PERFORMANCE SENSITIVITY OF SAMPLING SYSTEMS - A UNIFIED APPROACH

The performance sensitivity of sampled-data systems is studied via discrete-time optimum control theory. A unified approach to sensitivity studies is presented. Internal disturbances (e.g. parameter variations) and external disturbances (e.g. wind gusts) can be treated within the same formulation by studying the performance sensitivity when the system is subject to bounded disturbances. A measure of the performance sensitivity is obtained by determining the worst effect of the bounded disturbance sequence on a chosen performance measure. Such a sensitivity study, when it is posed as an optimum control problem, amounts to solving a two-point-boundary-value problem. A computational technique for the solution is proposed. A sampled-data system which is most insensitive to the effects of the worst disturbances is designed by determining the parameters of the system that minimize the worst effect on the performance sensitivity. An algorithm is developed for such a design procedure. The presentation is illustrated by examples. © 1969.