International Journal of Engineering Trends and Technology (IJETT) – Volume 22 Number 2- April 2015
Error feedback based speed control of DC motor
drive for variable load torque using neural network
Akhilesh Sharma#1; Krishanu Nath#2; Amlesh Kumar#3; Amarjit Roy#4
#1 Assistant Professor, Dept. of Electrical Engineering
North Eastern Regional Institute of Science and Technology
Nirjuli, Arunachal Pradesh, India.
#2,3,4 B-Tech students, Dept. of Electrical Engineering
North Eastern Regional Institute of Science and Technology
Nirjuli, Arunachal Pradesh, India.
Abstract— Due to versatile speed control characteristic, the dc
motors have been inseparable from industry. The DC motors are
perhaps the most widely used energy converters in the modern
machine tools and robotics. With the increasing use of power
semi-conductor units, the speed control of DC motor is
increasingly getting sophisticated and precise. Speed of the DC
motor can be controlled by armature voltage control, field
control and armature resistance control methods. The
introduction of MATLAB and Simulink has made the designers
to simulate complex circuits and study their characteristics. In
this paper, an attempt has been made to control the speed of a
separately excited DC motor by armature voltage control method
incorporating a neural network as the speed controller for
constant as well as variable load torque. Using MATLAB,
Simulink and Neural Network toolbox, a comprehensive study
has been demonstrated.
Keywords— DC motor; neural network; speed control;
modelling
I. INTRODUCTION
Although surplus amount of energy is available in different
forms, but it is difficult to directly harness them due to
geographical and economical reasons. These energy resources
are under utilized. So, it is necessary to convert available
energy to fulfill one’s need and society altogether. In the
energy conversion, DC Motor plays an important role;
converting electrical energy into mechanical energy. In
mechanical system, speed control is necessary to do
mechanical work in a proper way. It makes motor to operate
easily [1]. This method of speed control is independent of load
on the motor and permits remote control of speed. The
introduction of variable-speed drives increases the automation
and productivity as well as its efficiency. In place of constant
speed operation, if a variable speed drive is introduced, then
efficiency of the drive can be increased from 15 to 27%. This
has lot of benefits like reduction of atmospheric pollution
through lower energy production, conservation of valuable
natural resources and consumption [2].
The artificial neural network (ANN) also known as neural
network processes information in a similar way as human brain
ISSN: 2231-5381
does. The network is composed of a large number of highly
interconnected processing elements called neurons, working in
parallel to solve a specific problem. It learns by example hence
it can be programmed to perform a specific task [4, 5]. It has
many advantageous features like parallel and distributed
processing, efficient nonlinear mapping between inputs and
outputs and robustness, without prior knowledge of the system
model [3]. Multilayer neural networks have been applied in the
identification and control of dynamic systems. These are used
in control systems with the help of following three typical
commonly used neural network controllers: model predictive
control, NARMA-L2 control, and model reference control [2].
As with most neural controllers, they are based on standard
linear control architectures. There are number of articles that
use ANNs applications to identify the mathematical D.C.
motor model and then this model is applied to control the
motor speed. They also use inverting forward ANN with input
parameters for adaptive control of D.C. motor. This paper is
about the study of steady-state and dynamics control of dc
machine. By using speed of the DC motor as feedback, the
error signal is generated. A variable load torque is applied to
check the stability in speed of the motor.
.
II. DC MOTOR
DC motor consists of two types of winding, rotor winding also
known as armature placed on the armature and stationary
winding placed on the stator of the DC motor. In all, DC
motors, except permanent magnet brushless motors, current
conducts through armature windings by passing current
through carbon brushes that slide over a set of copper surfaces
called a commutator, which is mounted on the rotor. Many
applications require the speed of a motor to be varied over a
wide range. One of the most attractive features of DC motors
in comparison with AC motors is the ease with which their
speed can be varied. The governing equations of DC motor
are:
𝑑𝑖
𝑣𝑎 = 𝑒𝑏 + 𝑖𝑎 𝑅𝑎 + 𝐿𝑎 𝑑𝑡𝑎
(1)
𝑒𝑏 = 𝐾∅𝜔𝑚
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(2)
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International Journal of Engineering Trends and Technology (IJETT) – Volume 22 Number 2- April 2015
𝑇𝑀 = 𝐾∅𝑖𝑎
𝑇𝑀 − 𝑇𝐿 = 𝐽
(3)
𝑑𝜔𝑚
𝑑𝑡
+ 𝐵𝜔𝑚
(4)
Where
𝑣𝑎 – The armature voltage (V)
𝑒𝑏 – The motor back emf (V)
Fig 1: Closed loop model of DC motor
𝑖𝑎 – The armature current (A)
Using the above model, the Simulink model of DC motor
constructed and is stored in a subsystem as shown in Fig. 2. A
gain of 9.54 is applied to convert the speed of the motor from
rad/sec to revolution per minute (rpm).
𝑅𝑎 – The armature resistance (Ω)
𝐿𝑎 – The armature inductance (H)
∅ – The flux per pole (Wb)
𝐾 – The motor back emf and torque constant (NmA−1)
𝜔𝑚 – The speed of motor (rad/s)
𝑇𝑀 – The motoring torque (Nm)
𝑇𝐿 – The load torque (Nm)
𝐽 – The moment of inertia of motor shaft (Nm2)
𝐵 –The viscous friction co-efficient (Nm-s)
Using (1) and (2), the back emf can be expressed as
𝑑𝑖
𝑒𝑏 = 𝑘∅𝜔𝑚 = 𝑣𝑎 − 𝑖𝑎 𝑅𝑎 − 𝐿𝑎 𝑑𝑡𝑎
(5)
Rearranging the terms, speed can be expressed as
𝑑𝑖
𝜔𝑚 = (𝑣𝑎 − 𝐼𝑎 𝑅𝑎 − 𝐿𝑎 𝑑𝑡𝑎)/𝐾∅
Fig 2: Simulink model of DC motor
(6)
It is obvious that the speed can be controlled by varying
 Flux/pole, ∅ (Flux Control)
 Resistance 𝑅𝑎 of armature circuit (Rheostat Control)
 Applied armature voltage 𝑣𝑎 (Voltage Control).
In this paper, voltage control method of the speed
control of DC motor has been used.
.
A. Modeling of DC motor
The modeling part of DC motor has been done keeping the
fact that the applied voltage to the field is constant hence the
flux per pole is constant. Taking the Laplace transform of (1)
and (4) and rearranging the terms (7) and (8) are obtained:
𝐼𝑎 (𝑠)
𝑉𝑎 (𝑠)−𝐸(𝑠)
= 𝑠𝐿
𝜔𝑚(𝑠)
𝑇𝑀 (𝑠)−𝑇𝐿(𝑠)
1
𝑎 + 𝑅𝑎
1
= 𝐽𝑠+𝐵
(7)
(8)
B. Speed control strategies
The speed control strategies which are incorporated in this
paper are:

Open-loop speed control

Close-loop speed control
In the open loop speed control, the neural network used,
acts as an armature voltage provider which directly controls the
speed of the motor. This technique initially proved to be good
for light loads and no-load conditions. But, in real time
applications, it is necessary to have fine speed control
irrespective of the nature of load torque applied. The motor has
to run at specified speed or sets in range of within 5% of the set
speed. To achieve this set level of speed condition, close loop
system is used and the motor speed is used as a feedback
signal. The feedback allows limiting the error and producing
better speed control compare to the earlier case. The block
diagram of the control strategies are shown in Fig.3 and Fig. 4
respectively.
Using (2), (3), (7) and (8) a closed loop block diagram of
DC motor is formed which is shown in Fig. 1.
Fig 3: Open-loop speed control strategy
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Fig 4: Close-loop speed control strategy
Fig 6: MATLAB model of neural network
III. NEURAL NETWORK
A neural network structure can be categorized as a
biological neural network or artificial neural network. The
neuron receives signals from the other similar neurons through
dendrites, collects in the nucleus or soma, and then distributes
to the neurons through the axon as shown. The input signal
passes through a synapse or synaptic junction which is
infinitesimal gap in the dendrites that is filled with
neurotransmitter fluid that either accelerates or decelerates the
flow of electrical charge.
After training the neural network it is observed that the mean
square error (m.s.e.) is reduced to 2.2611x10-6after 1000
iterations. The plot for m.s.e versus training iteration is shown
in Fig.7.
Fig 6: Plot of mean square error v/s iteration
Fig 5: Nonlinear model of a neuron
An artificial neural network consists of an input layer, one or
more hidden layer, and output layer. Each layer consists of
several neurons. The structure of an artificial neuron consists
of input nodes, synaptic weight, bias, summing junction,
activation function and output node. The set of synapse is
characterised by set of synaptic weights. Each input gets
multiplied with the synaptic weight and gets added at the
summing junction. The bias which lowers or increases the
level of net output also gets added at the summing junction.
The output from the summing junction is applied to an
activation function which is used to limit the output of the
neuron[6]. There are various types of activation functions of
which tan-sigmoid and linear functions have been used in this
paper. The Levenberg-Marquadt algorithm is used for training
the neural network.
The neural network used for speed control is trained and
simulated using neural network toolbox as shown in Fig. 6.
The data for training is obtained from an m-file. The objective
of the neural network is to provide the armature voltage
according to the input reference speed (in rpm). The network
has 1-5-1 structure with tan sigmoid activation function in
hidden layer. A linear function activation function has been
applied at the output layer.
IV. SIMULATION AND RESULTS
The entire simulation work has been done using MATLAB,
Simulink and neural network toolbox. The neural network
used is 1-5-1 structured and feed-forward back propagation
type. The simulated model has been subjected to various types
of loads and reference speed for both speed control strategies.
The parameters of the DC motor used are provided in Table
1[7].
Table 1: Parameters of DC motor
Sl no.
Parameters
Value
1.
2.
3.
4.
5.
6.
Power
Supply Voltage
Speed of the motor
Field Voltage
Moment of inertia
Torque constant
5 HP
240V
1750 RPM
150V
J=0.02215Nm2
K=1.976NmA−1
7.
8.
9.
Damping factor
Armature resistance
Armature inductance
B=0.002953 Nm-s
Ra=11 Ω
La=0.1215 H
A. Open-loop speed control
For the open loop speed control, the neural network
generates the armature voltage as per the reference speed. As
stated earlier, it provides good speed control only for light
loads. The Simulink model of the open loop control strategy is
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shown in Fig.8. Initially a constant torque of 5 N-m has been
applied with 1500 rpm as reference speed and later the
reference speed is increased to 1750 rpm at t=3.5 sec and
again then decreased to 1600 rpm at t=6 sec. On application of
neural network controller, motor picks up the reference speeds.
This is done by controlling the armature voltage and hence the
speed of the DC motor is controlled. This system, when
introduced to a nonlinear or varying load torque, does not
provide satisfactory results. As the load increases, the
armature current increases as shown in Fig 9 thereby reducing
in motor speed as shown in Fig 10. The difference of motor
speed and reference speed at full load is around 500rpm. This
is not a desirable feature especially when DC motor is used
for industrial applications. To compensate this speed drop a
close loop strategy has been adapted.
Fig 7: Plot of speed for load torque 2 Nm
Fig 10: Plot of speed for variable load torque (open-loop).
B. Close-loop control
The close loop strategy has dual neural network, one of
them gives the armature voltage required as per the reference
speed.. The second neural network feeds an additional voltage
to the armature which compensates the error. The Simulink
model is shown in Fig. 11. The load applied in second case is
reapplied to this model. From the Fig. 12, it is evident that
applying the same load, better speed of the motor is achieved
and error in speed is in the range of 4% of the reference speed.
The armature current curve for the same is shown in Fig. 13.
Initially, the reference speed is set to 1500 rpm with 5 N-m
load torque. At t=1 sec, the load torque is changed from 5N-m
to 10 N-m. the speed of the motor settles to 1488 rpm, with an
error in speed of 0.8% . The armature current sets to 2.8A after
an over shoot of 0.4A (14.28%). At t=2.5 sec, the full load
torque (20 N-m approx.) is applied, with controller, the speed
drops down to 1450 rpm but without controller, speed of motor
sets to 1000 rpm with reduction in error from 30% to 3.33%.
The armature current overshoots to 11A and sets to 10.2A in
0.17sec.
Fig 8: Simulink model of open-loop sped control
Fig 11: Simulink model of close-loop speed control
Fig 9: Plot of armature current for variable load torque (open-loop)
Fig 12: Plot of speed for variable load torque (close-loop)
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International Journal of Engineering Trends and Technology (IJETT) – Volume 22 Number 2- April 2015
Fig 13: Plot of armature current for variable load torque (close-loop)
This model is then applied with three more types of load
sinusoidal load, saw-tooth and random function. The plots for
each type of loads are given in Fig. 14, 15 and 16 respectively.
It can be concluded from these curves that with the close-loop
control, the motor picks up the reference speed.
Fig 16: Plot of speed for random load torque (close-loop)
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Fig 14: Plot of speed for saw-teeth load torque (close-loop)
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Fig 15: Plot of speed for sinusoidal load torque (close-loop)
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