IQC-Based Analysis Techniques for Clearance

Abstract

This chapter presents the use of Integral Quadratic Constraints (IQCs) for solving flight control clearance problems. The theory of IQCs provides a powerful framework for the robustness analysis of control systems with respect to a very broad range of uncertainties and nonlinearities. The clearance criterion of robust stability with respect to parameter variations is addressed by employing the standard robust stability theorem of IQCs and by a suitable choice of an IQC for real parametric uncertainty. In addition, we use IQCs to solve two specific flight control clearance problems which are formulated as robust performance problems with respect to real parameter variations. These problems are the stability margins criterion and the comfort criterion with respect to turbulence which are formulated as robust \(\mathcal{H}_\infty\) and \(\mathcal{H}_{2}\) problems respectively. The formulation of a flight control clearance problem using IQCs results in a convex optimization problem involving Linear Matrix Inequalities (LMIs) for which there exist efficient, numerical solvers. Even so, there exist limitations related to increased computational complexity in case of optimization problems resulting from the analysis of large systems.