Effect of Varying Controller Parameters in Closed-Loop Subspace Identification

It is well known that subspace identification methods that assume open loop data without correlations between the input and noise, may give biased estimates when applied to closed loop data. The effect of the controller gain parameters on the quality of the identified model is studied when closed loop data are used. Several subspace identification methods (both open loop and closed loop methods), and different simulated data sets ranging from ideal 2 x 2 linear systems, to a fairly realistic nonlinear debutanizer process simulator, are considered. The results show that up to a point, higher controller gain during the identification experiment gives more accurate models than with lower controller gain, for both open and closed loop subspace identification methods. It is observed that the sensitivity to the controller gain is very small for the closed loop sub-space method tested for the ideal cases when its assumptions are satisfied. An explaination for this is that in this case there will be no bias, while the open loop methods may have a bias that depends on the controller parameters. Another interesting observation is that for the debutanizer example, the nonlinearities seem to lead to biased estimates also with the closed loop subspace method, and the choice of controller gain appears to be just as important as the use of a closed loop subspace identification method for the accuracy of the estimates.