ONLINE, CLOSED-LOOP IDENTIFICATION OF MULTIVARIABLE SYSTEMS

A new method to determine the open-loop transfer functions in an interactive N x N linear multivariable system based on a simple experimental test, for example, a step change in the controller set point carried out during closed-loop proportional integral derivative (PID) control operation, is presented. Simulation results for 2 x 2, 3 x 3, and 4 x 4 systems over a frequency range adequate for control purposes show good agreement between the transfer functions obtained from the experimental test and the transfer functions used in the simulations, even for very strongly interactive cases. The method also proved to be very robust with regard to measurement noise and load disturbances that may enter the system during the closed-loop test. A nonparametric model obtained by this technique can then be used directly in a PID control alogrithm or an internal model control configuration or as the basis of a parametric model more useful for dynamic matrix control for example.