Fault Detection of a DC Motor

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Fault Detection of a DC Motor

This example shows the simulation of fault detection of a DC motor using

QFIRE Studio

Introduction

As presented in [1], a DC motor can be modeled as in the diagram of Figure 1:

Figure 1 - Model of a DC motor diagram

The motor parameters in Figure 1 are listed in Table 1.

Table 1 - Parameters of the DC Motor model in Figure 1

Variable	Symbol	Value
Armature Resistance	$R_{A}$	$1.52 \Omega$
Armature Inductance	$L_{A}$	$6.82 \times10^{-3} \Omega s$
Magnetic Flux	$\Psi$	$10.33 V s$
Voltage Drop Factor	$K_{B}$	$2.21 \times10^{-3} V s / A$
Inertia Constant	$J$	$1.92 \times10^{-3} kg m^2$
Viscuos Friction	$M_{F1}$	$0.36 \times10^3 N m s$
Dry Friction	$M_{F0}$	$0.11 N m$

The input and output signals are listed in Table 2.

Table 2 - I/O signals in the DC motor model in Figure 1

Variable	Symbol	Type
Armature Voltage	$U_{A}$	Input
Friction	$M_{L}$	Input
Armature current	$I_{A}$	Output
Speed	$\omega$	Output

In Figure 1, there is a block for a non-linear function. This function is the

M_{F0}

block. It represents the the dry friction which occurs when starting the DC motor. If the

U_{A}

voltage is negative, it means the dry friction must be negative as it can be seen in Figure 2.

Figure 2 - Non-linear friction torque

M_{F0}

Finally, using the block modeled in Figure 2, it is possible to create the whole model from Figure 1 in

QFIRE Studio

as follows in Figure 3.

Figure 3 - Diagram from Figure 1 using

QFIRE Studio

Still in Figure 3, there are some inputs that are responsible for simulating failures, for example,

\Delta R_{A}

Simulation

Aiming to simulate a failure detector presented by [1], the diagram from Figure 3 was used as the plant and the

QFIRE CTR-101

was used as the fault detection system.

Figure 4 - DC Motor and

QFIRE CTR-101

In Figure 4, the green blocks are the inputs from Table 2 and the red blocks are the step blocks that allow to simulate failures. In [1], there are residual filters used to detect faults in the motor.

\begin{align*}r_{1}(kT) &= \Psi I_{A}(kT)- J \dot{\omega}(kT)- M_{F1}\omega(kT)-M_{L}(kT)\\r_{2}(kT) &= \Psi U_{A}(kT)- (\Psi^{2}+R_{A} M_{L})\omega(kT)-(R_{A}J+L_{A}M_{F})\dot{\omega}(kT)-L_{A}J\ddot{\omega}(kT)-R_{A}M_{L}(kT)-L_{A}\dot{M_{L}}(kT)\\ r_{3}(kT) &= M_{F}U_{A}(kT)-(R_{A}M_{F}+\Psi^{2})I_{A}(kT)-(M_{F}L_{A}+J R_{A})\dot{I_{A}}(kT)-L_{A}J\ddot{I}_{A}(kT)+\Psi M_{L}(kT)+J\dot{U_{A}}(kT)\\ r_{4}(kT) &= U_{A}(kT)-L_{A}\dot{I}_{A}(kT)-R_{A}I_{A}(kT)-\Psi\omega(kT)\end{align*}

The residuals need the signals from the Table 2 and their derivates. To obtain the derivatives of the signals we use a butterworth low-pass filter arranged as a state-variable filter.

Figure 5 - Butterworth filter

Using the state-variable filter and the residual filters, the fault detection system was completed as shown in Figure 6 and detailed in Figures 7, 8, 9 and 10.

Figure 6 - Fault detection system

Figure 7 -

r_1(kT)

digital filter

Figure 8 -

r_2(kT)

digital filter

Figure 9 -

r_3(kT)

digital filter

Figure 10 -

r_4(kT)

digital filter

Results

In Figures 11 and 12, it is possible to see the behavior of the DC Motor starting and having an Armature Resistance fault at time of 8s.

Figure 11 - Armature current behavior

Figure 12 - Speed behavior

The behavior of the residuals after fault injection at 8s can be seen in Figure 13.

Figure 13 - Response of the residuals to the fault injected into motor resistance at 8s

Bibliographic References

[1] Isermann, R., 2005.

Fault-diagnosis systems: an introduction from fault detection to fault tolerance.

Springer Science & Business Media

About MWF

MWF is a traditional Brazilian company that provides a wide range of electronic and mechatronic products for industry sectors such as automotive, agricultural machinery and aerospace.

Rua Doutor Siqueira, 139 / Sala 804 Campos dos Goytacazes - RJ, Brasil

contact@mwf-technologies.com

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