Newton–Raphson based scalar speed control and optimization of IM

Abstract

In this study, Newton-Raphson Based (NRB) scalar speed control (SSC) is recommended to control the speed of Induction Motors (IM). As is known, the Newton-Raphson method, which is often used in numerical analysis, is one of the methods that provide a rapid convergence of the desired value. In this study, the frequency value required for the desired speed value is calculated by Newton-Raphson method. Three different models including Newton-Raphson Based + Scalar Speed Control (NRB_SSC), Difference Speed + NRB_SSC (DS_NRB_SSC), DS + NRB_SSC + Difference Frequency (DS_NRB_SSC_DF) were used for optimization tests. Simulation of the work was done in Matlab/Simulink programme. According to obtained test results DS_NRB_SSC_DF has produced better results.

Gradient descent for quadratic functions using geometric mean and the Kai Fang method

“…The x-intercept is then set as the next initial value, and through successive iterations, the true value can be gradually obtained. [7][8][9][10][11][12][13] In Figure 2, we want to calculate the coordinate of the x-intercept of f(x). To do this, we first arbitrarily set(x (0) , f(x 0 )) as the initial value and calculate the x-intercept of the tangent line at (x (0) , f(x 0 )).…”

“…The Newton–Raphson method first calculates the gradient of the tangent using derivatives and uses that gradient to find the x ‐intercept (of the tangent line). The x ‐intercept is then set as the next initial value, and through successive iterations, the true value can be gradually obtained 7‐13 …”