The sensitivity problem in sampled-data feedback systems

This paper is devoted to a discussion of the effect of parameter variations on the system response in sampled-data feedback systems. It is shown that in any single degree of freedom feedback configuration, the system response and especially its overshoot are inherently very sensitive to parameter variation. By means of a suitable transformation, the properties of the sensitivity function can be studied in terms of the usual continuous system frequency concepts, e.g., bandwidth and loop transmission shaping on the Bode plane. There is a basic limitation on the loop transmission bandwidth that can be obtained in any sampled-data feedback configuration. This limitation makes it impossible to secure the unlimited sensitivity reduction which is theoretically available in minimum phase continuous systems. It is shown how one must achieve a compromise between the values of the sampling period, the system response, and the sensitivity function. The design procedure is illustrated in detail with a numerical design problem in which there is substantial parameter variation.