Robust performance study for lateral autopilot of a quasi-linear parameter-varying missile

Abstract

A sideslip velocity autopilot is designed for a model of a tactical missile, and the robust performance of the system is investigated. A systematic tool to attain some robust performance is developed. The tail-controlled missile in the cruciform fin configuration is modelled as a second-order quasi-linear parameter-varying system. This nonlinear model presents explicit dependency of the aerodynamic derivatives on a state (sideslip velocity) and external parameters (longitudinal velocity and roll angle). The autopilot design is based on input-output pseudo-linearisation which brings the closed-loop system independent of the choice of equilibria. Thus, if the operating points are in the vicinity of the equilibria, then only one nominal linear model will describe closed-loop dynamics. However, parametric uncertainties lead to a multi-affine uncertain system even in the transformed space. Using multi-linear approximation of the uncertainties, coefficients of a pole placement controller can be estimated for some achievable robust performance. The performance is understood as a D-stability criteria and linear matrix inequalities are solved to design the controller in a Lyapunov approach. Finally, the robust performance analysis of the overall closed-loop system is presented.