Iterative Guidance Scheme for Satellite Launch Vehicles

Abstract

The purpose of this paper is to implement and ascertain the optimality of the Iterative Guidance Algorithm for higher altitude orbits by comparing it with the Optimal Control Algorithm. The objective of SLV guidance is to ensure that the SLV injects the given payload into its orbit, as specified by its mission profile, that too in the presence of various kind of perturbations and other parametric variations which cannot be reliably anticipated or predicted before the launch. These parametric variations include propulsion system performance, launch day winds, weight and other atmospheric parameters like density and temperature uncertainties. This paper discusses the implementation of iterative algorithm in an exo-atmospheric phase to provide near optimal guidance in real-time. The guidance is carried out in an inertial 2-D reference frame and a closed loop simulation in which inputs are taken from the on-board navigation system; also the guidance is carried out in the last stage of the vehicle. In the algorithm, the equations of motion of the launch vehicle are first taken for a flat earth surface with the gravity field being uniform, then those equations are extended over a spherical earth model where gravity follows the inverse square law. The control vector is computed as a function of the state variables of the vehicle and the guidance commands are updated at the end of each guidance cycle using the current state variables. In order to check the optimality of the algorithm, the same problem is solved using the Optimal Control Theory and the results are compared. The optimal control problem is converted into a two-point boundary value problem using Pontryagin’s Minimum Principle. Both the algorithm’s are implemented on MATLAB/SIMULINK. Simulation results and the comparisons show that the iterative guidance approach gives highly accurate results and retains its optimal properties under any kind of perturbation. Hence, the iterative guidance scheme is a very reliable and effective method of guidance for a launch vehicle in real-time as the results indicate that the execution time that is required for a single guidance loop stays within the domain of real-time implementation.