Study and implementation of microcontroller-based system dynamics emulator using numerical method and reduction of order technique

Abstract

This paper presents the study and implementation approaches of microcontroller-based system dynamics emulator for Mechanical system and Electrical system. The main goals of this research are to prove that fixed-point microcontrollers can be used for system dynamics emulator, to study numerical approximation methods for system dynamics modeling and to make a microcontroller working as a system dynamics. Both systems, mechanical and electrical are modeled by Ordinary differential equation method (ODE). The numerical approximation techniques based on Euler's method are studied and used as implementation approaches. The obtained second-order differential equations are then applied by the Reduction of order technique to convert them to first-order differential equations that can be solved by the first-order Euler's methods. The final version of the system equations are finally implemented on a microcontroller and examined thoroughly. The microcontroller that works as a system dynamics connects to a computer through internet network using a standard 802.11b/g Wi-Fi module. Therefore, we can interact with the system running on the microcontroller directly from a web-browser. Web-applications running on a web-browser are used to control and visualize all of system parameters. We closely analyze the experimental results by comparing them with the results obtained by reliable computer software tools, Matlab and Octave. The experimental results show that the proposed approach acquires many desired requirement of system dynamics modeling and it obviously shows that many fixed-point microcontrollers can be properly used for system dynamics emulator.