Lyapunov stability analysis of discrete-time robust adaptive super-twisting sliding mode controller

Hollweg, Guilherme Vieira; Evald, Paulo Jefferson Dias de Oliveira; Milbradt, Deise Maria Cirolini; Tambara, Rodrigo Varella; Gründling, Hilton Abílio

doi:10.1080/00207179.2021.2008508

Cited by 27 publications

(22 citation statements)

References 36 publications

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“…With the advancement of machine learning, a lot of control strategies take benefits from these algorithms, such as neural networks, 30,31 deep neural networks, 32 interpretable neural networks, 33 reinforcement learning, 34,35 deep reinforcement learning, 36 and others strategies. These techniques can be used offline for optimisation of the controller gains or online for adjustment of the gain in response to system perturbations 37 . However, most of these techniques may require relevant computational capacity to run online, being unfeasible for some microcontrollers used in diverse industrial applications.…”

Section: Introductionmentioning

confidence: 99%

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A hybrid robust model reference adaptive controller and proportional integral controller without reference model for partially modeled systems

Evald

Hollweg

Tambara

et al. 2023

Adaptive Control & Signal

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Summary This work presents the discrete‐time stability analysis of a hybrid robust model reference adaptive controller and proportional‐integral controller (MRAC‐PI) controller using Lyapunov criterion. The control structure merges the classical PI controller with a robust model reference adaptive control, resulting in an adaptive and robust control strategy, where the gains unite both control techniques in a unique structure and it does not require the design of a reference model, being able to track straightforwardly the reference signal. The adaptive gains are updated continuously by a modified gradient algorithm regarding control action, regulation error, and the system output. The stability analysis provides the controller design constraints, while also demonstrate the tendency of regulation error to a residual set, and proves the boundedness of all closed‐loop signals. Furthermore, as the controller is robust to unmodeled dynamics, it is feasible to control partially modeled systems. Simulation results in a real‐world engineering application are presented to corroborate the robustness of this controller and show its fast response in the face of critical exogenous system perturbations.

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Section: Introductionmentioning

confidence: 99%

“…These techniques can be used offline for optimisation of the controller gains or online for adjustment of the gain in response to system perturbations. 37 However, most of these techniques may require relevant computational capacity to run online, being unfeasible for some microcontrollers used in diverse industrial applications.…”

Section: Introductionmentioning

confidence: 99%

A hybrid robust model reference adaptive controller and proportional integral controller without reference model for partially modeled systems

Evald

Hollweg

Tambara

et al. 2023

Adaptive Control & Signal

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“…In order to reduce chattering of SMC, various methods of adaptation of the switching gain can be found in literatures. 12,14,24,46,47 In, 12 the design of an internal model principle-based sliding-mode DOB with switching-gain adaptation law is addressed for a class of nonlinear systems subject to exogenous signals. Utilizing the Lyapunov-Krasovskii functional, 14 designs the observer-based adaptive SMC for nonlinear uncertain singular semi-Markov jump systems, in which two adaptive gains are required.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the barrier function, the distributed consensus for multi-agent systems via adaptive SMC is considered in, 24 in which the control gains can be chosen randomly, whereas the adaptive switching gains are divided into two stages, and they are increasing in the first stage. Robust model reference adaptive control-based techniques, 46,47 study discrete-time hybrid robust adaptive SMC and robust adaptive super-twisting SMC for partially modeled systems, respectively. However, the design of adaptive switching gains mentioned in the above literatures depends on many model parameters and requires lots of calculation.…”

Section: Introductionmentioning

confidence: 99%

Novel sliding‐mode control for a class of second‐order systems with mismatched disturbances

Fu,

Che,

Liu

et al. 2023

Intl J Robust & Nonlinear

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This article investigates a novel sliding‐mode control (SMC) approach for a class of second‐order nonlinear systems subject to mismatched disturbances. To solve this problem, a novel sliding surface is designed based on the disturbance estimation of the nonlinear disturbance observer (DOB). By designing a novel time‐varying switching gain, a DOB‐based improved SMC law is constructed to compensate the influence of mismatched disturbances on the system output and make the system output converge asymptotically to zero. The novel SMC scheme owns two advantages. One is that the switching gain is an exponential decay function varying synchronously with the disturbance estimation error, which substantially alleviates the chattering problem. The other one is that a new function is defined as the switching gain coefficient based on the disturbance estimation, which helps the proposed approach to maintain the nominal control performance of the system, that is, the novel SMC law degrades to the baseline SMC law in the absence of disturbances. A numerical simulation example verifies the effectiveness and superiority of the developed approach by comparisons.

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“…Therefore, some adaptive mechanisms based on Lyapunov stability and switch-time have been proposed as two typical alternative solutions. For the former, it can lead the control gain to decrease dynamically as the system converges to the equilibrium point and guarantee the stability of the system in the range of convergence [51], for example, the literature [52] proposes a novel adaptive intelligent global sliding mode control based on the Lyapunov stability theory to overcome the time-varying uncertainties of buck converters. In the literature [53], a Lyapunov-based adaptive-robust current controller is developed for DC-DC converters.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Continuous Sliding Mode Control of Buck Converters With Multidisturbances Based on Zero-Crossing Detection

2022

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In this paper, a novel adaptive continuous sliding mode (SM) control approach is proposed based on the robust stability analysis of buck converters with multi-disturbances. Instead of the traditional first-order SM methods, the twisting algorithm is adopted to realize the control continuity and further weaken their inherent chattering problem. By introducing the zero-crossing detection innovatively, the influence of the traditional twisting algorithm with fixed control gain led to the low precision is effectively eliminated, and the small region can be controlled due to the implementation of the adaptive time-varying control gain. In addition, the magnitude of the controller can be reduced to a minimal admissible level determined by the system stable conditions and the selection of optimization parameters. Furthermore, multiple model uncertainties and external disturbances are considered into the modeling of the buck converters and the proposed adaptive SM controllers to ensure the strong robustness of the whole system while suffering possible disturbances. Finally, comparative simulations and experiments are given to validate the effectiveness of the proposed adaptive control strategy.INDEX TERMS Adaptive continuous sliding mode control, buck converters, zero-crossing detection, multidisturbances, twisting sliding mode control.

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Lyapunov stability analysis of discrete-time robust adaptive super-twisting sliding mode controller

Cited by 27 publications

References 36 publications

A hybrid robust model reference adaptive controller and proportional integral controller without reference model for partially modeled systems

A hybrid robust model reference adaptive controller and proportional integral controller without reference model for partially modeled systems

Novel sliding‐mode control for a class of second‐order systems with mismatched disturbances

Adaptive Continuous Sliding Mode Control of Buck Converters With Multidisturbances Based on Zero-Crossing Detection

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