Linear Perturbation Equations Used in Control Analysis

Perturbation equations are used for analyzing vehicle stability in the frequency domain, robustness to parameter uncertainties, and for designing control laws at fixed flight conditions. The total variation in the external forces on a vehicle consists of force variations due to aerodynamics, engines (TVC and throttling), propellant sloshing, wind-gust disturbance, and gravity. The translational accelerations at the TVC engine gimbals are used in the load torque calculations. This chapter examines the load torques at the nozzle gimbals and at the control surfaces separately, beginning with the load torques at the TVC gimbals. The output variables are included in dynamic models and in linear simulations for flight control feedback stabilization and for evaluating the system performance in response to excitations. Modern and robust flight control design algorithms use state feedback in order to stabilize the vehicle and to achieve the desired performance characteristics.