Closed-Loop Identification of Multivariable Systems, Using B-Spline Series Expansions for Step Responses

Closed-loop identification is vital in improving underperforming controllers. This paper presents a novel closed-loop identification method for multivariable systems from step responses. The full transfer function matrix of an interactive n x n multivariable process is identified through a sequential step change in the setpoint. The proposed method first approximates the closed-loop step responses, using B-spline series expansions. Based on these expansions, a matrix formulation that represents the closed-loop tests is used to obtain the analytical expressions of open-loop transfer functions. Finally, the reduced low-order models are identified based on the frequency response data by a linear least-squares technique. The proposed identification method is simple and applicable to general multivariable control systems, such as decentralized or centralized control. This method is robust to measurement noise due to the filtering property of the B-splines. Simulation examples have demonstrated the effectiveness of the proposed method for a wide range of multivariable systems.