Asian Research Journal of Mathematics

Abstract

Mathematical models of control systems are mathematical expressions which describe the relationships among system inputs, outputs and other inner variables. Establishing the mathematical model describing the control system is the foundation for analysis and design of control systems. The present study designed a DC motor- gear-alternator (MGA) model where DC motor is the prime mover used to drive an alternator through specialized gears employed in between alternator and DC motor. The fundamental equations that describe the system were presented, and then developed transfer function and Simulink model for the system. The workability of the model is then tested using some numerical values. Results showed that the output voltage increases exponentially with time. Finally, the effect of each of the PID parameters on the closed-loop dynamics were discussed and demonstrated how to use a PID controller to improve the system performance.

Aims:

(i) To construct a mathematical model describing the dynamics of the MGA set coupled through a gear ratio.
(ii) To design transfer function, which is a compact description of the input/output relation for the model.
(iii) To construct a Simulink model of MGA System.
(iv) Test the model using numerical values (assumed data).

Place and Duration of Study: Moi University, Department of Mathematics and Physics, between May 2015 and July 2016.