Q. Effect of feedback on sensitivity to parameter changes?

A good control system, in general, should be rather insensitive to parameter variations, while it is still able to follow the command quite responsively. It is apparent from Figure that in an open-loop system the gain of the system will respond in a one-to-one fashion to the variation in G. Let us now investigate what effect feedback has on the sensitivity to parameter variations.

The sensitivity S of a closed-loop system with Equation to a parameter change p in the direct transmission function G is defined as

where Gp denotes that the derivative is to be taken with respect to the parameter p of the function G. From Equation it follows that

Equation shows that the sensitivity function can be made arbitrarily small by increasing HGp, provided that the system remains stable.