Fuzzy model based controller for an inverted pendulum

Leung, F.H.F.; Wong, L.K.; Tam, P.K.S.

doi:10.1049/el:19961134

Cited by 30 publications

(16 citation statements)

References 2 publications

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“…Thus, we can draw the following conclusion: for a fuzzy control system described by (6), if the input variables adopt SFPs, then the equilibrium of the fuzzy system is asymptotically stable in the large if there exists a local common positive definite matrix P l in each overlapped-rules group satisfying (11) and (12).…”

Section: Resultsmentioning

confidence: 92%

“…If there exists a common positive definite matrix P l satisfying (11) and (12) in the lth overlapped-rules group:…”

Section: Resultsmentioning

confidence: 99%

“…In [9], in order to cope with parametric uncertainties of nonlinear systems, a numerical analysis method of a robust feedback linearization control scheme was proposed based on fuzzy models. However, all these stability approaches usually appeal to a common positive definite matrix P , which is a very difficult task even by the linear matrix inequality (LMI) method [10,11] when the number of fuzzy rules is large.…”

Section: Introductionmentioning

confidence: 99%

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Controller design of uncertain nonlinear systems based on T-S fuzzy model

Zhang

Bai

2009

J. Control Theory Appl.

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A robust control for uncertain nonlinear systems based on T-S fuzzy model is discussed in this paper. First, a T-S fuzzy system is adopted to model the uncertain nonlinear systems. Then, for the system with input variables adopting standard fuzzy partitions, the efficient maximal overlapped-rules group (EMORG) is presented, and a new sufficient condition to check the stability of T-S fuzzy system with uncertainty is derived, which is expressed in terms of Linear Matrix Inequalities. The derived stability condition, which only requires a local common positive definite matrix in each EMORG, can reduce the conservatism and difficulty in existing stability conditions. Finally, a simulation example shows the proposed approach is effective.

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Section: Resultsmentioning

confidence: 92%

“…If there exists a common positive definite matrix P l satisfying (11) and (12) in the lth overlapped-rules group:…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Controller design of uncertain nonlinear systems based on T-S fuzzy model

Zhang

Bai

2009

J. Control Theory Appl.

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“…There exist many types of inverted pendulums. The Furuta pendulum 2 has been used by some authors 3,4,5 . Generalized models such as 3D pendulums have also been more recently developed 6 .…”

Section: Co-published By Atlantis Press and Taylor And Francismentioning

confidence: 99%

Control of a chain pendulum: A fuzzy logic approach

Aranda-Escolástico¹,

Guinaldo²,

Santos³

et al. 2016

IJCIS

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In this paper we present a real application of computational intelligence. Fuzzy control of a non-linear rotary chain pendulum is proposed and implemented on real prototypes. The final aim is to obtain a larger region of attraction for the stabilization of this complex system, that is, a more robust controller. As it is well-known, fuzzy logic exploits the tolerance for imprecision, uncertainty and partial truth to achieve tractability, robustness and low solution cost when dealing with complex systems. In this case, the control strategy is based on a Takagi-Sugeno fuzzy model of the strongly non-linear multivariable system. Simulation and experimental results on the real plant have been obtained and tested in a rotary inverted pendulum and in a double rotary inverted pendulum. They have been compared to other feedback control strategies such as Full State Feedback or Linear Quadratic Regulator with encouraging results. Fuzzy control allows to enlarge the stability region of control. Indeed, the region of attraction and therefore the stabilization has been enlarged up to over 17% for the real system.

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“…Fuzzy logic system [12] that uses adaptive sliding mode control can approximate the unknown function of nonlinear systems. The FLC [13] which produces desirable transient performance for nonlinear systems which promises closed loop stability. An adaptive fuzzy control scheme [14] employs a fuzzy controller and a compensation controller for a class of nonlinear continuous systems.…”

Section: Introductionmentioning

confidence: 99%

Takagi-Sugeno Fuzzy System based Stable Direct Adaptive Control of Nonlinear Systems

Bhushan¹,

Valluru²,

Singh³

2013

IJCA

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This paper proposes a novel idea for stable direct adaptive control of nonlinear systems using Lyapunov function with fuzzy approach. Stable direct adaptive control law consists of an ideal control, and a sliding mode control. Sliding mode controller is used to ensure the stability of Lyapunov function. Stability of direct adaptive control law is tested on two nonlinear systems. Non linear systems analyzed are ball beam system and cart pole system. A computer simulation is performed on nonlinear systems by using MATLAB. KeywordsFuzzy system, Lyapunov function, adaptive control, ball beam system and cart pole system.

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Fuzzy model based controller for an inverted pendulum

Cited by 30 publications

References 2 publications

Controller design of uncertain nonlinear systems based on T-S fuzzy model

Controller design of uncertain nonlinear systems based on T-S fuzzy model

Control of a chain pendulum: A fuzzy logic approach

Takagi-Sugeno Fuzzy System based Stable Direct Adaptive Control of Nonlinear Systems

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