机械系统的随机建模、控制和应用

【作者】 崔明月；

【导师】 解学军；

【作者基本信息】 曲阜师范大学 ， 应用数学， 2014， 博士

【摘要】 众所周知,机械系统经常受到随机干扰,这些干扰会以某种不确定的方式影响系统的性能.随着随机稳定性的发展,随机力学及控制的研究已经成为一个活跃的领域.本文针对机械系统的随机建模,跟踪控制及其应用的若干重要问题,发展了一些基本分析工具,并基于这些工具,深入研究和解决了这些问题.主要成果包括:1.通过合理的引入随机噪声,我们构造一类随机拉格朗日控制系统和一类随机哈密顿控制系统来描述遭受随机干扰的机械系统的运动.2.对一类带有未知参数的随机拉格朗日控制系统,在一些合理的假设下,设计了一种自适应跟踪控制器使得跟踪误差的均方可通过调节设计参数收敛到一个零的任意小邻域.假设的合理性和控制策略的有效性可由一个在随机振动环境中的机械模型说明.3.对于一类速度不可测的随机拉格朗日控制系统,在一些合理的假设下,应用拉格朗日系统的结构性质,巧妙的构造了一个降阶的观测器来估计速度.基于这个观测器,设计了一个输出反馈跟踪控制器使得跟踪误差的均方通过调节参数可以收敛到一个零的任意小邻域内.控制器的有效性通过一个随机力学模型来说明.4.对一类带有未知扩散和漂移函数的随机哈密顿控制系统,设计了一个向量形式的自适应backstepping控制器使得闭环随机哈密顿系统有唯一解且是依概率全局有界,并且跟踪误差的收敛到零的任意小的邻域.作为一个应用,研究了随机环境中的弹簧摆的建模和控制.5.对一个二级刚性机械臂,构造了一个随机拉格朗日模型来描述其在随机振动环境中的运动.基于这个模型,针对所有状态可测的情形,设计了一个状态反馈控制器使得误差系统是4阶矩指数实用稳定.当速度不可测时,设计了一个输出反馈控制器使得闭环系统的位移尽可能的跟踪一个给定的参考信号.6.对于在随机振动环境中带有多个旋转结点的机械臂,通过分析环境对质点的影响和引入等价的随机噪声过程,建立了一个随机哈密顿动态模型来描述其运动.基于这个模型,设计一个控制器使得闭环系统的位移近似的跟踪一个给定的参考信号.7.对于状态依赖切换的随机非线性系统,当给定的活动区域集可以由它的内部来代替时,通过定义一列停时作为切换时间,构造了切换系统的局部解并通过Lyapunov方法提出了解的全局存在和稳定性的判定.对于活动区域集不能由它的内部来代替这种情形,切换系统不一定有解.对这一基本问题构造了准解并提出了有界性判定.更多还原

【Abstract】 It is well known that mechanical systems are often subjected to random disturbances,which significantly affects the performance in a uncertain manner. With the development ofstochastic stability, the research on stochastic mechanics and control has been an active field.In this paper, for several important problems on stochastic modeling, tracking control and theapplication of mechanical systems, some basic analysis tools are developed, and based on sometools, these problems are deeply investigated and solved. The main results include:1. By reasonably introducing random noise, a class of stochastic Lagrangian control sys-tems and a class of stochastic Hamiltonian control systems are constructed to describe the mo-tion of the mechanical systems subjected to random disturbance.2. For a class of stochastic Lagrangian control systems with unknown parameters, undersome milder assumptions, an adaptive tracking controller is designed such that the mean squareof the tracking error converges to an arbitrarily small neighborhood of zero by tuning design pa-rameters. The reasonability of assumptions and the efficiency of the controller are demonstratedby a mechanics model in random vibration environment.3. For a class of stochastic Lagrangian systems with the unmeasurable velocity, undersome milder assumptions, using the structural properties of Lagrangian systems, a reduced-order observer is skillfully constructed to estimate the velocity. Based on the observer, anoutput feedback tracking controller is designed such that the mean square of the tracking er-ror converges to an arbitrarily small neighborhood of zero by tuning design parameters. Theefficiency of the controller is demonstrated by a stochastic mechanical model.4. For a class of stochastic Hamiltonian control systems with unknown drift and diffusionfunctions, a vector form of adaptive backstepping controller is designed such that the closed-loop stochastic Hamiltonian system has a unique solution that is globally bounded in probabilityand the tracking error converges to an arbitrarily small neighborhood of zero. As application,the modeling and the control for spring pendulum in stochastic surroundings are researched.5. For a two-link planar rigid robot manipulator, a stochastic Lagrangian model is con-structed to describe the motion of the manipulator in random vibration environment. Based on the constructed model, for the case that all states are measurable, a state feedback controller isdesigned such that the error system is4-th moment exponentially practically stable. When thevelocity is unmeasurable, a output feedback controller is designed such that the configurationof the closed-loop system can track a given smooth reference signal as close as possible.6. For the manipulator with multi-revolute joints in random vibration environment, byanalyzing the effect of environment to the mass points and introducing an equivalent stochasticnoise process, a stochastic Hamiltonian dynamic model is constructed to describe the motionof the manipulator. Based on the constructed model, a state feedback controller is designedsuch that the configuration of the closed-loop system can approximatively track a given smoothreference signal.7. For stochastic nonlinear systems with state-dependent switching, when the given active-region set can be replaced by its interior, the local solution of the switched system is constructedby defining a series of stopping times as switching instants, and the criteria on global existenceand stability of solution are presented by Lyapunov approach. For the case where the active-region set can not be replaced by its interior, the switched systems do not necessarily havesolutions, thereby quasi-solution to the underlying problem is constructed and the boundednesscriterion is proposed.更多还原