On the Use of Model Error Systems in the Control of Large Scale Linearized Systems

Abstract

One of the most critical deficiencies of modern control theory in application to physical problems is the reliance of the theory upon the fidelity of the mathematical model of the physical system.The approach to model synthesis advanced here is the simultaneous evolution of the control design and the construction of the model. Specifically, three linearized models of different fidelity are utilized. The first is a maximum dimension linear system, the “evaluation model.” The second is a truncated version of the first (required to avoid high controller implementation costs associated with the first). The third is obtained by augmenting a “model error system” to the second (to avoid the sensitivity of the second to model errors). The model error system is capable of generating a model error vector which approximately compensates for model errors in parameters and model order. The error system is characterized in such a way that the “measurement residual,” (the difference between the actual measurements and those predicted by the model) is approximated by a set of orthogonal functions over an interval, T. The model error-corrected signal is then used for control. The state of the error system is obtained by standard linear estimation techniques. Such model error estimators with orthogonal functions are labeled “orthogonal filters,” and lend to the closed loop system a certain quality of model error insensitivity. It is also shown that special cases of the “model error system” provide convenient interpretations of several popular control techniques, such as parameter sensitivity, singular perturbation, disturbance accommodation and Kalman filter approaches.