Vol. 5(14) Jan. 2015, PP. 1940-1948
Armature Voltage Speed Control of DC Motors Based Foraging Strategy
WISAM NAJM AL-DIN ABED
Electronic Department, Engineering College, University of Diyala, Iraq
*Corresponding Author's E-mail: Wisam_alobaidee@yahoo.com
Abstract
T
his paper presents the speed control of separately excited dc motor (SEDM) using armature
voltage control method based foraging strategy. Armature voltage speed control system is done
using state feedback controller with parameters tuned using bacterial foraging optimization
(BFO) technique. The motor angular speed and armature current are sensed and feeding back (state
feedback controller) for comparison with its reference values to generate control signal in order to
control armature voltage as well as the motor speed. The proposed design problem of speed controller
is formulated as an optimization problem. Bacteria Foraging Optimization Algorithm (BFOA) is
employed to search for optimal controller parameters. The SEDM mathematical model is used because
it's more reality to the actual plant rather than linear transfer function model in the control design and
studies and give more accurate results. BFO technique improves the controller performance by
choosing optimal parameters values which leads to improve the transient and steady state
specifications. The proposed method is very efficient and could easily be extended for other global
optimization problems.
Keywords: Bacteria Foraging Optimization Algorithm (BFOA), Separately Excited DC Motor (SEDM), state
feedback controller.
1. Introduction
The DC motors have been popular in the industry control area for a long time, because they have
enormous characteristics like, high start torque, high response performance, easier to be linear
control etc. [1].DC motors provide excellent control of speed for acceleration. The power supply of a
DC motor connects directly fed to the field of the motor which allows for precise voltage control, and
is necessary for speed and torque control applications. DC drives, because of their simplicity, ease of
application, reliability and favorable cost have long been backbone of industrial applications. DC
drives are less complex as compared to AC drives system. DC drives are normally less expensive for
low horse power ratings. DC motors have a long tradition of being used as adjustable speed
machines and a wide range of options have evolved for this purpose. DC regenerative drives are
available for applications requiring continuous regeneration for overhauling loads. AC drives with this
capability would be more complex and expensive. Properly applied brush and maintenance of
commentator is minimal. DC motors are capable of providing starting and accelerating torques in
excess of 400% of rated. Separately excited DC drives have been used for variable speed applications
for many decades and historically was the first choice for speed control applications requiring
accurate, speed control, controllable torque, reliability and simplicity. The basic principle of a DC
variable speed drive is that the speed of a separately excited DC motor is directly proportional to the
voltage applied to the armature of DC motor. The main changes over the years have been concerned
with the different methods of generating the variable DC voltage from the 3- phase AC supply [2].
1940
Article History:
IJME DOI: 649123/10116
Received Date: Dec. 07, 2014
Accepted Date: Feb. 03, 2015
Available Online: Feb. 14, 2015
WISAM NAJM AL-DIN ABED / Vol. 5(14) Jan. 2015, PP. 1940-1948
IJMEC DOI: 649123/10116
Optimization is associated with almost every problem of engineering. The underlying principle in
optimization is to enforce constraints that must be satisfied while exploring as many options as
possible within tradeoff space. There exists numerous optimization techniques. Bio-inspired or
nature inspired optimization techniques are class of random search techniques suitable for linear and
nonlinear process. Hence, nature based computing or nature computing is an attractive area of
research. Like nature inspired computing, their applications areas are also numerous. To list a few,
the nature computing applications include optimization, data analysis, data mining, computer
graphics and vision, prediction and diagnosis, design, intelligent control, and traffic and
transportation systems. Most of the real life problem occurring in the field of science and
engineering may be modeled as nonlinear optimization problems, which may be unimodal or
multimodal [3].
In last few years, many researchers have posed different optimization techniques for enhancing
speed tracking system [4]. A BFA is one such direct search optimization techniques which are based
on the mechanics of natural bacteria and A PSO is one such direct search optimization techniques
which are based on the behavior of a colony or a swarm of insects, such as ants, termites, bees and
wasps. Advantages of the BFA and PSO for auto tuning are that they do not need gradient
information and therefore can operate to minimize naturally defined cost functions without complex
mathematical operations [5]. However, PSO suffers from the partial optimism, which causes the less
exact at the regulation of its speed and the direction. In addition, the algorithm cannot work out the
problems of scattering and optimization. Also, the algorithm pains from slow convergence in refined
search stage, weak local search ability and algorithm may lead to possible entrapment in local
minimum solutions. Moreover, BFOA due to its unique dispersal and elimination technique can find
favorable regions when the population involved is small. These unique features of the algorithms
overcome the premature convergence problem and enhance the search capability. Hence, it is
suitable optimization tool for power system controllers [4].
2. Mathematical Model of Separately Excited D.C. Motor
Figure (1) shows the equivalent circuit with armature voltage control and the model of a general
mechanical system that incorporates the mechanical parameters of the motor and the mechanism
coupled to it [6].
Figure 1: Equivalent circuit of separately excited dc motor
The characteristic equations of the DC motor are represented as,
(
(
(
)
(1)
)
(2)
)
(3)
1941
International Journal of Mechatronics, Electrical and Computer Technology (IJMEC)
Universal Scientific Organization, www.aeuso.org
WISAM NAJM AL-DIN ABED / Vol. 5(14) Jan. 2015, PP. 1940-1948
IJMEC DOI: 649123/10116
Where the is the development electrical torque, is the back EMF, B denotes the viscous friction
coefficient, and J is the moment of inertial [7]. The armature circuit consists of an inductor L a and
resistor Ra in series with a counter electromotive force which is proportional to the DC motor speed
[8].
(4)
is the voltage constant and is the machine angular speed. In a separately excited DC machine
model, the voltage constant
is proportional to the field current ( ) as in (5).
(5)
Where
is the field armature mutual inductance. The electromechanical torque (Te) developed by
the DC machine is proportional to the armature current ( ) as in (6).
(6)
Where
is the torque constant. In the SI unit, the torque and voltage constants are equal as in (7).
(7)
3. Bacterial Foraging Optimization
The Bacterial Foraging Optimization (Passino 2002) is based on foraging strategy of E. coli bacteria.
The foraging theory is based on the assumption that animals obtain maximum energy nutrients ‘E’ in
a suppose to be a small time ‘T’. The basic Bacterial Foraging Optimization consists of three principal
mechanisms; namely chemotaxis, reproduction and elimination-dispersal. The brief descriptions of
these steps involved in Bacterial Foraging are presented below [3]. To define our optimization model
of E. coli bacterial foraging, we need to define a population (set) of bacteria, and then model how
they execute chemotaxis, swarming, reproduction, and elimination/dispersal. After doing this, we
will highlight the limitations (inaccuracies) in our model [9].
3.1. Chemotaxis
The movement of E. coli bacteria in the human intestine in search of nutrient-rich location away
from noxious environment is accomplished with the help of the locomotory organelles known as
flagella by chemotactic movement in either of the ways, that is, swimming (in the same direction as
the previous step) or tumbling (in an absolutely different direction from the previous one). Suppose
θi(j, k, ℓ) represents the ith bacterium at jth chemotactic, kth reproductive, and ℓth eliminationdispersal step. Then chemotactic movement of the bacterium may be mathematically represented by
Equation (8). In the expression, C(i) is the size of the unit step taken in the random direction, and Δ(i)
indicates a vector in the arbitrary direction whose elements lie in [−1, 1] as follows:
θi(j+1,k,ℓ) = θi(j,k,ℓ) + C(i)
√
()
(8)
() ()
3.2. Swarming
This group behavior is seen in several motile species of bacteria, where the cells, when stimulated
by a high level of succinate, release an attractant a spertate. This helps them propagate collectively
as concentric patterns of swarms with high bacterial density while moving up in the nutrient
gradient. The cell-to-cell signaling in bacterial swarm via attractant and repellant may be modeled by
Equation (9), where Jcc(θ(i, j, k, ℓ)) specifies the objective function value to be added to the actual
objective function that needs to be optimized, to present a time varying objective function, S
1942
International Journal of Mechatronics, Electrical and Computer Technology (IJMEC)
Universal Scientific Organization, www.aeuso.org
WISAM NAJM AL-DIN ABED / Vol. 5(14) Jan. 2015, PP. 1940-1948
IJMEC DOI: 649123/10116
indicates the total number of bacteria in the population, p is the number of variables to be
optimized, and θ= *θ1, θ2, . . . , θp]T is a point in the p-dimensional search domain. The coefficients
dattractant,wattractant, hrepellant, and wrepellant are the measure of quantity and diffusion rate of
the attractant signal and the repellant effect magnitude, respectively [10],
Jcc(θ(i, j, k, ℓ)) = ∑
∑
(θ θ (
(
*
ℓ)) = ∑
∑
(
*
(θ
∑
(θ
θ ) )+
θ ) )++
(9)
3.3. Reproduction
For every Nctimes of chemotactic steps, a reproduction step is taken in the bacteria population.
The bacteria are sorted in descending order by their nutrient obtained in the previous chemotactic
processes. Bacteria in the first half of the population are regarded as having obtained sufficient
nutrients so that they will reproduce. Each of them splits into two (duplicate one copy in the same
location). Bacteria in the residual half of the population die and they are removed out from the
population. The population size remains the same after this procedure. Reproduction is the
simulation of the natural reproduction phenomenon. By this operator, individuals with higher
nutrient are survived and duplicated, which guarantees that the potential optimal areas are searched
more carefully [11]. The fitness value for ith bacterium after travelling Ncchemotactic steps can be
evaluated by the following equation:
=∑
(
ℓ)
(10)
Here
represents the health of ith bacterium. The least healthy bacteria constituting half of the
bacterial population are eventually eliminated while each of the healthier bacteria asexually split into
two, which are then placed in the same location. Hence, ultimately the population remains constant
[10].
3.4. Eliminate and Dispersal
In nature, the changes of environment where population lives may affect the behaviors of the
population. For example, the sudden change of temperature or nutrient concentration, the flow of
water, all these may cause bacteria in the population to die or move to another place. To simulate
this phenomenon, eliminate-dispersal is added in the BFO algorithm. After every Nre times of
reproduction steps, an eliminate-dispersal event happens. For each bacterium, a random number is
generated between 0 and 1. If the random number is less than a predetermined parameter, known
as Pe, the bacterium will be eliminated and a new bacterium is generated in the environment. The
operator can be also regarded as moving the bacterium to a randomly produced position. The
eliminate-dispersal events may destroy the chemotactic progress. But they may also promote the
solutions since dispersal might place the bacteria in better positions. Overall, contrary to the
reproduction, this operator enhances the diversity of the algorithm [11].
4. Simulation and Results
A mathematical model of SEDM is simulated using MATLAB toolbox based on it's dynamic
electrical and mechanical equations. The armature control method is simulated with feeding back the
armature current (Ia) and motor angular speed (ɷ) as a state variables that must be measured. The
state variables are sensed and adjusted using appropriate state feedback controller gains (K1 and K2).
The parameters values of SEDM used are shown in Table (1).
1943
International Journal of Mechatronics, Electrical and Computer Technology (IJMEC)
Universal Scientific Organization, www.aeuso.org
WISAM NAJM AL-DIN ABED / Vol. 5(14) Jan. 2015, PP. 1940-1948
IJMEC DOI: 649123/10116
Table 1: SEDM parameters
Motor ratings and parameters
values
Power
Armature voltage
Speed
Field voltage (Vf)
Armature resistance (Ra)
Armature inductance (La)
Field resistance (Rf)
Field inductance (Lf)
Laf
Inertia of the rotor (J)
damping coefficient (B)
5 HP
240 V
183.2596 radian/second
150 V
0.78 Ω
0.016 H
150 Ω
112.5 H
1.234 H
2
0.05 Kg.m
0.01N.m.s
4.1. Simulation of SEDM Using Matlab/Simulink
The proposed mathematical model is developed from the mechanical and electrical dynamic
equations of the SEDM (Equations (1-7)). Figure (1) and Figure (2) show the the internal and complete
closed loop simulink models respectively of SEDM with state feedback controllers for.
Figure 1: Internal Simulink model of SEDM
Figure 2: Armature control system of SEDM with state feedback controller
The parameters of BFO algorithm are listed in Table (2), while the obtained controller's parameters
are listed in Table (3).
1944
International Journal of Mechatronics, Electrical and Computer Technology (IJMEC)
Universal Scientific Organization, www.aeuso.org
WISAM NAJM AL-DIN ABED / Vol. 5(14) Jan. 2015, PP. 1940-1948
IJMEC DOI: 649123/10116
Table 2: BFO parameters used in tuning state feedback controller
BFO parameters
Number of bacteria in the population (s)
The length of swim (Ns)
Number of reproduction steps (Nre)
Number of chemotactic step (Nc)
Number of elimination/dispersal events (Ned)
Parameters values
10
2
4
10
2
Table 3: State feedback controller's parameters
Controller parameters
Armature control method
K1
1359.9973
K2
0.0014279
Figures (3) shows the bacteria (S=10) motility behavior (bacteria trajectories) and the average cost
plots for each generation for two elimination/dispersal events (Ned =2) for tuning the controller
parameters. The particular values of the parameters were chosen with the nutrient profile that
would used are illustrated in Figures (3-g).
1000
1360
5
Iteration, j
Generation=3
1359.98
10
1360.02
5
Iteration, j
Generation=4
0
10
1360.03
1360
1360.02
0
5
Iteration, j
10
1360.01
0
5
Iteration, j
Generation=3
1359.98
1360.01
1359.96
1360
0
5
Iteration, j
10
Generation=2
0
5
Iteration, j
10
-0.01
10
K2
-50
10
6
0
5
Iteration, j
10
-5
x 10
5
Iteration, j
Generation=3
Generation=2
0
5
Iteration, j
Generation=4
10
5
Iteration, j
10
0
-5
10
-3
10
4
0
-2
0
-3
K2
K2
x 10
5
Iteration, j
Generation=4
5
0
-4
0
-3
2
x 10
0
K2
4
x 10
10
-3
5
K2
K2
-3
5
Iteration, j
Generation=3
10
1360
50
0
-0.005
0
5
Iteration, j
1360.01
1359.99
100
0.005
K2
-5
0
1360.02
Generation=1
0.01
0
10
(b)
Generation=1
5
5
Iteration, j
Generation=4
5
2
0
0
0
5
Iteration, j
10
(c)
-2
x 10
K2
-3
x 10
0
1360.03
(a)
10
1360
10
K1
K1
K1
1359.99
1359.98
0
1360.02
1360.01
1360
1360.02
500
1359.99
0
1000
K1
1100
1360.03
K1
1360.01
1200
1500
K1
1300
Generation=2
Generation=1
Generation=2
1360.02
K1
K1
Generation=1
1400
0
5
Iteration, j
10
-5
0
(d)
1945
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Universal Scientific Organization, www.aeuso.org
WISAM NAJM AL-DIN ABED / Vol. 5(14) Jan. 2015, PP. 1940-1948
IJMEC DOI: 649123/10116
Bacteria trajectories, Generation=2
30
20
20
20
20
K2
10
0
10
10
0
K2
Bacteria trajectories, Generation=1
30
K2
Bacteria trajectories, Generation=2
30
K2
Bacteria trajectories, Generation=1
30
0
10
20
30
K1
Bacteria trajectories, Generation=3
30
20
30
K1
Bacteria trajectories, Generation=4
30
20
20
20
20
10
0
10
10
0
10
20
0
30
10
K2
10
K2
K2
0
0
0
10
K1
20
30
0
10
0
10
K2
20
30
K1
Bacteria trajectories, Generation=4
30
10
0
0
20
30
K1
Bacteria trajectories, Generation=3
30
0
10
0
10
20
0
30
K1
K1
20
30
K1
(e)
(f)
Nutrient concentration (valleys=food, peaks=noxious)
6
4
z=J
2
0
-2
-4
30
30
20
20
10
y=K2
10
0
0
x=K1
(g)
0.115
0.114
0.112
0.112
0.11
0
5
Iteration, j
Generation=3
0.108
10
Generation=2
0.116
0.114
0.11
0.112
0.108
0
5
Iteration, j
Generation=4
0.106
10
0
5
Iteration, j
Generation=3
0.11
10
0.118
0.115
0.112
0.116
0.114
0.112
0.11
0.114
0.11
0.108
0.112
0.108
0.106
0.11
0
5
Iteration, j
10
0
5
Iteration, j
10
(h)
cost
0.114
0.114
cost
0.116
cost
cost
0.114
cost
cost
cost
0.12
0.11
Generation=1
Generation=2
0.116
cost
Generation=1
0.125
0
5
Iteration, j
Generation=4
10
0
5
Iteration, j
10
0.113
0.112
0
5
Iteration, j
10
0.111
(i)
Figures (3): Bacteria trajectories and average cost plot for tuning the controller parameters
(a), (b) first& second elimination/dispersal event for (K1) respectively
(c), (d) first& second elimination/dispersal event for (K2) respectively
(e), (f) contour plot for first & second elimination/dispersal event for (K1 &K2)
(g) Surface plot for nutrient landscape
(h), (i) average cost plot for first& second elimination/dispersal event respectively
1946
International Journal of Mechatronics, Electrical and Computer Technology (IJMEC)
Universal Scientific Organization, www.aeuso.org
WISAM NAJM AL-DIN ABED / Vol. 5(14) Jan. 2015, PP. 1940-1948
IJMEC DOI: 649123/10116
Figures (5) show torque, voltages, speed and speed error of the SEDM.
Torque of SEDM with Armature Control System
Back EMF of SEDM with Armature Control System
250
1200
Full-Load
Full-Load
1000
200
800
Back EMF (V)
Torque (N.m)
600
400
200
150
100
0
-200
50
-400
-600
0
0.02
0.04
0.06
0.08
0.1
0.12
Time (Sec.)
0.14
0.16
0.18
0
0.2
0
0.5
1
1.5
(a)
2
2.5
Time (Sec.)
3
3.5
4
4.5
5
(b)
Speed of SEDM with Armature Control System
Speed Error of SEDM with Armature Control System
250
250
Full-Load
Full-Load
200
Speed Error (rad/Sec.)
Speed (rad/Sec.)
200
150
100
150
100
50
0
50
-50
0
0
0.02
0.04
0.06
0.08
0.1
0.12
Time (Sec.)
0.14
0.16
0.18
0.2
0
0.02
0.04
(c)
0.06
0.08
0.1
0.12
Time (Sec.)
0.14
0.16
0.18
0.2
(d)
Figures (5): Time responses of SEDM for armature control at full-load
(a) Torque (N.m) (b) Back EMF (V)(c) Angular speed (rad/sec.) (d)Speed Error (rad/sec.)
The time response specifications of SEDM speed are listed in Table (4) for armature control systems.
Table 4: Time response specifications
Rise time (Sec.)
Peak time (Sec.)
Overshoot (rad/Sec.)
Settling time(Sec.)
SEDM at full-load
0.015
0.02
234.175
0.056
Armature control has the advantage of controlling the armature current swiftly, by adjusting the
applied voltage. The response is determined by the armature time constant, which has a very low
value. The large time constant of the field causes the response of a field-controlled dc motor drive to
be slow and sluggish. Armature control is limited in speed by the limited magnitude of the available
dc supply voltage and armature winding insulation. If the supply dc voltage is varied from zero to its
nominal value, then the speed can be controlled from zero to nominal or rated value. Therefore,
armature control is suitable for rated speed and speeds lower than rated speed while field control is
suitable for speeds greater than the rated speed.
1947
International Journal of Mechatronics, Electrical and Computer Technology (IJMEC)
Universal Scientific Organization, www.aeuso.org
WISAM NAJM AL-DIN ABED / Vol. 5(14) Jan. 2015, PP. 1940-1948
IJMEC DOI: 649123/10116
Conclusions
In this work the state feedback controller parameters are tuned based foraging for speed control
of SEDM. From simulation results the following tips can be concluded:
1) BFO due to its unique dispersal and elimination technique can find favourable regions when
the population involved is small. These unique features of the algorithms overcome the
premature convergence problem and enhance the search capability.
2) BFO technique required less execution time, due to the small numbers of populations.
3) BFO technique has fast convergence ability.
4) BFO technique has potential to be useful for other practical optimization problems (e.g.,
engineering design, online distributed optimization in distributed computing, and
cooperative control) as social foraging models work very well in such environments.
5) Armature control is suitable for rated speed and speeds lower than rated speed.
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1948
International Journal of Mechatronics, Electrical and Computer Technology (IJMEC)
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