Closed loop Identification of Quadruple Tank System using an Improved Indirect Approach

The well known, indirect method of closed loop identification is difficult to apply for multivariable systems owing to its two step procedure of first identifying the loop sensitivities which are then used in the second step to estimate the plant dynamics. In this paper, we propose an improved indirect method of closed loop identification that exploits (i) simple proportional output feedback control law and (ii) inherent dynamic relationships that results from the implementation of this control law to estimate the plant dynamics in a single step. In the proposed methodology, we used state-space parameterization of the open loop dynamics for both the plant and the loop sensitivities so as to accomodate multivariable systems. The use of the simple proportional output feedback control law in the proposed methodology obviates the need for inverse filtering using the loop sensitivities which could be a problem for large multivariable systems. Since, the proposed methodology involves a single open loop identification between the dither and the output, other problems of noise-output correlation are also not seen. The proposed methodology is demonstrated by a simulation study on a benchmark Quadruple Tank system proposed by Johansson (2000). The simulation results presented in this paper shows the effectiveness of the proposed method for system identification.