High gain H∞ feedback control for an anti-air missile

A singular perturbation approach is applied to characterize the properties of linear time invariant high gain feedback systems with additive disturbance. Using the two time scale property of the high gain system, the near optimum high gain H_∞ state regulator is the composition of the slow subsystem H_∞ state regulator and the fast subsystem LQ state regulator. This approach is used to design an angle of attack command autopilot for an anti-air missile. The solution to the near optimal high gain H_∞ state feedback is shown to be equivalent to the solution of the slow H _∞ state feedback problem and the fast LQ state feedback problem. For sufficiently large γ, the conditions for the existence of solutions are shown to be equivalent to the existence conditions for the high gain LQ problem. Moreover, the optimality of H _∞ composite control system with respect to the H_∞ performance measure is equivalent to the optimality of the LQ composite control with respect to the LQ performance measure, for ε sufficiently small. Finally, the simulation results show that the high gain H_∞ autopilot is comparable to the high gain LQ autopilot. However, for the 180° manoeuvre in the presence of turbulence the H_∞ autopilot exhibits slightly better disturbance rejection properties