Robust Stability and Tracking for Operator-Based Nonlinear Uncertain Systems

Bi, Shuhui; Deng, Mingcong; Xiao, Yongfei

doi:10.1109/tase.2014.2325953

Cited by 46 publications

(10 citation statements)

References 20 publications

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“…Moreover, the robust stability and stabilization for the uncertain nonlinear feedback systems (UNFSs) are discussed 12,13 wherein the sufficient condition is given in the form of null set, which cannot be applied into the general UNFS. Therefore, based on the definition of Lipschitz norm, a sufficient condition (“robust condition”) in the form of inequality is proposed by which the robust control for the general UNFS can be extended 14‐17 …”

Section: Introductionmentioning

confidence: 99%

Robust passive tracking control for an uncertain soft actuator using robust right coprime factorization

Liu

2021

Intl J Robust & Nonlinear

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As a research of human arm activities, the research of soft actuator is one of the important topics in the field of robotics. This article is concerned with the robust passive tracking control for an uncertain soft actuator by robust right coprime factorization (RRCF). First, applying the recursive least squares identification algorithm, the identification of the actuator modeling is studied by which the parameter of radius is estimated by using the experimental data. Second, the passivity of the soft actuator with inflatable rubber tube is discussed; meanwhile, the robustness of the soft actuator is ensured by the designed robust controllers. Third, by combining the RRCF and integral sliding mode control methods, the tracking performance is improved, for the soft actuator with time‐varying radius. Finally, the proposed methods are confirmed by the simulation with experimental data.

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Section: Introductionmentioning

confidence: 99%

Robust passive tracking control for an uncertain soft actuator using robust right coprime factorization

Liu

2021

Intl J Robust & Nonlinear

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“…This is an open and challenging problem. An operator-based robust nonlinear control scheme is one way to solve such problems because of the usefulness of operator theory in the stability and robust stability of nonlinear systems (Bi et al, 2015; Chen and Han, 1998; Deng et al, 2011; Wang and Deng, 2012). The robust right coprime factorization approach is proposed to tackle the uncertain term in nonlinear systems, such as a miniature pneumatic curling rubber actuator and a Peltier actuated thermal process (Deng and Kawashima, 2016; Wen and Deng, 2013).…”

Section: Introductionmentioning

confidence: 99%

Operator-based robust nonlinear control of an uncertain wireless power transfer system using sliding mode technology

Gao

Deng

2018

Transactions of the Institute of Measurement and Control

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In this paper, a mathematical modelling of a wireless power transfer system with a buck circuit is presented. Based on this modelling, an operator-based robust nonlinear control design scheme using sliding mode technology is proposed to consider the uncertain coupling coefficient, which results from an inaccurate distance between the transmit coil and receive coil in the wireless power transfer system. The proposed control design scheme has two advantages. First, in order to tackle the uncertain coupling coefficient, operator-based right coprime factorization is applied to guarantee robust stability of the nonlinear system. Sliding mode technology is also adopted to guarantee the tracking performance of the nonlinear system. Finally, simulations and experiments of the wireless power transfer system are tested using the proposed control design scheme. Results of both the simulations and experiments show the effectiveness of the proposed control design scheme.

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“…In most cases, the existing internal perturbation and external disturbance have a critical effect on the stability of the overall system. With regards to these aspects, many results have been achieved (Bi et al, 2011, 2015; Bu and Deng, 2011; Chen et al, 2000; Deng et al, 2011; Katsurayama et al, 2016; Li et al, 1995). In Chen and Han (1998), the authors investigated robust right coprime factorization to consider nonlinear systems with perturbation, which provided a fairly general operator-theoretic setting for system analysis, control and design.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the robust sufficient condition of Deng et al (2006), in Bu and Deng (2011) the authors provided an operator-based isomorphism method to obtain factorization of nonlinear systems quantitatively. In Bi et al (2015), the authors proposed an internal model control to analyse the effects of uncertainties of nonlinear systems. The robust right coprime factorization method has also been developed for real applications, such as the robust controller design of uncertain discrete time-delay systems with input saturation and disturbance in Xu et al (2012), employment of low-order modes to design the control scheme using the operator-based approach in Katsurayama et al (2016), and so on.…”

Section: Introductionmentioning

confidence: 99%

Operator-based external disturbance rejection of perturbed nonlinear systems by using robust right coprime factorization

Deng

2017

Transactions of the Institute of Measurement and Control

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In this paper, a class of nonlinear systems with external disturbance and internal perturbation are considered by using operator-based robust right coprime factorization for guaranteeing robust stability, rejecting adverse effects resulting from the existing disturbance and perturbation quantitatively and, meanwhile, realizing output tracking performance. In detail, firstly, robust stability is guaranteed based on a Lipschitz norm inequation using robust right coprime factorization. Secondly, based on the proposed design scheme, a convenient framework is obtained for discussing rejection issues for external disturbance and internal perturbation. Thirdly, from an error signal point of view, the adverse effects resulting from the external disturbance and internal perturbation of the nonlinear system are removed by the designed nonlinear operator. Moreover, output tracking performance is realized using the proposed design scheme simultaneously. Finally, a simulation example is given to confirm the effectiveness of the proposed design scheme of this paper.

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Robust Stability and Tracking for Operator-Based Nonlinear Uncertain Systems

Cited by 46 publications

References 20 publications

Robust passive tracking control for an uncertain soft actuator using robust right coprime factorization

Robust passive tracking control for an uncertain soft actuator using robust right coprime factorization

Operator-based robust nonlinear control of an uncertain wireless power transfer system using sliding mode technology

Operator-based external disturbance rejection of perturbed nonlinear systems by using robust right coprime factorization

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