滑模变结构法实现旋转圆盘混沌振动的控制

摘要

为了消除旋转圆盘横向混沌振动,克服其对整个系统及工作状况的不利影响,对旋转圆盘横向振动的四维非线性方程进行了复杂动力学特征分析,包括相轨迹图、Lyapunov指数和庞加莱映射图.利用比例积分滑模变结构法,将旋转圆盘从其横向混沌振动的混沌轨道先后控制到任意固定点和周期轨道,并用MATLAB模拟验证其有效性.重点讨论了滑模变结构方法的增益系数对抖振问题、受控系统的过渡过程的时间、峰值和控制器的过渡时间、峰值和稳定后的状态及其上下界的影响.结果为比例积分滑模变结构法的应用和相关机械系统混沌态的有效控制提供了理论依据.%In order to eliminate lateral oscillations of spinning disks and dispel their adverse effect on the system performance or the working conditions of the system, the chaotic complex dynamic characteristics of the four-dimensional nonlinear equations of lateral oscillations of spinning disks were analysed, including the space trajectory, the Lyapunov exponent and the Poincare map. These characteristics indicate that the four-dimensional dynamical system contains chaotic attractor. For overcoming the shortcomings that the system can never be controlled to reach target orbit precisely in feedback control theory, the chaotic orbits of the spinning disks were stabilized to approach arbitrary chosen fixed points and periodic orbits by means of sliding mode method, and MATLAB simulations were presented to confirm the validity of the controller. The results show that using sliding mode method can control the chaotic orbits of the rotating disks to any fixed points and periodic orbits strictly. The control process can make the system track target orbit smoothly in short transition time, and provides reference to relevant chaos control in mechanical system.