Speed Control of Separately Excited DC motor

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Control of Separately Excited Dc Motor
Article in Journal of Electrical and Electronics Engineering · May 2011
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Journal of Electrical and Electronics Engineering
7
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Control of Separately Excited Dc Motor
ALIM Abdul1 and ABUBOKAR Talukdar2
1
University of Chittagong, Department of Applied Physics,
Electronics & Communication Engineering, Chittagong-4331, Bangladesh. E-mail: [email protected]
2
Chittagong University of Engineering & Technology (CUET),
Dept. of Electrical & Electronic Engineering, Bangladesh. Email: [email protected]
Abstract – Speed control of separately excited DC
motor and performance analysis by software
simulation has been done. The objective of this paper
is to describe the principle of DC motor speed control
using nonlinear combined control (armature voltage
and field current) and proportional integral- derivative
(PID) controller for DC motor drives. In the field
control mode, the armature voltage is held constant
and an adjustable voltage is applied to the field.
Simulation models of separately excited DC motor
have been developed using MATLAB/Simulink.
Keywords: Separately excited DC motor, armature
voltage and field current control, performance
analysis, simulation.
I. INTRODUCTION
Direct current (DC) motors have been widely used in
many industrial applications such as electric vehicles,
steel rolling mills, electric cranes, and robotic
manipulators due to precise, wide, simple, and
continuous control characteristics. Traditionally rheostat
armature control method was widely used for the speed
control of low power dc motors. One method of speed
control is applicable for speeds below rated or base
speed by Controlling Terminal Voltage VT and keeping
If or Φ constant at rated value. Another method of speed
control is applicable for speeds below rated speed by
Controlling (reducing) Field Current If or Φ and keeping
VT at rated value [2, 3]. The desired torque-speed
characteristics could be achieved by the use of
conventional proportional integral- derivative (PID)
controllers. As PID controllers require exact
mathematical modeling, the performance of the system
is questionable if there is parameter variation [1, 5].
This paper lies in the application of PID controller for
the speed control of separately excited dc motor.
Simulation results demonstrate the successful
application of PID controller to control the speed of a
separately excited dc motor. MATLAB/SIMULINK is
used because of the short learning curve that most
students require to start using it, its wide distribution,
and its general-purpose nature [8]. This will demonstrate
the advantages of using MATLAB for analyzing power
system steady state behavior and its capabilities for
simulating transients in power systems and power
electronics and control system dynamic behavior.
II. IMPLEMENTATION
Voltage speed control of a separately excited DC
motor: The field current, If is constant (and hence the
flux density B is constant), and the armature voltage is
varied. A constant field current is obtained by separately
exciting the field from a fixed dc source. The flux is
produced by the field current, therefore, essentials
constant. Thus the torque is proportional only to the
armature current [4].
Field speed control of a separately excited dc
motor: We can also control the dc motor, which is
varying its speed by varying the field flux. The method
of control is generally used when the motor has to run
above its rated speed. To understand the operations of
field control suppose that the dc motor running at a
constant speed. If the field current is reduced by
reducing the voltage across the field coil, the flux
density will be reduced. This will reduce the back emf
instantaneously and will cause armature current to
increase resulting in the motor speed increasing.
Consequently the back emf will increase and a new
equilibrium will be established at a higher speed. With
field control one can achieve as high a speed as five
times the rated speed [1, 2]. The armature current, Ia, is
kept constant and the flux density B is varied by varying
I f.
Combined armature and field control of
separately excited DC motor: The speed of a
separately excited dc motor could be varied from zero to
rated speed mainly by varying armature voltage in the
constant torque region. Whereas in the constant power
region, field flux should be reduced to achieve speed
above the rated speed. Torque and limitations in
combined armature voltage and field control can be
shown in Figure 1.
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Volume 4, Number 1, May 2011
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This is followed by a transformer which is then fed
into a “6-Pulse Rectifier” which produces a directed
voltage and current [1, 7]. This is connected across the
motor. To simplify the design, the armature resistance
and inductance has been shown as one impedance. A
PID Speed Controller was used, where the following
figures elaborate on the design. The speed of a
separately excited dc motor could be varied from zero to
rated speed mainly by varying armature voltage in the
constant torque region. Whereas in the constant power
region, field flux should be reduced to achieve speed
above the rated speed [6]. The specifications of the dc
motor are detailed in the Table1.
Fig. 1: Combined armature voltage and field current
control.
Proportional integral- derivative (PID) controller
for DC motor drives: DC Motors of different genres
abound. They are used abundantly across different
industries including paper mills, robotics, guided
vehicles, and conveyors. As can be noted the voltage
source is AC. The following diagram shows the basic
DC motor design.
TABLE 1: Parameter values
Parameter
Ra
La
Kp
Ki
Kd
Kα
Ke
Km
B
J
Fig.2: Basic DC Motor Design
TL
Vm
Pm
ωm
Vs
Label
Armature
Resistance
Armature
Inductance
Voltage to Speed
correction parameter
Voltage to Speed
correction parameter
Voltage to Speed
correction parameter
Phase Angle to
Voltage correction
parameter
Motor Torque to
Motor Current
proportionality
constant
Motor EMF to
Speed proportionality
constant
Motor Viscosity
Motor Moment of
Inertia
Load Torque
Rated Voltage
Rated Power
Rated Speed
Transformer
Secondary Voltage
Value
0.139Ω
0.045H
5.262
26.586
0.3498
0.2
1.91
1.91
0.6Nms
3.5Nms2
200 + ωm +
0.05ωm2
240V
40kW
1150 rpm
240V
(L-L)
Mathematical modeling: Using Kirchoff’s
Voltage Law in Figure 2, the following equation can be
derived.
(1)
V m = I m R a + L a di m / dt + E m
Fig. 3: MATLAB/SimPowerSystems model of
separately excited dc motor speed control
Where,
Vm is the input voltage to the motor,
Im is the motor current,
Em is the voltage left for the motor, not affected by its
impedance.
Using Newton’s Second Law, the following equation
can be derived.
Journal of Electrical and Electronics Engineering
9
_______________________________________________________________________________________________
T m = T e − Jd ω m / dt + B ω m
(2)
III. SIMULATION RESULTS
300.00
250.00
EMF Torque (Nm)
Where,
Tm is the Motor Torque and
Te is the torque produced by the voltage not accounting
the losses.
EMF Torque
350.00
Simulation is carried out in Matlab-Simulink.
The inputs of the controller are the reference speed and
the actual speed and the output is the driving voltage to
the motor. From Table 1 that TL = 200 + ωm + 0.05ωm2,
the following plot can be made.
200.00
150.00
100.00
50.00
0.00
0
2
4
6
8
10
12
14
16
18
Time (s)
Fig. 6: Plot of Induced EMF Torque VS Time
The inertial torque can be defined as Tacc = J dωm/dt. We
know ωm = 120.4sin (0.628t) and J = 3.5Nms2.This
implies that dωm/dt. = 75.6112cos (0.628t), so
Tacc=3.5(75.6112cos (0.628t)). Finally, Tacc = 264.64cos
(0.628t), the following graph show its plot.
Inertial Torque VS Time
300
200
Inertial Torque (Nm)
100
Fig. 4: Plot of Angular Speed VS Torque Load
0
0
2
4
6
8
10
12
14
16
18
20
-100
It can be noted that there is a positive relationship
between the torque load and angular speed. As one
increase, so does the other. According to reference [1],
for such parameters Te = 50 + ω + 0.0115ω2. According
to references [1] and [7] we can assume sinusoidal
speed variation. With ωref = 120.4 rad/s. So let’s assume
ωm= 120.4sin (0.628t). This would generate the
following graph of ωref vs time.
-200
-300
Time (s)
Fig. 7: Plot of Inertial Torque VS Time
Also the damping torque Tb = Bωm, but since B =
0.6Nms and ωm = 120.4sin (0.628t). This means Tb =
0.6(120.4sin (0.628t)). The following graph depicts this.
Reference Angular Speed VS Time
Damping Torque VS Time
1.500
80
1.000
0.500
40
0.000
0
2
4
6
8
10
12
14
16
18
-0.500
-1.000
Damping Torque (Nm)
Ref. Angular Speed (rad/s)
60
20
0
0
2
4
6
8
10
12
14
16
18
-20
-40
-60
-1.500
Time (s)
-80
Time (s)
Fig. 5: Plot of Reference Angular Speed VS Time
Fig. 8: Plot of Damping Torque VS Time
Bearing in mind that Te = 50 + ωm + 0.0115ωm2, the
following graph can be plotted.
Using equation (2), note that Tm = Te – Tacc – Tb. This is
10
Volume 4, Number 1, May 2011
_______________________________________________________________________________________________
plotted on the following graph.
IV. CONCLUSION AND DISCUSSION
MotorTorque
400.00
300.00
Motor Torque (Nm)
200.00
100.00
0.00
0
2
4
6
8
10
12
14
18
16
-100.00
-200.00
-300.00
Time (s)
Fig. 9: Plot of Motor Torque VS Time
Recall, Te = 50 + ωm + 0.0115ωm2. Also Te = keIm. From
table 1, ke = 1.91. This means Im = (1/1.91) (50 + ωm +
0.0115ωm2) ==> dim/dt = (1/1.91) (dωm/dt +
2(0.0115)ωm dωm/dt) Also recall, Vm = ImRa + Ladim/dt +
Em . Also Em = kmωm. Using parameters from table 1 it
can be written Vm = 0.139Im + 0.045 dim/dt + 1.91ωm.
Knowing ωm = 120.4sin (0.628t) and dωm/dt. =
75.6112cos (0.628t), plot variations in Vm, Im & Tm.
Motor Voltage VS Current
Non-linearity of the combined field and
armature control system has been studied and carried
out using Matlab/Simulink. A DC motor drive for the
armature and associated field winding of the motor
includes an armature feedback loop responsive to the
current flow in the armature, an input command signal
such as a speed control signal, and the actual speed of
the armature for providing a control of the current
supplied by a DC source means to the armature to
thereby provide speed control of the motor. A field
feedback loop control is also provided and includes
means responsive to the voltage across the armature and
to the line voltage supplied to the armature for providing
a control of the field intensity to assure that the back
EMF of the armature is always less than the available
DC voltage supplied to the armature. This dual feedback
control provides for a faster response time of the
armature throughout its total speed range together with
the feature of a constant torque for different speeds.
V. ACKNOWLEDGMENT
The authors would like to acknowledge the
Dept. of Electrical & Electronic Engineering, CUET for
giving lab facilities and supports to accomplish this
work.
300
REFERENCES
200
Motor Voltage (V)
100
0
0
20
40
60
80
100
120
140
160
180
-100
-200
-300
Current (A)
Fig. 10: Plot of Motor Voltage VS Current
Motor Torque VS Current
400.00
300.00
Motor Torque (Nm)
200.00
100.00
0.00
0
20
40
60
80
100
120
140
160
-100.00
-200.00
-300.00
Current (A)
Fig. 11: Plot of Motor Torque VS Current
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180
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