Convex-Designs of Controllers for Resonant Systems

This paper considers design of controllers for highly resonant systems. Resonant systems are generally modeled as lightly damped linear systems. The purpose of control design is to damp the resonances. The plant and controller are written in a second order form, and their states are concatenated to form a closed loop. The controller parameters are determined by matching the eigen-values and eigen-vectors of the closed loop with that of a desired plant. This matching, referred to as Quadratic Eigen structure Assignment, leads to a set of linear equations. These equations may or may not have a solution. A least squares approximation is an alternative when no solution exists. However, least squares could lead to an unstable closed loop. Stability constraints are derived and enforcing the constraints while solving the least squares renders a stable closed loop as well as a stable controller. The constraints derived (Linear Matrix Inequalities) and the cost function are Convex. Hence, have a unique solution and are numerically tractable.