Abstract

In this survey, the stability of input-constrained control for a widely used class of second-order systems is investigated. A continuous prediction-based approach is utilized to calculate the limited current control input by minimizing the next tracking error of nonlinear second-order system. The Karush–Kuhn–Tucker theorem is used to analytically solve the resulting constrained optimization problem. The constrained stability is analyzed by equating the constrained solution with the solution obtained from an optimal controller with time-varying weight on the control input. The proposed constrained controller adapts itself to real conditions by using information about the perturbations obtained from an extended state observer (ESO). Simulation studies for a lever arm indicates that the constrained controller presented in the closed form is much faster than the common nonlinear model predictive control method which requires an online dynamic optimization at each sampling time. Accordingly, experimental implementation of the proposed controller is conducted on a fabricated platform consisting of a lever arm. The results show that the proposed constrained controller can successfully track different time-varying positions for the arm by admissible torques generated by a DC motor. The comparative results with an adaptive backstepping controller indicate higher performance for the proposed ESO-based controller in compensating for the perturbations and external disturbance.

中文翻译：

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基于观测器的新型非线性二阶系统稳定性分析输入约束控制：杠杆臂实验

摘要

在本次调查中，研究了广泛使用的二阶系统的输入约束控制的稳定性。采用基于连续预测的方法通过最小化非线性二阶系统的下一个跟踪误差来计算有限电流控制输入。卡鲁什-库恩-塔克定理用于分析解决由此产生的约束优化问题。通过将约束解与从控制输入上具有时变权重的最优控制器获得的解相等来分析约束稳定性。所提出的约束控制器通过使用从扩展状态观察器（ESO）获得的扰动信息来适应实际条件。杠杆臂的仿真研究表明，以封闭形式呈现的约束控制器比需要在每个采样时间进行在线动态优化的常见非线性模型预测控制方法要快得多。因此，所提出的控制器的实验实现是在由杠杆臂组成的制造平台上进行的。结果表明，所提出的约束控制器可以通过直流电机产生的允许扭矩成功地跟踪手臂的不同时变位置。与自适应反步控制器的比较结果表明，所提出的基于 ESO 的控制器在补偿扰动和外部干扰方面具有更高的性能。