Mathematical model of position master unit of electric drive and development of its software

Abstract

Various computational algorithms to perform automatic control of motion are widely used in microprocessor control systems of electric drives. The requirements for such algorithms are the minimum execution time, the minimum amount of calculations, the compactness of the software, the convergence in the statics and dynamics of the control system. It ensures the stability and accuracy of coordinates control. The above-mentioned issues are applicable to the computational algorithm to develop a S-shaped trajectory of the electric drive by the position master unit. The position master unit based on the well-known mathematical model has some disadvantages that limit its use. They are incorrect calculation of the trajectory depending on the speed, acceleration, and sampling interval, as well as the self-oscillatory processes in case of the output and intermediate coordinates. As a result, it leads to a decrease of the accuracy of the electric drive control. Despite the standard solutions, such position master unit require improvement. In this regard, upgrading such a position master unit is relevant. The aim of upgrading is to eliminate these shortcomings by introducing corrective calculations and logical sequences that transfer the position master unit into a stable state as soon as it reaches a given value of the output coordinate. To control the motion of the electric drive when we develop a mathematical model and software based on it, it is necessary to use computational algorithms and numerical methods of calculation that are the least costly in terms of execution time. A modernized mathematical model of the S-shaped trajectory of position master unit is proposed. Restrictions of the parameters of this master unit have been eliminated. They may lead to incorrect path generation, as well as self-oscillations of the output and intermediate coordinates during the path generation, which reduces the accuracy of the electric drive control and cause vibration and noise. The software of the modernized position master unit, in comparison with its original form, does not contain cumbersome arithmetic that is costly in terms of execution time. The software has been successfully implemented into the microprocessor control system of the electric drive. At the same time, it is necessary to observe a time-stable execution of computational sequences and to consider the influence of the values of the numerical parameters used in the calculations.