Simulation of Hybrid Step Motor by State Space at Variable Torque of Load

Abstract

The work presents continuous and discrete optimal vector-matrix models of the hybrid step motor by the space of states. At each step of the control algorithm, the required torque is calculated in the state matrix, corresponding to the variable torque of load on the engine shaft and the harmonically modified torque with a frequency proportional to the number of motor poles and the speed of the shaft rotation. The torque of the motor shaft is calculated depending on the current angular speed of rotation, determined by the turn angle of the step motor shaft between two fixed moments and the calculated angular velocity in future moments of time, determined by the algorithm of calculating the trajectory (or by a fixed statute). The harmoniously variable torque of the step motor is determined in the model by the function of the sinus during the period of movement between the two nearby poles. To implement the optimal control of the step motor, a quadratic quality functionality was used, minimizing the energy of control and movement. A step motor model has been developed in the SimInTech software product, which allows you to represent vector-matrix continuous and discrete models. In order to implement the controls, phase voltages are calculated using the Park's reverse conversion.