Armature Voltage Speed Control of DC Motors Based Foraging ...aeuso.org/.../Vol5_Iss14_1940...Speed_Control_of_D.pdf · control etc. [1].DC motors provide excellent control of speed

Vol. 5(14) Jan. 2015, PP. 1940-1948

1940

Article History:

IJME DOI: 649123/10116 Received Date: Dec. 07, 2014 Accepted Date: Feb. 03, 2015 Available Online: Feb. 14, 2015

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: [email protected]

Abstract

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].

T

mailto:[email protected]

WISAM NAJM AL-DIN ABED / Vol. 5(14) Jan. 2015, PP. 1940-1948 IJMEC DOI: 649123/10116

1941

International Journal of Mechatronics, Electrical and Computer Technology (IJMEC)

Universal Scientific Organization, www.aeuso.org

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)


1942



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 La 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 elimination-dispersal 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


1943



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).


1944



Table 1: SEDM parameters

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).

Motor ratings and parameters values Power 5 HP

Armature voltage 240 V

Speed 183.2596 radian/second

Field voltage (Vf) 150 V

Armature resistance (Ra) 0.78 Ω

Armature inductance (La) 0.016 H

Field resistance (Rf) 150 Ω

Field inductance (Lf) 112.5 H

Laf 1.234 H

Inertia of the rotor (J) 0.05 Kg.m2

damping coefficient (B) 0.01N.m.s


1945



Table 2: BFO parameters used in tuning state feedback controller

BFO parameters Parameters values

Number of bacteria in the population (s) 10

The length of swim (Ns) 2

Number of reproduction steps (Nre) 4

Number of chemotactic step (Nc) 10

Number of elimination/dispersal events (Ned) 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).

(a) (b)

(c) (d)

0 5 101000

1100

1200

1300

1400Generation=1

Iteration, j

K1

0 5 101359.98

1359.99

1360

1360.01

1360.02Generation=2

Iteration, j

K1

0 5 101359.98

1359.99

1360

1360.01

1360.02Generation=3

Iteration, j

K1

0 5 101359.96

1359.98

1360

1360.02Generation=4

Iteration, j

K1

0 5 100

500

1000

1500Generation=1

Iteration, j

K1

0 5 101360

1360.01

1360.02

1360.03Generation=2

Iteration, j

K1

0 5 101360

1360.01

1360.02

1360.03Generation=3

Iteration, j

K1

0 5 101359.99

1360

1360.01

1360.02

1360.03Generation=4

Iteration, j

K1

0 5 10-5

0

5

10x 10

-3 Generation=1

Iteration, j

K2

0 5 10-0.01

-0.005

0

0.005

0.01Generation=2

Iteration, j

K2

0 5 10-4

-2

0

2

4x 10

-3 Generation=3

Iteration, j

K2

0 5 10-5

0

5

10x 10

-3 Generation=4

Iteration, j

K2

0 5 10-50

0

50

100Generation=1

Iteration, j

K2

0 5 10-5

0

5x 10

-3 Generation=2

Iteration, j

K2

0 5 10-2

0

2

4

6x 10

-3 Generation=3

Iteration, j

K2

0 5 10-5

0

5

10x 10

-3 Generation=4

Iteration, j

K2


1946



(e) (f)

(g)

(h) (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

Bacteria trajectories, Generation=1

K1

K2

0 10 20 300

10

20

30Bacteria trajectories, Generation=2

K1

K2

0 10 20 300

10

20

30


K1

K2

0 10 20 300

10

20


K1

K2

0 10 20 300

10

20

30


K1

K2

0 10 20 300

10

20


K1

K2

0 10 20 300

10

20

30


K1

K2

0 10 20 300

10

20


K1

K2

0 10 20 300

10

20

30

0

10

20

30

0

10

20

30-4

-2

0

2

4

6

x=K1

Nutrient concentration (valleys=food, peaks=noxious)

y=K2

z=

J

0 5 100.11

0.115

0.12

0.125Generation=1

Iteration, j

cost

0 5 100.108

0.11

0.112

0.114

0.116Generation=2

Iteration, j

cost

0 5 100.108

0.11

0.112

0.114

0.116Generation=3

Iteration, j

cost

0 5 100.106

0.108

0.11

0.112

0.114Generation=4

Iteration, j

cost

0 5 100.106

0.108

0.11

0.112

0.114Generation=1

Iteration, j

cost

0 5 100.11

0.112

0.114

0.116Generation=2

Iteration, j

cost

0 5 100.11

0.112

0.114

0.116

0.118Generation=3

Iteration, j

cost

0 5 100.111

0.112

0.113

0.114

0.115Generation=4

Iteration, j

cost


1947



Figures (5) show torque, voltages, speed and speed error of the SEDM.

(a) (b)

(c) (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.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-600

-400

-200

0

200

400

600

800

1000

1200

Time (Sec.)

Torq

ue (

N.m

)

Torque of SEDM with Armature Control System

Full-Load

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

50

100

150

200

250

Time (Sec.)

Back E

MF

(V

)

Back EMF of SEDM with Armature Control System

Full-Load

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

0

50

100

150

200

250

Time (Sec.)

Speed (

rad/S

ec.)

Speed of SEDM with Armature Control System

Full-Load

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

-50

0

50

100

150

200

250

Time (Sec.)

Speed E

rror

(rad/S

ec.)

Speed Error of SEDM with Armature Control System

Full-Load


1948



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.

References [1] R. C. Chourasiaand M. Kumar, "Speed Control of S.E.D.C. Motor by Using Pi and Fuzzy Logic Controller", International Journal of Soft Computing and Engineering (IJSCE) ISSN: 2231-2307, Volume-3, Issue-2, May 2013. [2] R. Abhinav, J. Masand, P. Vidyarthi, G. Kumari, and N. Gupta," Separately Excited DC Motor Speed Control Using Four Quadrant Chopper", International Journal of Scientific & Engineering Research Volume 4, Issue 1, January-2013. [3] B. K. Panigrahi,Y. Shi, and M. Lim, "Handbook of Swarm Intelligence", Springer-Verlag Berlin Heidelberg, 2011. [4] A. S. Oshabaa and E. S. Ali, "Bacteria Foraging: A New Technique for Speed Control of DC Series Motor Supplied by Photovoltaic System", WSEAS TRANSACTIONS on POWER SYSTEMS, Volume 9, 2014. [5] A. H. Abo absa, M.A. Alhanjouri, "PID PARAMETERS OPTIMIZATION USING BACTERIA FORAGING ALGORITHM AND PARTICLE SWARM OPTIMIZATION TECHNIQUES FOR ELECTROHYDRAULIC SERVO CONTROL SYSTEM", The 4th International Engineering Conference –Towards engineering of 21st century, Copyright © 2012 IUG. [6] W. I. Hameed and K. A. Mohamad, "SPEED CONTROL OF SEPARATELY EXCITED DC MOTOR USING FUZZY NEURAL MODEL REFERENCE CONTROLLER", International Journal of Instrumentation and Control Systems (IJICS) Vol.2, No.4, October 2012. [7] C. LIU, B. LI, X. YANG, "Fuzzy Logic Controller Design Based on Genetic Algorithm for DC Motor", 978-1-4577-0321-8/11/$26.00 ©2011 IEEE. [8] V. Tipsuwanpom, A. Numsomran, N. Klinsmitth, S. Gulphanich, "Separately Excited DC Motor Drive With Fuzzy Self-Organizing", International Conference on Control, Automation and Systems 2007 Oct. 17-20, 2007 in COEX, Seoul, Korea. [9]V. Gazi and K. M. Passino, "Swarm Stability and Optimization", Springer Science + Business Media B.V. 2011. [10] S. S. Patnaik and A. K. Panda, "Particle Swarm Optimization and Bacterial Foraging Optimization Techniques for Optimal Current Harmonic Mitigation by Employing Active Power Filter", Hindawi Publishing Corporation Applied Computational Intelligence and Soft Computing Volume 2012, Article ID 897127, 10 pages. [11] X. Yan, Y. Zhu, H. Zhang, H. Chen, and B. Niu, "An Adaptive Bacterial Foraging Optimization Algorithm with Lifecycle and Social Learning", Hindawi Publishing Corporation Discrete Dynamics in Nature and Society Volume 2012, Article ID 409478, 20 pages.

Documents

Armature Voltage Speed Control of DC Motors Based Foraging ...aeuso.org/.../Vol5_Iss14_1940...Speed_Control_of_D.pdf · control etc. [1].DC motors provide excellent control of speed