During the last decade, classical and modern control system design methods, involving advanced mathematical techniques and time-consuming calculations have been greatly aided by software packages such as MATLAB/SIMULINK, SPICE, EMTP, SABER, SPECTRE, SIMPLORER, etc., which can provide accurate predictions of the systems behaviour in reality. In recent years, BLDCM has become a popular choice in industry applications such as automotive, aerospace, consumer, medical, instrumentation. BLDCM have advantages over brushed DC motors and induction motors. They have better speed versus torque characteristics, high efficiency, high dynamic response and so on. Also, torque delivered to the motor size is higher, making it useful in applications where space and weight are critical factors. However, BLDCM need position information for torque producing. The position information is usually obtained via measurement using device such as position encoder, resolver or Hall Effect sensors. These devices increase machine size, cost and rotor inertia, additionally also make the drive system complex and mechanically robustness[1,2].
A three phase BLDCM has three phase windings on the stator and permanent magnet rotor. The difference between this machine and the Permanent Magnet Synchronous Motor (PMSM) is that the machine back EMF is trapezoidal. Some confusion exists as to the correct models that should be used in each case. The BLDCM is very similar to the standard wound rotor synchronous machine except that the BLDCM has no damper windings and excitation is provided by a permanent magnet instead of a field winding[4,5].
MATHEMATICAL MODEL OF BLDCM
Figure 1 shows a dynamic equivalent circuit of the BLDCM. In simulation, the common y connection of stator windings, three phase balanced system and airgap uniform are assumed.
For this model, the stator phase voltage equations in the stator reference frame of the BLDCM are as Eq. 1;
||Equivalent circuit of BLDCM
||Block diagram of BLDCM
In here, back EMF is depend to magnetic flux in rotor because of permanent magnet with speed of rotor Eq. 2.
Motor equations can be expressed in state-space form as Eq. 3
Electrical exist power of motor can be calculated using Eq. 4.
Electromagnetic torque can be calculated as Eq. 5.
Electromagnetic torque to be motor dynamic equations can be expressed as Eq. 6.
Equation 6 can be arranged as Eq. 7 in state-space form (2).
Speed of motor is proportional position of rotor Eq. 8.
Figure 2 shows block diagram of mathematical model in three phases BLDCM.
SIMULATION OF THE BLDCM
The model of MATLAB/SIMULINK was shown in Fig. 3 according to rotor reference frame of the BLDCM for simulation of motor using equations which have been given above. Parameters which have been belong to motor used simulation are as below;
R = 11.05 ohm, L = 0.0215 henri, P = 6, J = 0.0001, B = 0.001 φ = 0.11weber, M = 0.002 henri, TL = 0.1 Newton, V = 2*10/π
ia, ib, ic currents in the result of simulation has been given in Fig. 4.
Speed of the BLDCM in the result of simulation has been given in Fig. 5.
||MATLAB/SIMULINK model of the BLDCM
||ia, ib, ic motor phase currents
||Speed of the BLDCM
||Position of the BLDCM
Position of the BLDCM in the result of simulation has been given in Fig. 6.
In this study, MATLAB/SIMULINK based modeling and simulation of the BLDCM is presented. This model can be provide a guide in the modeling of the BLDCM for investigators. This model has a flexible structure and enables to users to change motor parameters easily.
||Friction constant, N/rad/s
|ia, ib, ic
||Motor phase currents, A
||Moment of inertia, kg m2
|Ua, Ub, Uc
||Phase voltages, V
||Angle between stator and rotor, rad