Non-overshooting continuous in convergence sliding mode control of second-order systems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913750821371904 |
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| author | Ruderman, Michael Efimov, Denis |
| author_facet | Ruderman, Michael Efimov, Denis |
| contents | This paper proposes a novel nonlinear sliding mode state feedback controller for perturbed second-order systems. In analogy to a linear proportional-derivative (PD) feedback control, the proposed nonlinear scheme uses the output of interest and its time derivative. The control has only one free design parameter, and the closed-loop system is shown to possess uniform boundedness and finite-time convergence of trajectories in the presence of matched disturbances. We derive a strict Lyapunov function for the closed-loop control system with a bounded exogenous perturbation, and use it for both, the control parameter tuning and analysis of the finite-time convergence. The essential features of the proposed new control law is non-overshooting despite the unknown dynamic disturbances and the continuous control action during the convergence to zero equilibrium. Apart from the numerical results, a revealing experimental example is also shown in favor of the proposed control and in comparison with PD and sub-optimal nonlinear damping regulators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14000 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-overshooting continuous in convergence sliding mode control of second-order systems Ruderman, Michael Efimov, Denis Optimization and Control Systems and Control This paper proposes a novel nonlinear sliding mode state feedback controller for perturbed second-order systems. In analogy to a linear proportional-derivative (PD) feedback control, the proposed nonlinear scheme uses the output of interest and its time derivative. The control has only one free design parameter, and the closed-loop system is shown to possess uniform boundedness and finite-time convergence of trajectories in the presence of matched disturbances. We derive a strict Lyapunov function for the closed-loop control system with a bounded exogenous perturbation, and use it for both, the control parameter tuning and analysis of the finite-time convergence. The essential features of the proposed new control law is non-overshooting despite the unknown dynamic disturbances and the continuous control action during the convergence to zero equilibrium. Apart from the numerical results, a revealing experimental example is also shown in favor of the proposed control and in comparison with PD and sub-optimal nonlinear damping regulators. |
| title | Non-overshooting continuous in convergence sliding mode control of second-order systems |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2406.14000 |