Robust nonlinear control design for a missile using backstepping

Abstract: This thesis has been performed at SAAB Bofors Dynamics. The purpose was to derive a robust control design for a nonlinear missile using backstepping. A particularly interesting matter was to see how different design choices affect the robustness. Backstepping is a relatively new design method for nonlinear systems which leads to globally stabilizing control laws. By making wise decisions in the design the resulting closed loop can receive significant robustness. The method also makes it possible to benefit from naturally stabilizing aerodynamic forces and momentums. It is based on Lyapunov theory and the control laws and a Lyapunov function are derived simultaneously. This Lyapunov function is used to guarantee stability. In this thesis the control laws for the missile are first derived by using backstepping. The missile dynamics are described with aerodynamic coeffcients with corresponding uncertainties. The robustness of the design w.r.t. the aerodynamic uncertainties is then studied further in detail. One way to analyze how the stability is affected by the errors in the coeffcients is presented. To improve the robustness and remove static errors, dynamics are introduced in the control laws by adding an integrator. One conclusion that has been reached is that it is hard to immediately determine how a certain design choice affects the robustness. Instead it is at the point when algebraic expressions for the closed loop system have been obtained, that it is possible to analyze the affects of a certain design choice. The designed control laws are evaluated by simulations which shows satisfactory results.