Title: Design of Discrete-time LQR for Optimal Positioning Control of Deep Space Satellite Antenna
Authors: Kingsley Ugochukwu Anyanwu, Chidiebere N. Muoghalu, Emeka Cyril Ozumba, Miriam Kelechi Onuoha
Volume: 8
Issue: 8
Pages: 56-61
Publication Date: 2024/08/28
Abstract:
In optimally positioning of a satellite, a cost effective process can be achieved regarding the anticipated link margin necessary to receive most of the of the satellite transmission data from certain angle of elevation (or azimuth position). In this work, an optimal control system based on discrete-time linear quadratic regulator (LQR) has been designed and implemented with a DC servomotor-based antenna positioning control system in MATLAB/Simulink environment. The system response was initially analyzed considering the uncompensated state. The results obtained were presented in terms of steady-state transient response characteristics, which were rise time, peak time, settling time, overshoot, and steady-state error. In the uncompensated state, the rise time was 0.52s, peak time was 2.28s, settling time was 5.34s, overshoot was 34.6%, and steady state error was 0.181 rad. Considering the high value of overshoot, a LQR was designed and incorporated into the system to form a closed loop control system, and simulation conducted revealed that the oscillation or cycling (or instability) associated with the uncompensated because of high overshoot (34.6%) was largely reduced to 6.43% and steady state error of 0 was achieved. The performance of LQR was compared with that of PID controller. The comparison indicated that the LQR provided better stable system than PID controller by offering overshoot of 6.43% against 8.09%. Hence, for optimal control of deep space antenna, the optimal control scheme (LQR) will provide improved stability than PID controller.