Identification of Feedback Control Systems by Subspace Methods

对于运行在闭环系统中的线性系统的辨识问题在文献中引起了很大的兴趣，因为如果开环对象不稳定，或者反馈是系统的内在机制，则需要进行闭环系统的实验。我们取得了以下成果：1.通过将联合输入输出过程初步正交分解为随机分量和确定性分量，证明了闭环系统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将子空间辨识方法应用于联合过程的确定性部分来获得对象传递函数的方法。分析了两种闭环系统辨识方法：一种是基于最小二乘法的两阶段预测误差辨识方法，另一种是基于正交分解的子空间辨识方法。采用Bootstrap方法估计辨识模型的标准误差。仿真结果表明，该方法可以得到较准确的标准差估计。在假设一个外生输入是纯确定的，另一个是纯确定的假设下，基于具有外生输入的随机系统的实现结果，我们发展了一种辨识闭环系统的子空间方法。该方法可用于辨识被控对象和控制器的传递函数。数值结果表明，与其他子空间辨识算法相比，基于正交分解的算法具有更好的识别效果。子空间辨识方法应用于某化工企业的PID控制系统和精馏塔中，取得了较好的效果。在熊本举行的工业过程先进控制国际研讨会(2002)上介绍了一些结果。

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).