A common controller for a family of plant models

A desired region tor the closed-loop eigenvalues is mapped into the feedback gain space K. For different plant models (operating conditions) different regions in K space are obtained. The set of common controllers is the intersection of these regions. It can be investigated by graphical methods in two dimensional cross section planes of K space. A useful way of choosing such plane in one design step is to keep n-2 eigenvalues fixed for a selected plant model. This defines a plane in K space, in which only the two remaining eigenvalues can be shifted. The general derivation of this plane and its numerically efficient calculation by transformation to Schur-form are shown. The technique is applied to the automatic track control of a bus. One constant controller was found, which accomodates large variations in speed, mass and friction coefficient.