Performance Evaluation of the DC Motor using Robust H-Infinity and H₂ Controllers

Abstract

An evaluation studies for the position control of the Direct Current (DC) motor using two robust controllers have been presented. The primary objective of the DC motor is to control the motor’s speed on a particular reference when disturbances and uncertainties act on it. Regulating the angular speed through the adjustment of the power supply is complicated by uncertainties and disturbances which emphasized the need for a robust controller. The H<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> and H<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> were used for the control of the DC motor. Their performances were evaluated, and simulation was done in MATLAB 2022b environment. From the simulated results, it showed that the two robust controllers performed satisfactorily when measured against robust stability and robust performance. The designed H<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> controller had a better singular value plot of 40dB at the upper bound and -79.2dB at the lower bound. While it had a step response performance with regards to output one; rise time of 6.77 secs, settling time of 57.4 secs and steady state error of 0.515. Also, with regards to output two; it had a rise time of 72.3 secs, a settling time of 119 secs, with a steady state error of 0.756. The H<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> controller had a singular value plot of 37.4dB at the upper bound and -116dB at the lower bound. It also had a step response performance with regards to output one; with rise time of 6.94 secs, settling time of 63.9 secs and steady state error of 0.347. with regards to output two; it had a rise time of 91.2 secs, settling time of 154 secs and steady state error of 0.756. This shows good robust stability and robust performance for the DC motor’s position control. This demonstrates the effectiveness of the robust controllers on the DC motor.