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This paper presents the results of research on speed regulation of a brushless DC motor . This is mainly a comparative study between a PID regulator and a fuzzy regulator applied to the operation of this type of engine in order to find the best control. The BLDC engine must operate under various speed and load conditions with improved performance and robust and complex speed control. Because of this complexity, the traditional PID command encounters difficulties in controlling the speed of a BLDC. Another control technique is currently developing and is producing good results. This is the fuzzy controller that handles process control problems, that is, managing a process based on a given set point per action on the variables that describe the process. To achieve the desired results, the brushless DC machine model will be studied. With the model obtained, both types of regulator will be tested. A synthesis of the observed comparison results will enable a conclusion to be drawn on the performance of the two types of regulators driving a BLDC (Brushless DC) .

Industrial processes require precise regulation of the speed of the drive motors. To achieve this objective, a control based on electronic semiconductor variators was used for the DC motors. This technique consisted of varying the speed in proportion to the voltage. Due to the complexity of maintaining DC motors, recent applications rarely use this system. Thanks to advances in electronics, the development of brushless motors is booming in many fields of application and for powers up to a few tens of kilowatts. These permanent magnet synchronous type motors eliminate the drawbacks associated with the collector of direct current motors, and their performance surpasses that of asynchronous motors [

In many industrial applications of BLDCs, it is essential to know certain physical parameters (speed, torque, position, current, etc.) for proper speed regulation. For this, it is therefore necessary to have recourse to a PID type control, fuzzy, variable speed drive... Through the existing research work in the literature, the PID control is probably the most widely used in industrial control direct current motors [

The brushless motor works from three variable voltage sources, supplied by an inverter, and allowing to generate a rotating magnetic field. The rotor, generally equipped with a permanent magnet, tends to follow the rotating magnetic field.

In the simple case of the BLDC motor, at each switching, two phases are respectively connected to the supply voltage and to the ground, and one phase is not connected. Let us take the example of

A current flows through the coils from B to C and generates a stator magnetic fiel B in the next steered motor y S . The rotor supports a magnet whose magnetic moment m , oriented from south to north, tends to align with the stator magnetic field by rotating counter clockwise.

As soon as the rotor approaches y S , the commutation will be modified to make the current flow from B to A, the stator magnetic field B rotates by π/6, so as to attract the rotor and continue the rotation in the counter clockwise direction. The angle between m and B leads to a magnetic torque C m = m Λ B [

The modeling of a BLDC motor can be developed in the same way as a three-phase synchronous machine. As its rotor is mounted with a permanent magnet, these dynamic characteristics remain different. The flux due to its rotor depends on the magnet, which is why the saturation of the magnetic flux is typical for these motors. A BLDC motor is powered by a three-phase voltage source, as shown in

By applying the mesh law to the BLDC, we obtain the following system [

V a ( t ) = R i a ( t ) + L a d i a ( t ) d t + e a ( t ) (1)

V b ( t ) = R i b ( t ) + L b d i b ( t ) d t + e b ( t ) (2)

V c ( t ) = R i c ( t ) + L c d i c ( t ) d t + e c ( t ) (3)

With R, L and ( i a , i b and i c ) are respectively: the resistor, inductance and currents of stator’s phase.

e a = f a ( θ ) ⋅ K e ⋅ ω r , the electromotive force of phase A (4)

e b = f b ( θ − 2 π 3 ) ⋅ K e ⋅ ω r , the electromotive force of phase B (5)

e c = f c ( θ − 4 π 3 ) ⋅ K e ⋅ ω r , the electromotive force of phase C (6)

K_{e}: is the coefficient of force electromotive; f a ( θ ) , f b ( θ − 2 π 3 ) and f c ( θ − 4 π 3 ) : are the functions whom depend only on the position of the rotor; ω r : is the rotation speed θ : is the electrical angle which is calculated as follows θ = p ω r with p the number of pole.

The Writing voltage’s matrix is written:

[ V a V b V c ] = [ R 0 0 0 R 0 0 0 R ] [ i a i b i c ] + d d t [ L a 0 0 0 L b 0 0 0 L c ] [ I a I b I c ] + [ e a e b e c ] (7)

By applying the transform of Laplace we get:

[ V a V b V c ] = [ R + L ⋅ p 0 0 0 R + L ⋅ p 0 0 0 R + L ⋅ p ] [ I a I b I c ] + [ E a E b E c ] (8)

The Equations (1)-(3) allow determining the voltage’s expressions between phases:

V a b ( t ) = V a ( t ) − V b ( t ) = R [ i a ( t ) − i b ( t ) ] + L [ d i a ( t ) d t − d i b ( t ) d t ] + e a ( t ) − e b ( t ) (9)

V b c ( t ) = V b ( t ) − V c ( t ) = R [ i b ( t ) − i c ( t ) ] + L [ d i b ( t ) d t − d i c ( t ) d t ] + e b ( t ) − e c ( t ) (10)

(6) and (7) give: V c a ( t ) = V b c ( t ) − V a b ( t ) (11)

We get the expression of the currents below from Equations (9)-(11)

d i a ( t ) d t = 2 3 L V a b ( t ) + 1 3 L V b c ( t ) − R L i a ( t ) − 1 3 L e b c ( t ) − 2 3 L e a b ( t ) (12)

d i b ( t ) d t = 1 3 L V b c ( t ) − 1 3 L V a b − R L i b ( t ) − 1 3 L e b c ( t ) + 1 3 L e a b ( t ) (13)

d i c ( t ) d t = − ( d i a ( t ) d t + d i b ( t ) d t ) (14)

The electric torque generated by the BLDC is given like this:

T e = e a i a + e b i b + e c i c ω r (15)

By replacing the Equations (4)-(6) within (15) we have:

T e = K e [ f a ( θ ) i a + f b ( θ − 2 π 3 ) i b + f c ( θ − 4 π 3 ) i c ] (16)

The dynamics of the rotor is defined as see:

d Ω d t = 1 J ( T R − T e + f Ω ) (17)

When the rotor poles pass next to the hall effect sensors, the latter give 1 or 0