On overshoot and integrators

An extension of previous results concerning the effect of integrators on the closed-loop response overshoot is presented. It is shown that if the open-loop transfer function contains more integrators (i.e. [1/s]) than the Laplace transform of the reference signal, then the resulting output response must exhibit overshoot, assuming that a one degree-of-freedom control configuration is used. Several corollaries are also derived. The obtained results are applicable to minimum and non-minimum phase linear systems, and also strictly proper and non-strictly proper linear systems. A non-overshooting output tracking controller is then proposed for linear chain of integrators, whose structure and performance are analysed.