Minimum-norm Multivariable State Space Controller Design by Pole Shifting

Abstract The control signals of a closed loop system are bounded by constraints of the system. If the amplitudes of the control signals are too great, the system may become nonlinear. A method to avoid this problem is to reduce the amplitudes of the control signals. Small amplitudes could be achieved by small controller gains. Own experiences with single input/single output systems published in earlier papers showed that a special calculation of certain poles to be fixed in the closed loop system results in small controller gains. On the other hand, for an arbitrary pole placement in multivariable systems there exists a method to get small controller gains by the minimum-norm solution of the pole assignment equations. The question solved in the present paper was whether it would be possible to combine both mentioned ways to get smaller controller gains than those achieved by one method allone. As the positive result of the research a new method is proposed in the following, combining the advantages of both ways.