参数不定的旋转圆盘在有界扰动下混沌振动的滑模变结构控制

摘要

为了消除具有不确定参数的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,假设作用在旋转圆盘上的集中力不确定且有界,并鉴于干扰的普遍存在性,对有界扰动下的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,这些特征加深了对其的认识,同时也证明该四维动力系统含有混沌吸引子.为了保证系统控制的鲁棒性,利用滑模变结构法,将旋转圆盘从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.结果证明,用滑膜变结构法能够使系统严格地跟踪参考轨道,且具有过渡时间短、过渡平稳,对干扰不敏感等诸多优点,同时也为相关混沌系统的混沌态的有效控制提供了借鉴.%In order to eliminate lateral oscillation of spinning disk with uncertain parameter and dispel their adverse effect on the system performance or the working conditions of the system, supposing that the point force acting on the spinning disk is uncertain and bounded, the chaotic complex dynamic characteristics of the four-dimensional nonlinear equations in lateral oscillations of spinning disk under bounded disturbance were analyzed in view of the ubiquity of disturbance, including the space trajectory, the Lyapunov exponent and the Poincare map.These characteristics enable us to know them deeply, and indicate that the four-dimensional dynamical system contains chaotic attractor.To ensure the robustness of the system control, the author stabilized the chaotic orbits to 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 make the system track target orbit strictly and smoothly with short transition time, and its insensitivity to noise disturbance is shown.It provides reference for relevant chaos control in mechanical system.