Real Time Implementation of an Inertial Measurement Unit based on Fiber-Bragg Sensor Array using Legendre Polynomial
Parekh, Taher Saifee
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Missiles and launch vehicle are trending towards becoming more slender in shape to reduce aerodynamic drag. Bending vibrations of the rocket body occur when a flying object with a large slenderness performs pitch or yaw command. The onboard Inertia Measurement Unit (IMU) measures the attitude and the angular velocities of the deflected body as well as the rigid body motion and in turn feeds these signals back to the control loop. Feedback of the vibrating information degrades the control system stability and in the worst case makes the system unstable. These effects become more significant when the slenderness ratio of the launch vehicle increases. Another challenge with launch vehicle control is created by the time varying mass and inertia as well as the consequent change in modal shapes and modal frequencies of the structure as the fuel is exhausted. The main objective of the thesis was to demonstrate the real time performance between Fiber Optic Sensor Array System (FOSS) and the Navigation IMU (FOSS-IMU System) using the Legendre polynomial and compare it to a standard launch vehicle body. This thesis presents a method that enables accurate prediction of deflection, rate of rotation and acceleration at any point in the flexible structure relative to the rigid body frame. The FOSS-Legendre algorithm is based on modal matrices which are calculated using the finite element model of the structure whereas the spatial derivatives of the of the mode shapes are approximated using the legendre polynomials. The FOSS-Legendre system is based on taking deflection measurements at multiple points on the structure and allows accurate measurements of the states with no need to estimate the load forces or the damping matrix. To assess the performance of the system a Figure of Merit tables are generated for each test case to show how well the FOSS-Legendre system compares with the IMU.