Identification of linear stochastic systems from closed-loop data with known feedback dynamics

Abstract

A method is presented for identifying a linear statespace model of an open-loop stochastic system from closed-loop excitation and output data with a known feedback controller. For unstable systems, feedback control is required for identification to ensure overall system stability. For stable systems, feedback control may also be used to enhance the damping and thus shorten the input/output data required for identification. If a known dynamic output feedback controller is used, the closed-loop system and Kalman filter Markov parameters (i.e. pulse response samples) are first obtained from closed-loop input/output data Then the open-loop system and Kalman filter Markov parameters can be calculated through a recursive formulation derived by using z-transform. If a known constant-gain full-state feedback controller is used, the identification procedure is simpler. The closed-loop system matrices are identified and then used to compute the open-loop system matrices after removing the control gain. An experimental example is provided to demonstrate the proposed closed-loop system identification method.