Parameter Estimation with Closed-Loop Operating data

Data often mllst be collected under regulatory feedback control. After the form of the stochastic-dynamic model has been tentatively identified, estimates of system parameters are required from the data. It is important to separate the following distinct problems: (A) estimation of the dynamic and stochastic parameters of the system (B) estimation of only those functions of these parameters which occur in the control equation. This paper considers and illustrates for each problem the efects of (i) optimality and suboptimality of control, (ii) addition of a known dither signal, (iii) dead time in the system. Necessary and suflicient conditions for estimability using data collected under conditions of optimal control are given.