A sliding mode controller with improved adaptation laws for the upper bounds on the norm of uncertainties

Wheeler, G.; Su, Chun-Yi; Stepanenko, Y.

doi:10.1109/vss.1996.578594

Cited by 11 publications

(4 citation statements)

References 11 publications

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“…To adequately investigate the stability and the algorithm of these ASMC designs, the sufficient and necessary conditions of their existence are discussed in this paper. Slightly different from the existing conditions, the provided necessary and sufficient ones address the objective of switching gain design and demonstrate the FTC in ASMC designs introduced in the literature (Cong et al, 2012;Huang et al, 2008;Li and Xu, 2010;Li and Zheng, 2012;Pai, 2013;Plestan et al, 2010;Utkin and Poznyak, 2013b;Wheeler et al, 1998). Moreover, with the sufficient conditions, numerous ASMC schemes can be designed.…”

Section: Introductionmentioning

confidence: 97%

“…Among these schemes, a new integral/exponential reaching law mainly is proposed in this paper. While most commonly known ASMC designs (Cong et al, 2012;Huang et al, 2008;Li and Xu, 2010;Li and Zheng, 2012;Pai, 2013;Plestan et al, 2010;Utkin and Poznyak, 2013b;Wheeler et al, 1998) induce the overestimation of the switching gain, the new proposed algorithm significantly reduces the magnitude of the final switching gain, and thus the gain overestimation is further reduced. Simultaneously, it does not sacrifice the system response to perturbations; it even speeds up the response: thus the system reacts fast to the perturbations, the trajectory is confined close to the sliding surface and the stability is improved.…”

Section: Introductionmentioning

confidence: 98%

“…the position) is measured, SMCPE may encounter the risk of large estimation errors which will result in a degraded performance. On the other hand, to keep away from the risk of estimating VHOS in SMCPE, the design of an adaptive sliding mode controller (ASMC) with a time-varying switching gain dynamically compensating for the perturbation was introduced (Cong et al, 2012;Fei et al, 2012;Huang et al, 2008;Lee and Utkin, 2007;Li and Xu, 2010;Mahmoodabadi et al, 2014;Plestan et al, 2010;Utkin, 1992;Utkin and Poznyak, 2013b;Wheeler et al, 1998). For the ASMC designs, the system response to the perturbation is relatively slow; moreover, even though the overestimation is avoided somehow, the chattering phenomenon is still observed.…”

Section: Introductionmentioning

confidence: 99%

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A new approach for adaptive sliding mode control: Integral/exponential gain law

Zhu

Khayati

2015

Transactions of the Institute of Measurement and Control

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This paper proposes a new approach for adaptive sliding mode controller (ASMC) designs. The goal is to obtain robust, smooth, and fast transient performance for nonlinear systems with finite uncertainties of unknown bounds and limited available inputs so that the phenomena of the slow response and the gain overestimation in most ASMC designs can be greatly improved. Sufficient and necessary conditions for the existence of a sliding mode in the ASMC designs are discussed. Based on the sufficient conditions, we introduce an integral/exponential adaptation law targeting the reduction of the chatter levels of the sliding mode by significantly reducing the gain overestimation while simultaneously speeding up the system response to the uncertainties. An illustrative example and numerical simulations are performed to convey the discussed results.

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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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A new approach for adaptive sliding mode control: Integral/exponential gain law

Zhu

Khayati

2015

Transactions of the Institute of Measurement and Control

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“…It is clear that amplified chattering can stem from an excessive control gain with respect to the disturbance amplitude. Conventional

σ

‐modification, 15 dead‐zone scheme, 16 boundary layer technique, 17 and hyperbolic tangent or sigmoid approximation 18 are useful for softening chattering but will unfortunately extend the control precision 19 . In order to allow the control amplitude declining when disturbance becomes small, new types of adaptive laws have been developed in recent years, such as the leakage term‐combined adaptive law, 20,21 barrier function‐based adaptive law, 22,23 dead‐zone‐type adaptive law, 24 etc.…”

Section: Introductionmentioning

confidence: 99%

Nested adaptive integral terminal sliding mode control for high‐order uncertain nonlinear systems

Shao

2021

Intl J Robust & Nonlinear

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This paper aims to develop a nested adaptive integral terminal sliding mode control scheme for high‐order uncertain nonlinear systems. To achieve this goal, a recursive‐structure integral terminal sliding mode (ITSM) is presented, which consists of a nonsingular terminal sliding mode and a fractional power integral terminal sliding mode. Based on the ITSM, the reaching phase is eliminated and simultaneously, the system is stabilized in finite time. Moreover, due to the full‐order sliding mode inherent in ITSM, the reaching control input is obtained in an integral form instead of a signum function. To remove the needs for the upper bounds of the disturbance or its derivatives, a nested dual‐layer adaptive law is introduced to update the level of the control gain according to the disturbance variations without overestimation. Stability analysis demonstrates that under the proposed control, the system state starts on the sliding surface and then converges to the origin in finite time in the presence of system uncertainties. The novelty of the proposed method lies in its finite‐time origin convergence without reaching phase, nonoverestimation, nonsingular and chattering‐free control signal, and those properties have not yet been achieved by any other existing methods. A simulation example is provided to illustrate the superiorities of the proposed control by comparison to conventional method.

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Improved Adaptive Sliding Mode Control for a Class of Second‐Order Mechanical Systems

Cong¹,

Liu²,

Chen³

2012

Asian Journal of Control

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This paper considers the tracking control problem for a class of second‐order mechanical systems with bounded uncertain parameters. A solution to the over‐adaptation problem in current adaptive sliding mode control (ASMC) is presented by introducing a decay function in the sliding function definition. The switching gain generated by the proposed ASMC algorithm is significantly reduced as compared with current ASMC design. Simulation results verify the effectiveness of the proposed approach.

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A sliding mode controller with improved adaptation laws for the upper bounds on the norm of uncertainties

Cited by 11 publications

References 11 publications

A new approach for adaptive sliding mode control: Integral/exponential gain law

A new approach for adaptive sliding mode control: Integral/exponential gain law

Nested adaptive integral terminal sliding mode control for high‐order uncertain nonlinear systems

Improved Adaptive Sliding Mode Control for a Class of Second‐Order Mechanical Systems

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