Quaternion Based Optimal Controller for Momentum Biased Nadir Pointing Satellite

In this paper, a quaternion based linear quadratic controller (LQR) is designed for nadir pointing satellites. The stability of the proposed controller is proved for specified control input. Runge-Kutta (RK4) numerical scheme and constrained nonlinear optimization technique are adapted to perform the simulation for computation of optimal values of a gain matrix, control weighted matrix, error weighted matrix and Riccati matrix for designing LQR controller. Simulations are carried out for three categories of spacecraft's- nano, medium and large, showing quick response and high tolerance to variations in orbital and inertial parameters alike. As per novel aspect concern, a generalized linear state-space and simplified expression for an analytical solution are derived for a momentum-biased asymmetric satellite. Through analysis, observation is made that even in case of highly elliptical orbits, a single controller design could yield optimal results and the variation of angular rates on control output is minimal. Even in case of extreme variations in inertia matrix and orbital rates, the controller performs as intended and results promise the development of fast and robust controllers for nadir pointing spacecraft in elliptical orbits.