A technique for choosing zero locations for minimal overshoot

An approach is presented to the specification of optimal overshoot controllers when the controller order is fixed and the closed-loop system poles are at a fixed location. The essential effect of the technique is to pick the best possible locations of the free zeros of the system in terms of minimizing the overshoot. The solution is obtained by solving an affine minimax optimization problem. An example illustrates how this technique can be used as a design aid when it is necessary to trade off conflicting design requirements, such as overshoot and settling-time specifications. It is shown that the method is not restricted to the deadbeat case, but can also be used for any prescribed set of closed-loop poles