A fractional representation approach to closed loop system identification and experiment design

A simplifying assumption, frequently made in the analysis of system identification, is that the system to be identified is operating in open-loop. This assumption generally implies that the system input and noise are uncorrelated and that the system input is available for experiment design. Frequently, practical constraints require that the system be operated under closed-loop control, while many existing open-loop results can not be applied directly to the closed-loop problem, or give unsatisfactory results. For example, open-loop experiment design produces specifications on the optimal plant input, a variable which can not be directly chosen in a closed-loop experiment.;The (R,S) parameterization is used to develop a control oriented experiment design method having the property that when the estimated system is used to design a new compensator, the new compensator will perform well with the true system as well as with the estimate. A unique feature of this design method is that it results in specifications on the closed-loop inputs and on the compensator used during the identification; these are variables which can by chosen be the designer. This is in contrast to previously published methods which result in specifications on the plant input, a variable which the experimenter can not choose directly. Computer simulation results are also be presented which illustrate the effectiveness of the new method.;In this thesis, the fractional representation of the loop dynamics is used to show that one can always reparameterize the unknown system in terms of a known closed-loop part and an unknown open-loop part called the (R,S) system. This reparameterization essentially transforms the original closed-loop identification problem into an associated open-loop problem, allowing existing open-loop results to be applied directly to closed-loop problems for the first time. In addition, the input to the (R,S) system is dependent only on the closed-loop inputs and the compensator used during the identification experiment, greatly simplifying the problem of closed-loop experiment design.