【作者】 窦立谦；

【导师】 宗群；

【作者基本信息】 天津大学 ， 控制理论与控制工程， 2008， 博士

【摘要】 随着控制理论的发展,许多先进控制方法,如鲁棒控制、自适应控制、模型预测控制等,在实际中得到广泛应用,这些方法往往依赖于被控对象的精确数学模型。系统辨识是系统建模的重要方法,传统的辨识方法重在寻求一个确定的模型来逼近真实模型。然而,传统辨识与控制器设计往往分别依赖各自独立的性能指标进行优化求解,两者表面统一,本质分离。基于辨识模型设计的控制器不一定能够确保对真实对象的高质量控制效果。而面向控制的辨识以控制器设计作为系统辨识的目的,以控制性能的优劣作为评价辨识模型优劣的标准,能够较好地解决辨识与控制的结合问题,达到快速、准确、安全的控制目的。为此,本文研究一种面向控制的迭代辨识与控制设计方法,实现辨识与控制的一体化,达到快速、准确的模型辨识与控制器设计的目的。主要研究内容和创新是:(1)针对闭环条件下激励信号的选择问题,研究激励信号的优化设计方法。首先将激励信号的选择问题转变为一个求解最优激励信号功率谱的优化问题。综合考虑输入和输出的联合逼近,将辨识模型的鲁棒稳定性作为优化求解的约束条件,保证了辨识模型的稳定性。并且将信号能量的约束转化为线性矩阵不等式约束,确保可解性。在此基础上,建立了整个激励信号的最优化模型。最后针对优化求解中,最优激励信号的解依赖真实未知对象模型这个难点问题,进一步提出了自适应迭代的方法,分析了迭代方法的收敛性。仿真实例显示使用该方法得到的激励信号激励闭环系统,从而得到辨识数据,进行模型辨识,能够有效提高辨识模型的准确性。(2)针对面向控制的辨识与控制设计的联合设计问题,研究了迭代辨识与控制器设计方法。首先,使用预测误差(Prediction Error)不确定模型结构描述不确定被控对象,通过系统辨识建立相应的PE不确定模型。引入Vinnicombe距离描述模型不确定集合的大小,根据最坏情况下的稳定裕度的概念,提出了不确定模型闭环稳定的条件,这样将确保每次迭代设计的控制器均能镇定真实对象。然后,为了保证迭代过程性能的不断提高,提出了确保迭代过程闭环性能改善的条件,这将保证每次迭代设计的控制器使真实对象闭环系统性能得到不断提高;在此基础上,提出了满足闭环系统稳定性和性能改善的迭代控制器设计方法,以及整体设计的算法步骤。该方法改善了传统迭代辨识与控制设计在系统稳定性和收敛性的缺陷,使得每次迭代过程保证了系统的稳定性,同时也保证了闭环性能的收敛性。使用simulink搭建了方法验证的平台仿真结果显示了该方法的有效性。(3)针对辨识出的模型是否准确的问题,研究面向控制的模型检验方法。将面向控制的模型检验问题分为两个过程,一是模型的结构检验,一是闭环条件下模型准确性检验。首先,针对含有未建模动态不确定的系统,提出了基于残差互相关性测试的模型检验方法,将模型结构的检验问题转换为一个假设检验问题,设计了新的残差估计方法,提出了残差信号和输入信号互相关函数的估计方法,通过它们相关性,实现模型结构的检验。其次,提出了基于模型误差建模的闭环模型检验方法,并且针对控制器存在非最小相位零点的情况进行分析,提出了合理的模型检验方法和实现步骤,并且以概率的形式给出模型检验的结果;最后通过仿真实例说明方法的有效性。更多还原

【Abstract】 With the development of control theory, many of advanced control methods, such as robust control, adaptive control, model prediction control etc., are widely applied in practice. These methods usually depend on the accurate plant models which are mostly obtained via system identification methods. The classical identification methods always seek for a deterministic model to approximate the real plant model. However, the classical identification and controller design, which both depend on their own independent optimal criterion respectively, are consistent superficially but separate essentially, and the obtained controller on the basis of the identified model will not always ensure the stability and the desired control performance. The control-oriented identification is a modeling process with the aim to get the desirable controller, and the quality of identified model is evaluated by control performance. Therefore, this thesis will focus on the control-oriented iterative identification and control design method with the purpose of integrating identification with control design to achieve fast and accurate model identification and controller design.This thesis contains the following main sections:First of all, excitation signal optimal design for closed-loop system identification is investigated for selecting optimal excitation signal. The problem of excitation signal selection is transferred into an optimization problem to find the optimal signal spectrum. Its objective function is defined as the joint approximation of input and output. The constraints of this optimal problem include two parts: the one is the robust stability of closed-loop identification, which will ensure that the initial control can stabilize the identified model, and the other is the power restrictions of excitation signal, control signal and output signal, and these power restrictions are transfered into LMI that can be solved by optimization methods. On the basis of these, optimal excitation signal design problem is formulated. Finally, the adaptive iterative method is proposed and its convergence is analyzed to deal with the complicated problem that the excitation signal typically depends on unknown system model in optimal excitation design. Simulation result shows that identified model will be improved by using the excitation signal optimal methodSecond, the iterative identification and control design method is investigated to combine the identification with control design. The uncertainty model of the real plant is expressed by prediction error (PE) uncertainty model structure which is obtained by system identification, and the uncertainty model set is described by the Vinncombe distance. According to these, the closed-loop stability condition of the uncertainty system in the worst case obtained by the frequency dependent stability margin is proposed to ensure the closed-loop system stability during the iterative procedure. And, the condition of closed-loop system performance improvement in iterative procedure is proposed to guarantee a better close-loop system performance. According to the above two conditions, the iterative controller design method and the whole procedure for iterative identification and control design are developed. This method will improve the stability and convergence of classical iterative methods, and ensure the stability of closed-loop system and control performance in iterative procedure. Finally, a Matlab/Simulink platform is established to verify the proposed method. Simulation results show the good performance of the proposed method.Finally, model validation methods are investiaged to test the quality of identified model. The whole model validation procedure is divided into two different parts. The first part is the model structure validation. For that, a model validation method based on residuals cross-correlation test is presented to validate identified model with unmodelled dynamics. In open-loop condition, the model validation is firstly transferred into a hypothesis validation problem, and a new residual estimation method is proposed. Through analyzing the cross-correlation function of residual signal and input signal, model validation is implemented. The second part is a closed-loop model validation based on the model error modeling. In the case of the controller with non-minimum phase zeros, reasonable model validation method is analyzed, validation procedure is presented, and model validation result with probability is given. Simulation result shows the proposed method is effective.更多还原