This paper presents the design and validation of a new adaptive variable gain reaching law, integrated with sliding mode control (SMC), to control perturbed and unperturbed nonlinear systems. The novelty behind this law stems from its capability to overcome the main limitations involved with SMC. In contrast to existing reaching laws, system’s performance can be substantially enhanced via this law, with significant reduction in the chattering phenomenon, along ensuring rapid convergence time of system’s trajectories towards equilibrium. The designed law not only integrates the features of both the exponential reaching law (ERL) and the power rate reaching law (PRL), but also overcomes their limitations. Simulation and comparison studies against ERL and PRL were carried out to validate the effectiveness and advantages of the proposed reaching law scheme (Proposed-RL). Furthermore, controlled experimental investigations were conducted using an exoskeleton robot (ETS-MARSE) to validate the scheme in real-time.

中文翻译：

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微扰和非微扰非线性系统滑模控制性能的增强：康复机器人的理论与实验

本文介绍了一种新的自适应可变增益到达定律的设计和验证，该定律与滑模控制 (SMC) 相结合，用于控制受扰和未受扰的非线性系统。该法律背后的新颖之处在于它能够克服 SMC 所涉及的主要限制。与现有的到达定律相比，通过该定律可以显着提高系统的性能，显着减少颤动现象，同时确保系统轨迹向平衡的快速收敛时间。所设计的律不仅综合了指数到达律（ERL）和电率到达律（PRL）的特点，而且克服了它们的局限性。进行了针对 ERL 和 PRL 的模拟和比较研究，以验证所提出的到达律方案 (Proposed-RL) 的有效性和优势。此外，还使用外骨骼机器人 (ETS-MARSE) 进行了受控实验研究，以实时验证该方案。