Positivity-Based Robust Control of Flexible Systems

This paper proposes a method for designing robust control laws for flexible structures based on positivity concept. The method can be applied to flexible systems with noncolocated actuators and sensors. It can also be used in systems with unequal number of sensors and actuators, i.e. nonsquare plants. The approach is divided into three stages. First a post-compensator that squares down the nominal plant and renders it positive real is designed. Then an embedding (loop transformation) is employed to parametrize a class of controllers that robustly stabilize the uncertain system. Finally, a controller that meets performance specifications is determined from the class of robustly stabilizing controllers. An algorithm based on Linear Matrix Inequalities to compute the control law is presented. The Draper Tetrahedral Truss structure is used to demonstrate the proposed approach.