Filters for internal model control design for unstable plants

In this paper we study the design of a two-degree of freedom filter for the internal model control (IMC) method. The new filter alleviates some disadvantages of the standard IMC filter when the IMC method is applied to unstable plants that do not have nonminimum-phase zeros. We show that by employing the new filter, the resulting system has a flatter frequency response and little overshoot in the step response. Furthermore one of the filter´s design parameters can be related directly to the closed-loop bandwidth and the other design parameter can be used to control the recovery time of the step response, after an overshoot has occurred. These features are important when the IMC method is employed in a new approach to adaptive robust control. Examples are given in the paper to illustrate the new filter design