A comparative analysis of different approaches used for modelling and solving differential equations in Simulink/MATLAB

Abstract

In the paper, two new methods are developed and examined to implement a transfer function based approach in solving differential equations with Non-Zero initial conditions. A significant amount of time and effort is needed for solving differential equations theoretically or manually. Also, the obtained mathematical solutions to equations that represent various dynamic systems provide no graphical picture of the result. Using Simulink/MATLAB for modeling differential equations make the task of analyzing the behavior of systems easy and quick for the user. Beside, symbolic solutions and visual plots/graphs of the simulated results can be easily obtained and analyzed. Simulink uses different approaches to model a dynamic system such as differential equations in time domain (integrators based) or transfer function based and state space based. The paper addresses and compares different approaches used in Simulink for implementing block diagram based mathematical models of differential equations with non-zero initial conditions. Customarily, a transfer function based approach is used for analyzing systems with zero initial conditions. The paper demonstrated how to use a transfer function based approach for solving differential equations with non-zero initial conditions and two ways are devised to successfully implement the approach. To conclude, dynamic behavior of circuit and systems is analyzed and examined by obtaining graphical solutions with different approaches for chosen system parameters.