Parametric Identification of Nonlinear and Linear Mathematical Models of the BLDC Motor

The article presents the results of an analysis of the parametric identification process of typical mathematical models of a brushless DC motor with an electronic commutator (BLDC) in off-line conditions. The aim of the analysis was to examine the impact of changes in motor load and power supply conditions on the obtained parameter values of mathematical models. The experiments used a nonlinear and linear mathematical model of the BLDC motor drive system in the form of a system of differential equations of individual phases of the BLDC motor electric circuit and a differential equation of the input variable in the form of supply voltage and the output variable in the form of angular velocity, respectively. The identified parameters of the mathematical models were determined on the basis of electrical and mechanical measurements of the motors’s output values when excited with various stator voltage values (in relative units). The Nelder-Mead numerical static optimization method was used to identify the nonlinear and linear mathematical model of the motor. The identified model parameters were determined for various operating conditions of the drive system with an inertial mass load and a hydraulic pump operating in a power drive system with a proportional valve. The motor load torque in the hydraulic system was obtained by using the throttling method by changing the pressure and flow parameters of the working medium. The influence of supply voltage and load torque on the static and dynamic properties of the motor was also analysed. The assessment of the convergence of the time responses of the drive system recorded in experiments and obtained from the solution of mathematical models was carried out on the basis of the correlation function. Laboratory tests were carried out in a drive system with motor BLDC of power 2.5 kW operating in a drive system with a piston pump.