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Smooth Higher-Order Sliding Mode Control of a Class of Underactuated Mechanical Systems

机译：一类欠驱动机械系统的平滑高阶滑模控制

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摘要

This paper investigates the application of smooth higher-order sliding mode (HOSM) control to a class of underactuated mechanical systems. Underactuated mechanical systems have increasing practical importance, but their strong nonlinear behavior and increased vulnerability to uncertainties due to the absence of actuators for some of the configuration variables make the control design problem a challenging task. Sliding mode control (SMC) has the most effective role in controlling such strong nonlinear uncertain systems. However, the standard SMC has chattering in the control action, which is undesired and practically not applicable, especially in mechanical control systems. To achieve smooth control and robustness needed for underactuated mechanical systems, smooth HOSM control laws based on the Super-Twisting Algorithm and the Smooth Super-Twisting Algorithm are proposed. Closed-form analytic expressions are derived for performance design parameters of the sliding surface. These expressions determine the performance of the sliding mode dynamics and also guarantee its stability. For comparison of the results, a standard SMC law is also presented and its merits/demerits are discussed. The design procedure is illustrated by applying it to two well-known cases of the Beam-and-Ball system and the Cart-Pole system as representative examples of the class. Numerical simulation results verify the enhanced control performance and robustness of the theoretical work.
机译：本文研究了平滑高阶滑模控制在一类欠驱动机械系统中的应用。欠驱动机械系统具有越来越高的实际重要性，但是由于缺少一些配置变量的致动器，其强大的非线性性能和对不确定性的增加的承受能力使控制设计成为一项艰巨的任务。滑模控制（SMC）在控制这种强非线性不确定系统中具有最有效的作用。但是，标准SMC在控制动作中会产生抖动，这是不希望的，并且实际上不适用，特别是在机械控制系统中。为了实现欠驱动机械系统所需的平滑控制和鲁棒性，提出了基于超扭曲算法和平滑超扭曲算法的平滑HOSM控制律。为滑动表面的性能设计参数导出了封闭形式的解析表达式。这些表达式决定了滑模动力学的性能，并保证了其稳定性。为了比较结果，还介绍了标准SMC法，并讨论了其优缺点。通过将设计过程应用到梁球系统和Cart-Pole系统的两个众所周知的案例中作为该类的代表性示例，来说明该设计过程。数值仿真结果验证了理论工作的增强控制性能和鲁棒性。

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