Identification of Feedback Control Systems by Subspace Methods

线性系统在闭环中的辨识问题在文献中引起了很大的兴趣，因为如果开环对象是不稳定的，或者反馈是系统的固有机制，则闭环实验是必要的。我们得到了以下结果。1.我们已经表明，确定性部分的闭环系统的识别是完全解耦的随机部分的联合输入-输出过程的初步正交分解成随机和确定性组件。此外，我们还推导出了一种通过将子空间辨识方法应用于联合过程的确定性分量来获得被控对象传递函数的方法。分析了两种闭环辨识方法：一种是基于最小二乘法的两阶段预测误差法，另一种是基于正交分解的子空间辨识法。应用Bootstrap方法估计所识别模型的标准误差。仿真结果表明，该方法可以得到标准差的精确估计.在一个外生输入是纯确定性的，另一个是纯不确定性的假设下，基于外生输入随机系统的实现结果，提出了一种闭环系统辨识的子空间方法.该方法可用于对象和控制器传递函数的辨识。数值结果表明，基于正交分解的算法比其他子空间辨识算法具有更好的辨识效果.将子空间辨识方法应用于化工过程的PID控制系统和精馏塔的控制，取得了较好的效果。部分结果已在熊本国际工业过程先进控制研讨会（2002）上发表。

Identification problems for linear systems operating in closed-loop have received much interest in the literature, since closed-loop experiments are necessary if the open-loop plant is unstable, or the feedback is an inherent mechanism of a system. We have obtained the following results.1. We have shown that the identification of deterministic part of a closed loop system is completely decoupled from that of stochastic part by a preliminary orthogonal decomposition of the joint input-output processes into stochastic and deterministic components. Also, we have derived a method for obtaining the plant transfer function by applying a subspace identification method to the deterministic component of the joint process.2. We have analyzed two closed loop identification methods : the one is the two-stage prediction error method based on the least-squares method, and the other is a subspace identification method based on the orthogonal decomposition. A bootstrap method is applied to estimate the standard error of identified models. Simulation results are included to show that accurate estimates of standard deviation are obtained.3. Under the assumption that one of the exogenous inputs is purely-deterministic and the other is purely non-deterministic, we have developed a subspace method for identifying a closed loop system based on the realization results for stochastic systems with exogenous inputs. The present method can be used for identification of transfer functions of plant and controller. Numerical results show that the orthogonal decomposition-based algorithm gives better results over other subspace identification algorithms.4. Subspace identification methods are applied to a PID control system and a distillation column in a chemical industry with considerable success. Some results are presented at International Symposium on Advance Control of Industrial Processes, at Kumamoto (2002).