Cascaded robust fixed-time terminal sliding mode control for uncertain cartpole systems with incremental nonlinear dynamic inversion

IF 2.8 3区 工程技术 Q2 MECHANICS
Changyi Lei , Quanmin Zhu , Ruobing Li
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引用次数: 0

Abstract

This paper proposes a cascaded fixed-time terminal sliding mode controller (TSMC) for uncertain underactuated cartpole dynamics using incremental nonlinear dynamic inversion (INDI). Leveraging partial linearization and prioritizing pole dynamics for internal tracking, the proposed controller achieves efficient stabilization of the cart upon convergence of the pole. Stability analysis is carried out using Lyapunov stability theorem, proving that the proposed controller stabilizes the state variables to an arbitrarily small neighborhood of the equilibrium in fixed-time, along with the suboptimality (steady-state error), existence and uniqueness of the solutions. The INDI is also integrated into TSMC to further improve the robustness while suppressing the conservativeness of conventional TSMC. The stability of INDI is rigorously proved using sampling-based Lyapunov function under sampling-based control realm. The simulation results illustrate the superiority of the proposed method with comparison and ablation studies.

带增量非线性动态反演的不确定车杆系统的级联鲁棒固定时间终端滑模控制
本文提出了一种级联固定时间终端滑动模式控制器(TSMC),利用增量非线性动态反演(INDI)来控制不确定的欠驱动小车极点动态。利用部分线性化和内部跟踪的极点动态优先权,所提出的控制器在极点收敛后实现了小车的高效稳定。利用 Lyapunov 稳定性定理进行了稳定性分析,证明了所提出的控制器能在固定时间内将状态变量稳定在平衡点的任意小邻域,同时还证明了解的次优性(稳态误差)、存在性和唯一性。INDI 还被集成到 TSMC 中,以进一步提高鲁棒性,同时抑制传统 TSMC 的保守性。在基于采样的控制境界下,使用基于采样的 Lyapunov 函数严格证明了 INDI 的稳定性。仿真结果通过对比和烧蚀研究说明了所提方法的优越性。
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来源期刊
CiteScore
5.50
自引率
9.40%
发文量
192
审稿时长
67 days
期刊介绍: The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.
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