A novel two-stage identification of unstable systems

Issues in identification of unstable plant operating in a closed loop configuration are analyzed. It is shown that the unstable poles of the plant can be identified from the zeros of the input sensitivity function (transfer function relating the reference input to the plant input). A two-stage MIMO subspace identification scheme is proposed to identify the plant and the input sensitivity function. In the first stage, the input sensitivity function is identified using the reference input as the input, and the plant output and the plant input as outputs. In the second stage, the plant is identified using the input as the estimated plant input, the output the estimated plant output, where the estimates are obtained from the first stage. The proposed scheme is evaluated on a both simulated as well as on a physical laboratory scale magnetic levitation system.