Integrated damping parameter and control design in structural systems for $\bf{\mathcal{H}^2}$ and ${\mathcal{H}^{\infty}}$ specifications

Abstract

The paper presents a linear matrix inequality (LMI)-based approach for the simultaneous optimal design of output feedback control gains and damping parameters in structural systems with collocated actuators and sensors. The proposed integrated design is based on simplified \(\mathcal{H}^2\) and \(\mathcal{H}^{\infty}\) norm upper bound calculations for collocated structural systems. Using these upper bound results, the combined design of the damping parameters of the structural system and the output feedback controller to satisfy closed-loop \(\mathcal{H}^2\) or \(\mathcal{H}^{\infty}\) performance specifications is formulated as an LMI optimization problem with respect to the unknown damping coefficients and feedback gains. Numerical examples motivated from structural and aerospace engineering applications demonstrate the advantages and computational efficiency of the proposed technique for integrated structural and control design. The effectiveness of the proposed integrated design becomes apparent, especially in very large scale structural systems where the use of classical methods for solving Lyapunov and Riccati equations associated with \(\mathcal{H}^2\) and \(\mathcal{H}^{\infty}\) designs are time-consuming or intractable.