Closed-loop Identification for Cascade Regulatory Control Systems by Prediction Error Method

The prediction error method (PEM) is a system identification method for discrete-time, linear systems with stochastic disturbances generated by white noise. The PEM provides a direct method for closed-loop identification even when the reference signal is zero. In addition, the existing studies have clarified necessary and sufficient conditions of positive definiteness of information matrix that characterize the uniqueness of the identified parameters by way of the PEM. The present study extends the existing studies on the closed-loop identification to the case of cascade control systems. The main result of the study is to clarify the sufficient condition of positive definiteness of information matrices for both an inner and an outer loop in the case of the cascade regulatory control. The paper shows a numerical example that supports theoretical results on the information matrices.