Optimal Control Design of Slow Dominant Transient Response for Longitudinal Missile Dynamics

The missile dynamic characteristics inherit nonlinear behavior and fast velocity changes from subsonic to high supersonic. Accordingly, the missile’s responses to the control command must be very fast. Therefore, the autopilot system needs rigorous design to ensure the missile still maintains its performance during flight. Missile control characteristics with a dominant pole close to the origin of the S-Plane tend to have a very slow transient response. This characteristic is unacceptable because the control command is no longer compatible with the intended flight condition since the dynamics have already changed. This paper designs an optimal controller for a missile using Linear-Quadratic Regulator (LQR) and Model Predictive Control (MPC) approach subject to slow transient response in longitudinal dynamic. The flight control analysis covers boost phase, after-boost phase, and terminal phase. The dynamics of every phase are presented by linear models derived from the nonlinear 6 degrees of freedom (DOF) equation of motion. The LQR technique is modified by adding an integral and compensator to speed up the settling time dynamic response. The result revealed that the LQR control cannot reduce the settling time. The other technique, LQR with integrator and compensator, seems promising since this technique has been quite successful in reducing the settling time. However, this modified compensator LQR generates a huge fin deflection up to 874 degrees, making it unrealistic for the actuator. On the other hand, MPC control offers satisfying results. It successfully shortens the settling time while maintaining the control input does not exceed the allowable deflection.