Topics in Control. 4. The Analysis of Closed-Loop Dynamic-Stochastic Systems.
WISCONSIN UNIV MADISON DEPT OF STATISTICS
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Some of the problems involved in the identification, estimation, and diagnostic checking of univariate closed-loop systems are discussed. The procedure used in open-loop operation for identifying the process transfer function by cross-correlating the input and output sequences is shown to be invalid in closed-loop situations because the input and disturbance sequences are correlated. Under pure feedback where the input is calculated completely from the output this cross-correlation procedure is shown to identify not the process transfer function but rather the inverse of the controller transfer function. However, if the controller is known and if one adds an independent noise sequence to the input, then the process transfer function can be identified by cross-correlating this added noise with the output. Once given a particular model its parameters can be estimated from closed-loop data. Author Modified Abstract
- Statistics and Probability