【作者】 吴爱国；

【导师】 段广仁；

【作者基本信息】 哈尔滨工业大学 ， 控制科学与工程， 2008， 博士

【摘要】 在描述交链大系统,机械多体系统,电力系统等时,广义系统模型是一个更方便更自然的方法。作为一种方法,广义系统模型已经在获得一些复杂系统的鲁棒稳定性和鲁棒性能分析中得到广泛应用。因此,广义系统的研究无论从理论还是应用上都是非常重要的。广义系统与正常系统的一个最大区别就是系统响应可能含有脉冲,这可能给实际系统造成很大的破坏甚至摧毁系统。因此对脉冲消除的研究是非常必要的。另外,对实际系统来说,并不是所有的系统状态都能量测得到,这样就限制了状态反馈控制律的使用。为了克服这个障碍,一个可能的方法就是先通过观测器估计系统的状态然后再根据估计的状态设计控制律。为了保证观测器估计的准确性也要求观测器系统不含脉冲模。由于这些原因,本论文系统深刻地讨论广义线性系统的脉冲消除和观测器设计问题,其主要结果如下:一、对方广义系统考虑了通过最一般的控制器—动态输出反馈控制器的正则化。根据原始的系统矩阵建立了三类可正则化条件。而且进一步显示,对于可正则系统,所有正则化控制器的集合形成一个Zariski开集。二、考虑了通过状态反馈和PD状态反馈的脉冲消除问题。基于导数反馈标准型给出了使闭环系统无脉冲的状态反馈的参数化表示。为了考虑PD反馈脉冲消除问题,对方广义系统和非方广义系统分别提出了可I-能控性和可脉冲模能控性的概念。结论显示,可I-能控性和可脉冲模能控性分别是方广义系统和非方广义系统的PD反馈消除脉冲的充要条件。根据原始系统矩阵建立了两类可I-能控性和可脉冲模能控性判据,而且给出了闭环系统可达到的动态阶的范围。建立了I-能控化控制器和脉冲模能控化控制器的参数表示式。由于上面的工作,基于PD状态反馈的脉冲消除问题可以通过两步完成。第一步设计I-能控化或脉冲模能控化控制器,第二步根据状态反馈消脉冲的方法求解比例增益。另外,对PD状态反馈脉冲消除还建立了能同时提供比例增益和导数增益的设计方法。以上所有的设计方法都是采用奇异值分解,因此提出的方法有较好的数值稳定性。三、对正则广义系统提出了两大类观测器—比例积分观测器和比例积分导数观测器。基于一类Sylvester矩阵方程的显式参数化解给出这些观测器的参数化设计方法。提出的方法通过自由参数给出了所有观测器的增益矩阵的参数表达式。提出的方法能保证观测器系统是正则无脉冲的,且能提供所有的设计自由度。这些自由度能进一步参与优化满足系统额外限制并获得更好的系统性能。相比于文献中出现的PI观测器,本论文提出的广义PI观测器由于额外引入的观测器增益矩阵能提供更多的设计自由度,从而使系统获得更好的性能。四、考虑了基于观测器的鲁棒控制问题。鲁棒性能由环路传递复现(LTR)性能表征。所涉及的观测器有Luenberger观测器,全维状态反测器,PI观测器,高阶比例积分观测器。基于复现误差的概念通过复现矩阵给出了精确LTR功能的充分必要条件。五、考虑了柔性连接机器人系统基于PI观测器的状态反馈控制器的设计。结合提出的广义PI观测器的参数化方法和LTR条件根据设计自由参数建立控制器的LTR功能的性能指标。通过采用遗传优化算法给出了具有LTR功能的控制器的增益。通过与基于常规PI观测器的结果比较显示,广义PI观测器确实能够通过额外的自由度获得更好的LTR性能。更多还原

【Abstract】 Descriptor-system models are more convenient and natural than normal systemsin the description of interconnected large-scale systems, mechanical multi-body mo-tion systems, or electrical networks. In addition, as an approach the model of descrip-tor linear systems has been utilized to develop robust stability condition and robustperformance index for some complex systems, such as time delay systems and neu-tral systems. Therefore, study on descriptor linear systems is both theoretically andpractically important.A big difference between a descriptor linear system and a conventional linearsystem is that the response of a descriptor linear system may contain impulsive terms.Such infinite jumps are obviously destructive as they could completely destroy the sys-tem instantaneously. In addition, in practice the state of a system is usually not directlyavailable, so the state feedback control usually can not be realized directly. A feasiblemethod is to firstly asymptotically estimate the state vector by using an observer, andthen use the estimation of the state to construct the state feedback control. In orderto guarantee the accuracy of estimation, it is required that the designed observer sys-tem should be impulse free. Due to the above reasons, this dissertation systematicallyand deeply investigates the problem of impulse elimination and observer design. Thedetailed results are as follows.1 Regularization via dynamic output feedback is investigated for square descriptorlinear systems. Necessary and sufficient conditions of regularizability via dy-namic output feedback are established. In addition, it is shown that the set of allregularizing gain matrix groups is a Zariski open set for regularizable systems.2 The problems of impulse elimination via state feedback and proportional-derivative (PD) state feedback are dealt with. Based on a canonical equivalentform for descriptor linear systems, a general parametrization of all state feedbackgains which make the resulted closed-loop system impulse-free is presented. Inorder to deal with impulse elimination via PD state feedback, the concepts ofI-controllablizability and impulsive-mode controllablizability are introduced forsquare and nonsquare systems, respectively. Two class of criteria are given for the I-controllablizability and impulsive-mode controllablizability in terms of initialsystem matrices. General parametrization of all I-controllablizing and impulsive-mode controllablizing controllers are presented. With the above preparation, thesolution to impulse elimination via PD state feedback can be completed by atwo-step method.3 Several types of observers are proposed for regular descriptor linear systems, andparametric design approach for these observers are established. The proposedobservers include generalized proportional-integral (PI) observers, proportional-multiple-integral (PMI) observers, generalized proportional-integral-derivative(PID) observers, proportional-multiple-integral-derivative (PMID)observers, andso on. The proposed approaches give parameterizations of all observer gain ma-trices in terms of some free parameters which represent the degrees of designfreedom, and can be further utilized to achieve additional specifications and per-formances. The proposed approach, which guarantees the regularity of the ob-server system, realizes the elimination of impulsive behaviors of the observersystem.4 The problem of observer based robust control is investigated. The robustnessis characterized by the property of loop transfer recovery (LTR). The involvedobservers include Luenberger observers, full-order state observers, PI observersand PMI observers. Using the concept of recovery error, simple necessary andsufficient conditions for the controller are derived for exact LTR in terms of theso-called recovery matrices.5 Generalized PI observer based state feedback controller is designed with thefunction of LTR for ?exible joint robots. By combining the proposed parametricexpression of observer gains and the recovery condition, an index is proposed tocharacterize the function of LTR. By adopting genetic optimization algorithm,controllers with LTR are provided. Compared with the results in the case ofPI observers, it is also shown that the extra freedom degrees of generalized PIobservers can provide better LTR performance.更多还原