Abstract
It has already been shown that the stable inverse system can be constructed by using 2-delay input control. However, the control inputs may be often changed very largely between the sample points. The big change of inputs between the sample points causes ripples in the responses and is not desirable.
The purpose of this paper is to make as small as possible the input change between the sample points. The 2-delay input controller which constructs the inverse system contains free parameters involved in the general solutions of Diophantine equation. We will first show the existence of an inverse system that makes the input change during a sampling period settle down to zero in finite time for a specified class of desired inputs. This controller is also given by solving the Diophantine equation and thus contains some free parameters. Secondly, we propose the controller minimizing the input changes before settling down to zero. The summation of squared input changes is introduced as a cost function and the controller is obtained simply by minimizing the cost function.
