【作者】 王刚；

【导师】 吴志刚；

【作者基本信息】 大连理工大学 ， 一般力学与力学基础， 2006， 硕士

【摘要】 鲁棒性问题是控制系统中的一个具有普遍性的问题。所谓鲁棒性是指系统中存在不确定性因素时,系统仍能保持正常工作性能的一种属性。随着控制技术的发展,不确定性问题越来越引起国内外研究者的重视,尤其是被控对象中有限个参数的不确定性问题。而对于参数不确定系统的控制问题,Riccati方程的求解是实现鲁棒控制系统设计的重要途径之一,因此准确高效的求解Riccati矩阵方程,具有重要的理论意义和工程应用价值。 结构力学与最优控制的模拟理论为求解参数不确定性鲁棒控制问题提供了一条新的途径。源自于结构力学的精细积分法,用来求解Riccati方程不仅保证数值解的高精度,而且在积分步长大幅度变化时仍能保持计算结果的一致性。此外在求解方程的同时还可计算闭环系统的状态转移矩阵和可控性矩阵等系统设计和仿真中的参数。另外在Lyapunov函数法中应用区间分析技术,也为研究参数不确定性系统鲁棒镇定性问题提供了一种有效的方法。 从实际控制问题来看,不确定参数往往是有界的,因此区间参数不确定性定常系统鲁棒控制的关键是把有限个不确定性的参数作为区间参数来分析。使用区间分析的方法,通过Lyapunov区间函数及稳定性理论来分析系统的鲁棒镇定性,并讨论区间系统的能控性、能观性及其判定方法,用精细积分法准确的求出Riccati区间方程的解,并且得到系统响应的解区间,从而实现参数不确定性闭环区间控制系统的仿真算法。 本论文得到国家自然科学基金项目“大型不确定性动力系统的分散H_∞鲁棒控制”的(编号:10202004)资助。更多还原

【Abstract】 Robustness means the ability a system with uncertainties to maintain normal working performance and it is always taken as an important index to evaluate controller. With the development of control algorithms and techniques, uncertainty problems, especially the controls of system subjected to limited parameter uncertainties, have attracted more and more attention of scholars home and abroad. For robust design of systems subjected to parameter uncertainties, one of the most important approaches is to solve the matrix Riccati equations. Therefore, precise solution of matrix Riccati equations is necessary not only in control theories but also in actual engineering applications.Analogy theories between structural mechanics and optimal control provide a new approach to achieve robust control of systems subjected to parameter uncertainties. The precise integration method of the structure mechanics, which is used to solve matrix Riccati equations, can not only gives high accurate solution but also keep the consistency of the computed results even with a large integration step. Moreover, the parameters of state transfer matrix and controllability matrix of the closed-loop system are computed when solving the Riccati equation. In addition, Lyapunov function method with interval analysis adopted is also one effective way to study robust stability of parameter systems.Uncertain parameters always satisfy certain bounds in actual control systems. Therefore, the key of robust control of time-invariant systems subjected to parameter uncertainties is to deal with limited uncertain parameters as known intervals to study. Based on the Lyapunov interval function and the Lyapunov stability theory, a new method is proposed to analyze robust stability of interval systems. Besides, observability and controllability of linear interval systems are discussed through interval analysis approach as well as the performance criterions. Interval matrix Riccati equation is solved accurately through precise integration method with the interval solutions of system response attained at the same time. So simulation of the closed-loop systems with interval parameters can be executed.更多还原