Robustness of the independent modal-space control method
Robustness of the independent modal-space control method
复制标题
独立模态空间控制方法的鲁棒性
DOI：
10.2514/3.19797
复制
发表时间：
1983
影响因子：
2.6
通讯作者：
H. Baruh
中科院分区：
文献类型：
--
作者：
L. Meirovitch;H. Baruh
研究了参数不确定性对分布式参数系统控制系统性能的影响。因为一般情况下，实际分布式系统的运动方程中包含的参数是未知的，基于假设模型设计的控制力将不能有效地控制实际的分布式系统。本文通过稳定性定理表明，当独立模态空间控制（IMSC）方法与模态滤波器结合使用时，系统参数的任何误差都不会导致闭环系统的不稳定，因而控制系统具有很强的鲁棒性。提出了一种扰动分析来计算存在参数变化的大阶系统的闭环极点。 I. 简介 分布参数系统的运动通常由一组联立偏微分运动方程控制。 1 运动方程中包含的参数通常是空间变量的连续函数。对于柔性结构，这些参数代表质量、刚度和阻尼分布。为了控制分布式系统，必须构建分布式系统的数学模型。然后根据数学模型设计控制力。一种常见的建模方法是将分布式系统的偏微分方程转换为无限组常微分方程。1'3 然后，保留有限数量的模态（通常是最低的）进行控制。在设计控制系统时，假设与受控模式相关的本征解具有足够的精度，这反过来又假设系统参数是准确已知的。特征解中的错误会在控制的设计和实现中产生错误。那么，根据错误的系统参数设计的控制系统是否能够有效地控制实际系统呢？即控制系统是否鲁棒。答案显然取决于分布式系统估计状态的不准确程度。对于该误差不是很大的情况，人们直观地预计控制系统性能的偏差非常小。一般来说，在控制系统设计中应该考虑到参数的不确定性。对于运动方程中包含的参数（例如质量和刚度分布）在乘法常数内已知的情况，只有系统特征值发生变化，而特征函数保持相同的形状。4 基于将参数误差视为扰动的扰动分析的灵敏度研究表明，如果将独立模态空间控制 (IMSC) 方法与模态滤波器结合使用，则控制系统对参数误差相对不敏感。4 当然而，系统参数未知，估计的特征值和特征函数往往与实际值不同，因此参考文献的敏感性分析。 4 不适用。
The effect of parameter uncertainties on the control system performance of distributed-p arameter systems is examined. Because in general, the parameters contained in the equations of motion of the actual distributed system are, not known accurately, control forces designed on the basis of a postulated model will not control the actual distributed system effectively. In this paper it is shown by means of a stability theorem that, when the independent modal-space control (IMSC) method is used in conjunction with modal filters, any errors in the system parameters cannot lead to instability of the closed-loop system, so that the control system is very robust. A perturbation analysis is proposed for the computation of the closed-loop poles of large-order systems in the presence of parameter changes. I. Introduction T HE motion of a distributed-parameter system is governed generally by a set of simultaneous partial differential equations of motion. 1 The parameters contained in the equations of motion are, in general, continuous functions of the spatial variables. For flexible structures, these parameters represent mass, stiffness, and damping distributions. To control the distributed system, one must construct a mathematical model of the distributed system. The control forces then are designed on the basis of the mathematical model. A common approach to modeling is to convert the partial differential equations of the distributed system into an infinite set of ordinary differential equations.1'3 Then, a limited number of modes (generally the lowest) are retained for control. In designing the control system, one assumes that the eigensolution associated with the controlled modes is known with sufficient accuracy, which, in turn, assumes that the system parameters are known accurately. Errors in the eigensolution produce errors in the design and implementation of the controls. Hence, the question arises whether the control system designed on the basis of system parameters that are in error can control the actual system effectively; i.e., whether the control system is robust. The answer clearly depends on the degree of inaccuracy in the estimated state of the distributed system. For cases when this error is not very large, one intuitively expects very small deviations from the control system performance. In general, one should make some allowance in the control system design for parameter uncertainties. For cases when the parameters contained in the equations of motion, such as the mass and stiffness distributions, are known to within a multiplicative constant, only the system eigenvalues change and the eigenfunctions retain the same shape.4 A sensitivity study, based on a perturbation analysis treating the parameter errors as perturbations reveals that if the independent modal-space control (IMSC) method is used in conjunction with modal filters, the control system is relatively insensitive to parameter errors.4 When the spatial distributions of the system parameters are not known, however, both the estimated eigenvalues and eigenfunctions tend to differ from their actual values, so that the sensitivity analysis of Ref. 4 is not applicable.