Explicit solutions for collocated structural control with guaranteed norm performance specifications

Abstract

This paper presents explicit solutions for velocity feedback control of structuralsystems with collocated sensors and actuators to satisfy closed-loop and norm performance specifications. First, we consider an open-loop collocated structuralsystem and obtain upper bounds for the and system norms using a solution for the linear matrix inequality formulation of the normanalysis conditions. Next, we address the problem of static output velocity feedbackcontroller design for such systems. By employing simple algebraic tools, we derive anexplicit parametrization of the controller gains which guarantee a prescribed level of or norm performance of the closed-loop system. Finally, numerical examples are presentedto validate the advantages of the proposed techniques. The effectiveness of theproposed bounds and output feedback control design methods become apparent,especially in very large-scale structural systems where control design methodsbased on the solution of Lyapunov or Riccati equations are time-consuming orintractable.