Journal of Advances in Mathematics and Computer Science

The solar power technology looks to be a long-run efficient and sustainable energy model. In addition, its harvesting mode has increased significantly to higher levels. However, this type of technology is lacking exhaustive usability. Solar cells can be organized to serve in most upcountry areas which are mainly not covered by mains electricity. A number of research studies have been compelled by the depletion of natural oil deposits, high demand for electrical power, and frequent power outages and degradation of climate due to diesel- driven generator emissions which have contributed immensely to global warming. With strong vibrations from such generators, noise pollution is inevitable. A mathematical model of linear differential equations was developed in this study to describe the motor-gear-generator system that was used to amplify the usability of solar energy for domestic and commercial use. The model was analyzed using the MATLAB/Simulink software. The parameters of the system were determined using Nonlinear Square and Gradient descend approaches. The results obtained were presented graphically and discussed, for system performance analysis. The stability of the system obtained was examined using the Routh-Hurwitz approach. The Bode plot was used to assess the phase and gain margins. The limit for the excess voltage was most accurately determined by the gear ratio. This study results contributes to the system modeling which has become increasingly significant in control problems. Precise mathematical models determine optimal parameter values that guarantee stability and control. Errors in parameter values may lead to poor stability and control. As a result, accurate parameter identification becomes easily addressed.