  Bode's sensitivity integral constraints define a fundamental rule about the
limitations of feedback and is referred to as the waterbed effect. We take a
fresh look at this problem and reveal an elegant and fundamental result that
has been seemingly masked by previous derivations. The main result is that the
sensitivity integral constraint is crucially related to the difference in speed
of the closed-loop system as compared to that of the open-loop system. This
makes much intuitive sense. Similar results are also derived for the
complementary sensitivity function. In that case the integral constraint is
related to the sum of the differences of the reciprocal of the transmission
zeros and the closed-loop poles of the system. Hence all performance
limitations are inherently related to the locations of the open-loop and
closed-loop poles, and the transmission zeros. A number of illustrative
examples are presented.

Systems and Control