Identification of Feedback Control Systems by Subspace Methods

在闭环中运行的线性系统的识别问题在文献中引起了很大的兴趣，因为如果开环装置不稳定，或者反馈是系统的固有机制，则需要进行闭环实验。我们得到了以下结果：我们已经证明，通过将联合输入输出过程初步正交分解为随机和确定性分量，闭环系统的确定性部分的辨识与随机部分的辨识是完全解耦的。此外，我们还推导了一种通过对联合过程的确定性分量应用子空间识别方法来获得植物传递函数的方法。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方法。采用自举法估计已识别模型的标准误差。仿真结果表明，该方法得到了准确的标准差估计。在一个外生输入为纯确定性，另一个外生输入为纯非确定性的假设下，基于外生输入随机系统的实现结果，提出了一种识别闭环系统的子空间方法。该方法可用于被控对象和控制器传递函数的辨识。数值结果表明，基于正交分解的子空间识别算法优于其他子空间识别算法。将子空间辨识方法应用于PID控制系统和化工精馏塔中，取得了相当大的成功。一些结果在熊本（2002）的工业过程先进控制国际研讨会上提出。

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).