MODELING BLDC

MOTOR IN

MATLAB/SIMULINK

Aminata DEM GE3 2009/2010

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Introduction

This application note explains the different steps for modeling the BLDC motor.

To achieve this, I used the Mtalab / Simulink software. For that, I began by modeling the

DC motor as it is considered a BLDC motor which operates at low speed. And then I did

the modeling of BLDC motor.

I. Modeling of DC Motor

In this part, we must first declare all the specifications of the engine used in a file

.m to facilitate the changes if it is necessary. The file where I made those statements is

declar.m file.

1. Modeling in open-loop

I used the electrical and mechanical equations to make the following simulink

scheme :

This schema has been transformed into a block G (s). The parameter in entry is

the back emf. As we regulated the speed (in rad/s), I introduced the relationship

between the back emf and speed (e = KΩ) and the new scheme is the following:

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2. Modeling closed-loop

I used the block G (s) that I put in a closed loop with a PI corrector. The

calculating of parameters of the corrector is in the file declar.m. You make the

parameters of the motor used in this file.

The simulink schema of the motor is the following:

II. Modeling of the BLDC motor

For the speed control (in rpm) of the BLDC motor, we have the following schema:

The Decoder block gives the status of back emf depending on the position sensors

and the block Gates gives the status of switches in the voltage inverter.

In the motor block, enter the parameters motor in the following tab:

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In the voltage inverter block, the parameters of transistors are defined in the

following tab:

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III. Calculation of the digital corrector

In this part, we consider the following transfer function of the speed and voltage

of direct current motor in continuous:

With:

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This system is then converted into digital for the function GBo (z-1) (with Gbon (

z-1) as the numerator and GBoD (z-1) as the denominator).

The structure of the corrector is given by the following equation:

C (z-1) =

The parameters of the motor (excess over of the step response, rise time and

position error) must be defined to calculate the denominator HD+ of the transfer function

of the looped system H with :

HD+ = (1 – Z1z-1) (1 – Z1*z-1) = 1 – (Z1+ Z1*) z-1 + Z1 Z1* z-2

With

Z1, Z1* = exp(-ξωn*te ± ωn.te

By identifying it with the denominator of the following function H, we find the

coefficients a and b of the corrector.

H = K z-1