  This paper proposes an integrated design optimization framework for the gain
schedules and bending filter for the longitudinal control of a rocket during
its ascent flight. Dynamic models representing the pitch/yaw motion of a rocket
considering the elements such as the rigid body dynamics, aerodynamics,
sloshing, bending, sensor/actuator, and flight computer are introduced. The
linear proportional and differential (PD) control law with scheduled
(time-varying) gains and bending filter parameters are identified as key
decision variables for stabilizing the pitch/yaw motion of the rocket. The
integrated optimal design problem that determines the decision variables to
minimize the worst-case peak associated with the first bending mode with
constraints on the stability margins during the flight of the rocket is
mathematically formulated. A case study on design of gain schedules and bending
filter for an actual sounding rocket using the proposed framework is conducted
to demonstrate its effectiveness.
