Robust H∞ Hybrid Observer-Controller Design With Application to Attitude Control of 2-DOF Helicopter

In this paper, a class of uncertain piecewise affine (PWA) systems, subject to system and measurement external disturbances are studied. The uncertainties are assumed to be norm bounded and the external disturbance signals belong to the L2 space. The problem of optimizing the system response in the H∞ sense, by means of a piecewise affine observer-controller, is formulated as an optimization problem subject to a number of constraints in the form of matrix inequalities. The derived constraints are obtained by considering a partially piecewise quadratic Lyapunov function in combination with the general conditions for H∞ stability. Then the uncertain PWA approximation of the nonlinear attitude dynamics of a simplified helicopter model, subject to system and measurement external disturbances, is presented. The uncertainties arise in the form of the difference between the actual nonlinear dynamics and the PWA approximation. Utilizing the introduced methods, a robust PWA observer-controller is designed and implemented on the simplified nonlinear helicopter model to demonstrate the effectiveness of the proposed observer-controller design method.Copyright © 2014 by ASME