Analytical determination of the electromechanical system starting process efficiency index with regard to the distributed nature of input products consumption

Currently, an approach based on the lumped-parameter resource consumption model is used to determine the starting process efficiency index. This is due to the simplicity of analytical expressions for the efficiency index. In actual practice, the resource consumption of the starting process is time-phased in nature, which may lead to biased estimates of the efficiency index and inaccurate operation of the optimization system. In the paper, the actual form of the signal of the cost estimate of input products over time was determined using mathematical modeling of the controlled start system. It is proposed to use a fractional rational function to approximate these signals. The parameters of this approximation at different values of the control action were obtained using the Matlab Curve Fitting Toolbox. The analytical expressions for determining the resource consumption, potential effect and efficiency index of the starting process were obtained on the basis of the proposed approximation. It was found that the position of the maximum efficiency index on the x-axis, obtained when using the lumped-parameter and distributed-parameter starting operation models varies slightly (within the 5 % margin of error). This will reasonably facilitate hardware implementation of optimal control systems of starting processes through the application of the lumped-parameter starting operation model.