Modeling and tracking control design for a class of rotary pendulum systems with disturbance

DOI编号  10.7641/CTA.2020.90621
2020,37(10):2209-2217

 作者 单位 E-mail 李健 烟台大学 数学与信息科学学院 ytulijian@ytu.edu.cn 李俊艳 烟台大学 数学与信息科学学院 吴昭景 烟台大学 数学与信息科学学院

本文考虑一类受扰旋转单摆系统的建模与跟踪控制问题. 首先, 利用动静法和相对运动原理建立受扰情形下空间旋转摆系统的动力学模型. 然后, 分别以实际跟踪和渐近跟踪为控制目标, 给出相应的控制设计方法. 具体地,利用向量式的反推控制设计方法与不确定性动态补偿机制, 给出自适应实际跟踪控制器, 保证闭环系统所有状态都有界且在有限时间内系统输出到达并保持在参考信号给定的邻域内. 利用反推设计方法, 并结合扰动的学习、切换补偿机制设计自适应切换渐近跟踪控制器, 通过在线调节控制器参数, 保证闭环系统所有状态都有界且系统输出渐近跟踪到给定的参考信号. 最后, 仿真实验验证所提理论结果的有效性. 值得指出的是, 与相关文献相比, 本文所给出的控制设计方法允许系统同时含有未知参数和扰动, 并且扰动不必有已知上界, 因而具有更强的抑制不确定性的能力.

In this paper, the problem of modeling and tracking control is investigated for a class of disturbed rotary pendulum systems. Firstly, the dynamic model of rotary pendulum system under perturbation is obtained by using dynamicstatic method and relative motion principle. Then, procedures of control designing are given for practical tracking and asymptotic tracking, respectively. Specifically, a practical tracking controller is designed by using the backstepping method in the form of vector combining with adaptive dynamic technique, which guarantees that the system output goes and stay at a prior neighborhood of reference signal after some time instant while all the closed-loop system signals are bounded. Moreover, an asymptotic tracking controller is designed by using backstepping method combining with the learning and switching mechanisms, which ensures that the system output asymptotically tracks the given reference signal while all the states of the closed-loop system are bounded. Finally, a simulation example is provided to verify the effectiveness of the proposed theoretical results. It is worthwhile pointing out that, the proposed control scheme allows the presence of both unknown parameters and disturbance, and moreover the disturbance does not necessarily have known bound, and hence possesses stronger ability in overcoming the uncertainties when comparing with those of the related literature.