Least-squares identification of fixed multivariable processes operating in closed-loop

Although identification techniques have been developed to determine models of open-loop systems there are many instances where parameter estimation has to be undertaken without disturbing or breaking feedback paths in systems operating in closed-loop. For the purposes of identifying dynamic multivariable models of these systems it is convenient to define them as being fixed processes for one or more of three reasons. Firstly, the inputs may not be manipulable, secondly, frequently, both the forward and the feedback paths are inaccessible to the investigator and thirdly, no a priori information other than the input-output sequences is available. Before parameter estimation can proceed it is essential that the question of whether there are feedback loops present in the system be answered. In the paper correlation analysis and least-squares regression have been selected and combined in an algorithm aimed at detecting feedback loops. For the purpose of modelling fixed multivariable processes this algorithm is attractive due to its simplicity and efficiency