Analysis dynamic characteristics brushless motor of the mechatronic system in conditions of parametric uncertaintyby computer simulation methods

Abstract

THE PURPOSE. Currently, brushless motors – electric machines with permanent magnets on the rotor and a rotor position sensor controlled by a sinusoidal voltage from frequency converters, are widely used in mechatronic and robotic systems. The control algorithm is formed on the basis of information about the current values of the parameters brushless motor mechatronic system using a nominal or reference mathematical model, which is, as a rule, an idealized representation of a real device. The non-stationarity of the parameters object of study, as well as the possible uncertainty of its mathematical description due to the simplification of the mathematical model, lead to undesirable or unacceptable results when forming the control algorithm of the mechatronic system. The problem arises of analyzing the dynamic characteristics of a brushless motor under conditions of parametric uncertainty in order to determine the parameters that most affect the functioning of the mechatronic system and the phase coordinates that are sensitive to these changes.METHODS. When solving the problem, methods of the sensitivity theory are used to obtain the corresponding vector-matrix equations, the solution of which is carried out by means of the MatLab software environment.RESULTS. In this paper, sensitivity equations are obtained for the active resistance and projections of the stator winding inductance on the longitudinal and transverse coordinate axes, as well as for the moment of inertia of the brushless motor. A vector-matrix block diagram for calculating the sensitivity functions of a brushless motor is formed, the characteristic feature of which is the presence of a non-zero matrix of free terms, reduced to the input of the sensitivity model. The corresponding Simulink models were built to study the influence of the listed quasi-stationary parameters on the rotation speed and torque on the shaft of the object of study. An analysis of the statistical characteristics additional motion of the specified phase coordinates of the brushless motor has been carried out, and graphical dependencies and steady-state values of dispersions and relative estimates have been obtained.CONCLUSION. An analysis of the dynamic characteristics of a brushless motor under conditions of parametric uncertainty made it possible to determine that the rotation speed of the machine is the most sensitive to parametric disturbances. This coordinate is the most informative and is of maximum interest in the formation of an optimization algorithm for a mechatronic system. The decisive role in the formation of the additional movement of the output coordinates of the brushless motor is made by a change in the projection of the stator inductance on the transverse coordinate axis, which is an order of magnitude greater than the contribution to the additional movement of coordinates from other unstable parameters. It is expedient to use the results obtained in the course of the study when constructing an optimal control algorithm for a mechatronic system under conditions of parametric uncertainty.