Internal Model Control of A Class of Continuous Linear Underactuated Systems

This paper presents an Internal Model Control (IMC) structure designed for a class of continuous linear underactuated systems. The study treats the case of Minimum Phase (MP) systems and those whose zero dynamics are not necessarily stable. The proposed IMC structure is based on a specific controller which is obtained by the realization of an approximate inverse of the model plant. It is shown that, using such IMC structure, it is possible to remedy the problem of system underactuation and Non-Minimum Phase (NMP) behavior. The case of non-zero initial conditions and imperfect modeling are also presented and model parameters effects on the system evolution are discussed. Simulated examples are presented to prove the effectiveness of the proposed control method to ensure set-point tracking, stability and disturbance rejection. Keywords—Internal Model Control; continuous linear underactuated systems; specific controller; minimum phase systems; non-minimum phase behavior; non-zero initial conditions; model parameters effects; set-point tracking; stability; disturbance rejection