Clearance of flight control law based on structural singular value theory

Abstract

This paper studies the clearance of flight control law for a hypersonic gliding vehicle (HGV) and proposes two linear clearance criteria based on structural singular value (μ) theory. The first criterion is the multiinput-multioutput (MIMO) stability margin, which is defined independently of an exclusive region depicted in Nichols diagrams. Through introducing a measure matrix, the classic phase/magnitude margin can be expanded into an MIMO system, thereby becoming the robust stability criterion of the MIMO system with pure complex uncertainties. The second criterion is setup based on an analysis of the robustness, i.e., the stability under pure real parametric uncertainties. The study establishes a physical linear fractional representation (LFR) model of the HGV and then reduces it to an equivalent model of a lower order. Then a global optimization strategy is proposed to compute μ with real parametric uncertainties. The computational burden can be significantly reduced by model reduction and global optimization. The study evaluates an HGV as an example to demonstrate the validity and efficiency of the proposed methods.