【作者】 田伟；

【导师】 张彪；

【作者基本信息】 哈尔滨工业大学 ， 应用数学， 2010， 硕士

【摘要】 本论文提出了一种新的鲁棒函数观测器设计方法。函数观测器设计的目的是为了重构系统的状态组合,当系统存在不确定性时,其重构状态组合一般不再给出原来系统状态组合的渐近估计。因此,在观测器设计问题上考虑鲁棒性是十分必要的。鲁棒函数观测器设计是鲁棒控制系统设计中的一大类问题。本文通过建立适当的鲁棒函数观测器设计指标,将鲁棒函数观测器设计问题转化为目标函数的最优化问题。首先通过求解Sylvester矩阵方程,得到观测器系数矩阵T、L的参数形式。T、L均为自由参数的线性组合的形式,便于进行梯度计算。其次考虑系统矩阵的整体摄动,在不牺牲系统自由度的前提下,建立了鲁棒函数观测器设计的优化指标。由于指标中的矩阵范数采用Frobenius范数,所以易于建立指标的梯度公式。最后,利用共轭梯度法进行指标优化,得到观测器各系数矩阵的最优数值解。与已有方法相比,该方法的主要优点体现在:(1)利用梯度方法求解优化问题,收敛的速度很快;(2)将一个复杂的非线性观测器条件方程的求解问题转化为优化指标的优化问题,从而使算法得到简化。在论文的最后给出了上述鲁棒函数观测器设计方法的数值例子,并且在第一个例子中分别给出了系统存在结构扰动和不存在结构扰动情况下的数值模拟,通过计算结果可以看出文中提出的方法是有效的。更多还原

【Abstract】 In this dissertation, a new approach for design of robust functional observers is presented. The purpose of robust functional observer design is to reconstruct the state combination of the system. When there are uncertainties in the original system, the reconstructed state combination of the system generally can not give out asymptotic estimate of the state combination of the original system. Therefore, consideration of robustness in the issue of observer design is necessary. Robust functional observer design is a large class of problems in robust control system design. In this dissertation, an index for design of robust functional observers is proposed properly, and then the problem of design of robust functional observers is turned into an optimization problem of the proposed index. Firstly, by solving Sylvester matrix equation, the parametric expressions of observer gain matrices T and L are obtained. Since these expressions are in the form of linear combination of design parameters, the calculations of gradients of T and L are much easy. Secondly, under the overall perturbations of the system matrices the optimization index of robust observer design is established. The index does not sacrifice any design freedom in the observer. Since the Frobenius norm is used in the proposed index, gradient formula of the index can be obtained easily. Finally, the optimization problem is solved by using Conjugate Gradient Method, and then the numerical solution for all observer gain matrices is obtained.Compared with the other approaches, the main advantage of this approach is as follows: (1) The optimization problem is solved by applying gradient method. This leads to rapid convergence of the algorithm of this optimization problem. (2) The problem for finding the general solution of the complex, nonlinear observer condition matrix equation is turned into an optimization problem for an optimization index. By this way, the algorithm for robust observer design is made much easy.Two numerical examples are given to demonstrate the effect of the proposed approach. Especially in the first example, numerical simulations are given to support our results.更多还原