Abstract
In this paper, we propose a simple framework for closed-loop system identification: the stabilized output error method. Traditional closed-loop system identification methods rely on the linearity of the target system, and they require the identification of noise models or prior knowledge or identifiability of the feedback controllers to obtain unbiased estimates. But in many real-world applications, the noise dynamics and feedback controllers are complex and difficult to identify, and the nonlinearity may not be ignored. The proposed framework introduces a virtual controller that stabilizes the error between model prediction and the output of the target system. This enables us to apply the output error method, which gives unbiased estimates without depending on the noise model and is applicable to a wide range of models, including nonlinear systems, to closed-loop system identification problems. The paper describes the framework and gives the theoretical support and design guidelines for virtual controllers. Through numerical examples, we show the effectiveness of the proposed framework in various situations, which include identification of (a) linear gray box models, (b) systems in the presence of disturbances having realistic complexity, and (c) a nonlinear unstable system in a human-in-the-loop environment.
Highlights
Model construction based on the data acquired in a closed-loop environment, which is called closed-loop system identification, is an important problem in many real-world applications
We show the effectiveness of the proposed framework when using a gray box model, when disturbances have realistic complexity, when using data obtained in a human-in-the-loop environment, and when the target system is a nonlinear unstable system
The results show that the stabilized output error methods produce better models than the direct methods, which cannot use the knowledge on the feedback controller
Summary
Model construction based on the data acquired in a closed-loop environment, which is called closed-loop system identification, is an important problem in many real-world applications. In the joint input-output method, a system driven by white noise that generates the joint input-output signal is first identified, and a model of the target system is derived [8] This is very important in practice, because it is often the case in industry that the controllers are not exactly known due to various delimiters, anti-windup functions and other nonlinearities It does not need the knowledge of reference signal at all, which may be useful for example in handling systems directly operated by human (i.e., human-in-the-loop system). We denote the n × m zero matrix by 0n×m and define 0n 0n×1
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