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Additional resources for Control Engineering Solutions: A Practical Approach
6. An improvement is obtained in both loops if an extended model is identified. The result is clear for the Ts/qw loop (right). 13) may be considered. 2 x W II P r d i d i o n m o r . RLS. 2000 4000 6000 x |o' XIXKI KKKKI Noinialisol prut, c m r tiwrclatum. 6 2 Prediction error. RELS. (I 2000 40110 ,10" 6000 Prediction error. RLS. X000 KKKKI V n n a i i s o i | x o l m m airrclalion. 5 Signal excitability For a dynamic model to be correctly estimated, input signals to the process must be sufficiently exciting [2,12].
Afterwards, assuming that the controller is known, the process model is calculated by deconvolution; (2) Direct process identification — the process model is directly identified. The controller need not be known. Within direct process identification, two main alternatives can also be considered if the process input and output are measured for identification: (1) no external disturbance is applied; (2) an external disturbance (measurable or not) is applied. In the first case a set of identifiability conditions must be met to ensure convergence.
17 will eventually have large fluctuations, leading to similar effects in the estimated parameters, which is known as 'blow-up'. Additionally, if the forgetting factor is too low, noise tracking by the estimated parameters will appear as a side-effect. g. 98 for exponential windows), although they may be temporarily lowered so as to improve process parameter tracking. 10 it can be seen how a value that is too low for the exponential window X causes very noisy estimated parameters, although in this particular case the variation associated with the process input is high enough to prevent the estimated parameters from blowing-up.