacture

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“…Unfortunately, this intuitive approach increases the difficulties of stability analysis of the fuzzy control systems. A novel circle criterion-based method is proposed to guarantee the local asymptotic stability of a specific type of the Mamdani PI fuzzy controllers with linear plants 18 .…”

Section: Stability Analysismentioning

confidence: 99%

Stability Analysis of a Type of Takagi-Sugeno PI Fuzzy Control Systems Using Circle Criterion

Cao¹,

Gao²,

Huang³

et al. 2011

IJCIS

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A type of Takagi-Sugeno (T-S) Proportional-Integral (PI) fuzzy controllers is studied. The T-S PI fuzzy controller is formed by a T-S Proportional-Derivative (PD) fuzzy controller connected with an integrator. In this particular structure, the T-S PD fuzzy controller is a weighted sum of some linear PD sub-controllers. The mathematical properties of our T-S PI fuzzy controller are also investigated. Based on these properties, the global asymptotic stability of the fuzzy control systems, in which the T-S PI fuzzy controllers are employed, are analyzed by using the well-known circle criterion. A sufficient condition with an elegant graphical interpretation in the frequency domain is further derived to guarantee the global asymptotic stability of the above fuzzy control systems. Finally, two numerical examples are provided to demonstrate how to deploy this method in analyzing the T-S PI fuzzy control systems in the frequency domain with the aid of some simple graphs.

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Using circle criteria for verifying asymptotic stability in PI-like fuzzy control systems: application to the milling process

Cited by 33 publications

References 11 publications

Stability analysis of the simplest Takagi–Sugeno fuzzy control system using circle criterion

Stability analysis of the simplest Takagi–Sugeno fuzzy control system using circle criterion

Numerical robust optimization of spindle speed for milling process with uncertainties

Stability Analysis of a Type of Takagi-Sugeno PI Fuzzy Control Systems Using Circle Criterion

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