Robust control for a class of interval model: Application to the force control of piezoelectric cantilevers

A method to design robust performances controllers is proposed in this paper. The method is valuable for a class of uncertain parametric systems: systems with zero-order numerator. In this work, interval model that accounts parametric uncertainties is described using interval analysis. Robust controller is derived by combining the interval arithmetic with the classical direct synthesis. As the derived controller is also an interval, we prove using numerical analysis that the midpoint can be taken as the final controller to be implemented. The proposed design method is applied to the control of manipulation force in piezocantilevers where the compliance of the manipulated objects is uncertain. The experimental results show the efficiency of the proposed method.