On interval goal programming switching surface robust design for Integral Sliding Mode Control

This paper presents a systematic technique for Integral Sliding Mode Control design applied to linear time-invariant systems, subject to disturbances, whose uncertain parameters belong to closed intervals. This approach considers a computational optimization-based procedure for the switching surface design, formulated as an interval goal programming problem, equivalent to the interval Ackermann׳s equation for the robust eigenvalue placement problem. The design objective is the minimization of the overall deviation from the specified performance for the transient response of the controlled system, which is represented by a polytope of characteristic polynomials. The controllability of interval systems is also numerically treated within an interval analysis framework. An experimental implementation of this switching surface design technique was compared with a classic robust LMI-based design procedure of the switching surface in the position control of a DC motor, coupled to different loads, to illustrate its main features and efficiency.