Adaptive robust control of nonlinear systems with dynamic uncertainties

Liu, Xiangbin; Su, Hongye; Yao, Bin; Chu, Jian

doi:10.1002/acs.1048

Cited by 16 publications

(24 citation statements)

References 10 publications

(27 reference statements)

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“…The control law design follows the ARC synthesis procedure proposed in [16], [17] and [25]. First, de ne a tracking-errorindex-like variable [26] as (7) where is the output tracking error, and is any positive feedback gain.…”

Section: A Discontinuous Control Lawmentioning

confidence: 99%

“…To overcome these drawbacks, a dynamic friction compensation strategy is proposed in [15] by utilizing the idea of adaptive robust control (ARC) [16], [17], where the robust control term is used to guarantee desired transient response, and the adaptive control term is used to achieve favorable steady-state tracking accuracy. In this method, the parameters related to the Stribeck effect are assumed to be known.…”

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confidence: 99%

See 1 more Smart Citation

Adaptive Robust Control of Servo Mechanisms With Compensation for Nonlinearly Parameterized Dynamic Friction

Li¹,

Chen

Zhang

et al. 2013

IEEE Trans. Contr. Syst. Technol.

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Abstract-In this brief, an adaptive robust control (ARC) scheme with compensation for nonlinearly parameterized dynamic friction is proposed. Both parametric uncertainties and external disturbances are considered in this method. Our method takes advantage of a Lipschitzian property with respect to the parameters of nonlinearly parameterized model in the ARC design. The outcome is that the number of parameters to be updated in the ARC is equal to the number of unknown parameters in the plant, and thus the resulting control algorithm is convenient to be implemented. We have proved theoretically that the proposed method can not only guarantee desired transient performance for the system, but also make the magnitude of steady-state tracking error to be arbitrarily small in the presence of parametric uncertainties only. Experimental results are given to demonstrate the effectiveness of the proposed ARC scheme.

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Section: A Discontinuous Control Lawmentioning

confidence: 99%

mentioning

confidence: 99%

Adaptive Robust Control of Servo Mechanisms With Compensation for Nonlinearly Parameterized Dynamic Friction

Li¹,

Chen

Zhang

et al. 2013

IEEE Trans. Contr. Syst. Technol.

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show abstract

“…The sign problem was resolved in [8], [9] incorporating Nussbaum gains, under the restriction the control coefficients being bounded and state independent. Finally, dynamic uncertainties with and without known structural information are considered in [10].…”

Section: B Related Work and Technical Challengesmentioning

confidence: 99%

Robust Partial-State Feedback Prescribed Performance Control of Cascade Systems With Unknown Nonlinearities

Bechlioulis

Rovithakis

2011

IEEE Trans. Automat. Contr.

206

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A universal controller is designed for cascade systems, involving dynamic uncertainty, unknown nonlinearities, exogenous disturbances and/or time-varying parameters, capable of guaranteeing prescribed performance for the output tracking error, as well as uniformly bounded signals in the closed loop. By prescribed performance we mean that the output tracking error should converge to a predefined arbitrarily small residual set, with convergence rate no less than a certain prespecified value, exhibiting maximum overshoot less than a sufficiently small preassigned constant. The proposed control scheme is of low complexity, utilizes partial state feedback and requires reduced levels of a priori system knowledge. The results can be easily extended to systems affected by bounded state measurement errors, as well as to MIMO nonlinear systems in block triangular form. Simulations clarify and verify the approach.Index Terms-Dynamic uncertainty, measurement errors, prescribed performance control, unknown cascade systems.

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“…Unlike parameter uncertainties, 9 structured uncertainties had largely bothered the adaptive control theory in the 1980s, 3,10-12 such as the unknown relative degree and dynamics uncertainties, which means that the observer for part system dynamics cannot be designed, 11,12 and the unknown control direction, which possibly opposes control effect. 3,10 Control design has received continuous attention for the systems with unknown relative degree and/or dynamics uncertainties, particularly advanced with the breakthrough development of adaptive control and stability theory (see, for example, previous works 5,7,8,[11][12][13][14][15][16][17][18][19][20][21][22] ). First of all, with the information that the unknown relative degree is one or two, adaptive output-feedback control was addressed for linear systems in the work of Morse.…”

Section: Introductionmentioning

confidence: 99%

Global output‐feedback stabilization for nonlinear systems with unknown relative degree

Wang

Liu

Man

2017

Intl J Robust & Nonlinear

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Summary This paper is devoted to the global stabilization via output feedback for a class of nonlinear systems with unknown relative degree, dynamics uncertainties, unknown control direction, and nonparametric uncertain nonlinearities. In particular, the unknown relative degree is without known upper bound, which renders us to research for a filter with varying dimension rather than the ones with over dimensions in the existing literature. In comparison with more popular but a bit stronger input‐to‐state stable or input‐to‐state practically stable requirement, only bounded‐input bounded‐state stable requirement is imposed on the dynamics uncertainties, which affect the systems in a persistent intensity rather than in a decaying one. In this paper, to compensate multiple serious system uncertainties and realize global output‐feedback stabilization, a design scheme via switching logic together with varying dimensional filter is developed. In this scheme, 2 switching sequences, which separately generate the gains of the controller and act as the varying dimensions of the filter, are designed to overcome unknown control direction, dynamics uncertainties and nonparametric uncertain nonlinearities, and unknown relative degree, respectively. A 2‐mass lumped‐parameter structure is provided to show the effectiveness of the proposed method in this paper.

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Adaptive robust control of nonlinear systems with dynamic uncertainties

Cited by 16 publications

References 10 publications

Adaptive Robust Control of Servo Mechanisms With Compensation for Nonlinearly Parameterized Dynamic Friction

Adaptive Robust Control of Servo Mechanisms With Compensation for Nonlinearly Parameterized Dynamic Friction

Robust Partial-State Feedback Prescribed Performance Control of Cascade Systems With Unknown Nonlinearities

Global output‐feedback stabilization for nonlinear systems with unknown relative degree

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