Gain Scheduled Bank-to-Turn Autopilot Design Using Linear Parameter Varying Transformations

A gain-scheduled autopilot design for a bank-to-turn missile is presented. The approach follows previous work for a longitudinal missile autopilot. The method is novel in that the gain-scheduled design does not involve linearizations about operating points. Instead, the missile dynamics are brought to a linear parameter varying form via a state transformation. A linear parameter varying system is defined as a linear system whose dynamics depend on an a priori unknown but measurable exogenous parameter. This framework is applied to the design of a coupled longitudinal/lateral bank-to-turn missile autopilot. The pitch and yaw/roll dynamics are separately transformed to linear parameter varying form, where the cross axis states are treated as exogenous parameters. These are actually endogenous variables, and so such a plant is called quasilinear parameter varying. Once in quasilinear parameter varying form, a family of robust controllers using p, synthesis is designed for both the pitch and yaw/roll channels, using angle of attack and roll rate as the scheduling variables. The closed-loop time response is simulated using the original nonlinear model and also using perturbed aerodynamic coefficients. Nomenclature Q, Cm, Cn = aerodynamic moment coefficients about body x, y, and z axes Cx, Cy, Cz = aerodynamic force coefficients along body x, y, and z axes d = reference diameter Ixx, Iyy> hzi ^xz = nioments of inertia /i — /5 = constants dependent on moments of inertia (see Appendix) Ka = actuator bandwidth, 188.5 rad/s KQ = constant dependent on flight condition p = roll rate <2 = dynamic pressure q = pitch rate r = yaw rate S = reference area u = controller input z = controlled output a = angle of attack P = angle of sideslip 8C = commanded roll, pitch, or yaw fin deflection 8P = idealized roll control deflection &p>q,r- actual roll, pitch, or yaw fin deflection 8q = idealized pitch control deflection 8r = idealized yaw control deflection I