This work presents a comprehensive method for precisely determining the equivalent circuit characteristics of single-phase induction motors, including both direct and indirect steps. Firstly, a DC test, a no-load test, and a locked-rotor test are performed to ascertain the primary electrical characteristics of both the main and auxiliary windings. Next, the indirect phase consists of iteratively modifying the mechanical characteristics, such as the inertial moment and friction factor, in a motor simulation model in Simulink until they match the previously determined electrical parameters. In addition, the motor parameter estimate process can be improved by applying the Nelder-Mead optimization approach, which eliminates the need to calculate partial derivatives of a cost function. The study also applies the scalar control to the single-phase induction motor. Ultimately, the efficacy of the suggested methodology is confirmed through a comparison of simulated and actual outcomes.