Feedback Control for Course Correction of a Spin Stabilized Projectile
D. Mutters (TU Delft - Mechanical Engineering)
Riccardo Ferrari – Mentor (TU Delft - Team Jan-Willem van Wingerden)
H. Tol – Mentor (TNO)
Sergio Grammatico – Graduation committee member (TU Delft - Team Bart De Schutter)
Z. Feng – Graduation committee member (TU Delft - Team Jan-Willem van Wingerden)
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Abstract
This report presents the results of the graduation thesis from the TU Delft, performed at TNO unit Defence, Safety and Security, expertise group Weapon Systems. The goal of this graduation project is to develop a controller for a projectile equipped with the Precision Guidance Kit (PGK). The PGK is a Course Correction Fuze which can be used to retrofit 'dumb' artillery projectiles. It has canards to provide course correction and contains a GPS sensor to determine its position and velocity.
The dynamics of the projectile are described by a nonlinear 6 Degrees of Freedom (DoF) non-rolling body frame model. A static model is made of the PGK where its aerodynamics are calculated using computational fluid dynamics.
A Jacobian based guidance algorithm is developed for the 6 DoF model which calculates the changes in velocity needed along the perturbed trajectory to set the projectile back on the ideal path towards the target. These guidance signals function as a reference to be tracked by the controller.
A switching mode controller is designed, tuned and tested empirically in simulation. A nonlinear controller is designed to set the PGK actuator at an angle based on the guidance signals. Three switching laws are designed, the first to set the starting time of the controller, the second to switch the actuator off when the projectile is on a new ideal trajectory, and a third to avoid chattering, excessive switching, between the control modes.
The combination of the PGK actuator, the Jacobian guidance and the switching controller is shown to provide course correction successfully for four different trajectories with random offsets in initial velocity and pitch and yaw angle. The average miss distance and Circular Error Probable are decreased by 90%, to less than 50 m, without destabilizing the projectile.