Linearised optimal control and application to a gliding projectile
Abstract
The standard results of linearized optimal control theory are explored and examined to see how they can be applied to flight control systems. A feedback control system operating on the elevators of an aircraftlike gliding projectile is investigated. The projectile is required to closely follow a predetermined maximum range trajectory in the face of initial disturbances. Equations of motion are set up and linearized. Approximate solutions for the maximum range trajectory are given and approximate analytical expressions for the eigenvalues of the plant matrix and derived. After assigning weighting values to the state and control variables in the integral quadratic performance index, solutions to the Riccati matrix equation are computed and used to evaluate optimal state feedback gain vectors. The effect of this optimal feedback on glider performance is observed from computed trajectory simulations. An optimal feedback gain vector is selected subject to limitations on angle of attack, elevator deflection angle, and attitude. The question of incomplete state variable feedback is considered in the interest of simpler engineering design. Using a reduced order system representation, relationships between performance index weights and closed loop poles are established and a suboptimal system based on feedback of only one state variable is investigated.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 1981
 Bibcode:
 1981STIN...8418305J
 Keywords:

 Control Theory;
 Feedback Control;
 Flight Control;
 Gliding;
 Linearity;
 Midcourse Guidance;
 Projectiles;
 Aerodynamic Characteristics;
 Australia;
 Equations Of Motion;
 Feedback;
 Matrices (Mathematics);
 Optimization;
 Riccati Equation;
 Trajectories;
 Launch Vehicles and Space Vehicles