The effect of small time delays on large-scale systems

Abstract

In this research, model reduction techniques are used to design optimal control strategies with low sensitivity in order to model uncertainty. The source of uncertainty encountered is the time delay, and the reduced-order model of a system is obtained with the help of a method referred to as singular perturbation (SP). Performance sensitivity is reduced by adding a sensitivity measure to the performance index (PI), which represents the cost to be minimized. The sensitivity measure used in this paper is defined as a variable given by the partial derivative of the state with respect to the uncertain item evaluated at the nominal value. This results in an augmented model that includes the new sensitivity variable, which has the same size as the state vector of the original system. As a result, the order of the dynamic constraint of the optimization procedure will be as much as the original plant. Therefore, developing a reduced-order model and using it in the design procedure will alleviate the problem of large dimensions. The design is completed based on the reduced-order model. Then, such a design is used to obtain an approximate design for the full-order system. Numerical examples are presented to illustrate the effectiveness of the approximate design in reducing performance sensitivity in the full-order system.