Journal of Control Engineering and Technology

JCET

PID Controller Auto Tuning using ASBO Technique Sridhar N 1, Nagaraj Ramrao2, Manoj Kumar Singh3 1,2

The Oxford College of Engineering ,Bangalore, India. 3 Manuro Tech Research , Bangalore, India 1 [email protected]; [email protected]; [email protected] Abstract- Despite the popularity and usability of proportional– integral-derivative (PID) controllers in industrial applications, still its auto tuning is a challenge for researchers in terms of applied algorithmic efficiency and optimal definition of performance index. With a belief, compare to other species society, at present human society is more properly organized and developed; a new optimization method based on human social behavior called adaptive social behavior optimization (ASBO) has applied in this paper to auto tune the PID controller parameters in regards to achieving the global solution. A robust fitness function as performance index has also designed to get better exploration for optimal tuning in terms of various performance parameters. Experiments have given, with a number of systems having different types of characteristics and complexity like quadrotor, automatic voltage regulator (AVR) and DC motor systems etc. To understand the relative benefits of the proposed method, performance comparison with the number of other frequently applied algorithms in literatures like Genetic algorithm (GA) and its variant called self organize genetic algorithm (SOGA), Differential Evolution (DE), an extension of probabilistic distribution based Chaotic estimation of distribution algorithms (CEDA),Chaotic optimization and Convex-Concave optimization have presented with various practically applied fitness criteria’s in practice. Proposed method of auto tuning has shown the generalized applicability for PID controller design with different types of systems in optimum manner. Keywords- PID Controller; Auto tuning; ASBO; Genetic and Differential evolution; Quadrotor; AVR

I.

INTRODUCTION

With the three-term functionality, PID controller is having capability to cover the treatment to both transient and steady-state responses. Proportional-integral-derivative (PID) control offers the simplicity in architecture and yet most efficient solution to many real-world control problems, hence widely applied in industrial application around 90% of controller requirement. To enhance the capabilities of traditional PID tuning methods, many new solutions have been proposed such as several approaches have been documented in literatures for determining the PID parameters of such controllers which is first found by Ziegler Nichols tuning [1]. However, the conventional tuning methods for PID controller design might fail to achieve satisfactory performance when the plants are of high order, have time delay, are nonlinear and so on .Hence approaches based on artificial intelligence are taken as an alternate solution domain to solve this problem. In this regard, Genetic Algorithm [2], [11], [12], Neural network [3], [15], Fuzzy based approach [4], Particle swarm optimization techniques [5], [6], Bacterial foraging algorithm [13] are just a few. An overview on modern PID

technology including PID software packages, commercial PID hardware modules and patented PID tuning rules are presented in [7]. In this paper, a generalized method for designing the PID controller with a new performance index has presented. This method is based on the recently developed a new optimization method inspired by adaptive social behaviour of human society, called ASBO [9]. Chaotic version of Estimation of distribution algorithms (EDAs) has applied in [17] for quadrotor controller design. This is based on defining the distribution of better solution in the search process and chaos has included in obtaining the fine tune solution under available distribution. An extension of genetic algorithm called self organise genetic algorithm (SOGA) has proposed by Zhang in [18].They have tried to increase the capability of genetic algorithm to achieve the global solution with a variation of mutation operator and have applied to tune the controller for two different plants. A comparative study has made in [19] between differential evolution and genetic algorithm for different plants with various indices for tuning the corresponding controller. Based on concave-convex optimization, PID tuning has presented in [20].A hybrid strategy based on genetic algorithm and bacterial foraging algorithm has presented in [21].They have shown its relative benefit over individual algorithm for numeric optimization .They have applied the same for tuning the controller of AVR. Chaotic optimization based on Lozi Map has applied in [22] for tuning the AVR system for different conditions. The Concept of better exploration of the global solution by using the chaotic sequence in two stages has applied. In the section II understanding of PID controller presented with various performance indices including proposed one along with others available in literatures have given. Section III has a detail discussion about ASBO. Experimental results and discussion of numeric optimization have given in section IV. Tuning of PID with different plants has given in section V and conclusion has appeared in section VI. II.

PROPOSED PERFORMANCE INDEX FOR PID CONTROLLER

A PID controller may be considered as an extreme form of a phase lead-lag compensator with one pole at the origin and the other at infinity [7].A standard PID controller transfer function is generally written in the parallel form and given by (1). G (s ) = K P + K I

1 + KDs s

JCET Vol. 4 Iss. 3 July 2014 PP. 192-204 www.ijcet.org © American V-King Scientific Publish 192

 (1)

Journal of Control Engineering and Technology

JCET

Where KP, KI, KD is the proportional gain, the integral gain, the derivative gain. Functioning characteristics of these three parameters are defined as: •

The proportional term—providing an overall control action proportional to the error signal through the all-pass gain factor

•

The integral term—reducing steady-state errors through low-frequency compensation by an integrator.

•

The derivative term—improving transient response through high-frequency compensation by a differentiator.

Let be the continuously differentiable matrix real 3 function defined for , where { |0 i ∞,for i=1,2,3}. The auto tuning can be defined as an optimization problem involves finding *= [KP*,KI*,KD*] such that the defined performance index of the system is minimized. In general, for a controller design, the performance criterion or objective function can be defined according to our desired specifications and constraints under input testing signal. Typical output specifications in the time domain to understand the system response are the peak overshoot, rise time, settling time, and steady-state error. A number of performance indices have been introduced in past with respect to describe the goodness of the system response like integral square error (ISE) in eq.(2), Integral of the absolute magnitude of error (IAE) in eq.(3),integral error (IE) in eq.(4), mean square error(MSE) in eq.(5), integral time absolute error (ITAE) in eq.(6) and integral time square error (ITSE) in eq.(7) are some of them. ITAE and ITSE have developed with the concept to reduce the weighting of the large initial error and to penalize the small errors occurring later in the response more heavily. The ITAE performance index produces smaller overshoot and oscillations than the IAE and ISE indices. In addition it is most sensitive of among all, i.e. it has the best selectivity; hence in practice ITAE is taken as a better choice. But for many applications even smaller overshoot of ITAE is having its own implication from a practical point of view. T

2

f ISE = e(t ) dt

∫

(2)

0

T

f IAE =

∫ e(t )dt

(3)

0

T

f IE = e(t )dt

∫

(4)

Quality of index has a huge effect to the final solution quality, because the applied algorithm tries to minimize the index criteria, in result, as accordingly the final performance parameters appears. In most of the cases focus has given to reduce the overshoot but overall performance does not become very satisfactory. There are some indices reported in literatures which have crafted to increase the quality of performance parameters by imbedding the combination of performance parameters like in [17],[18],as defined in eq.(8) and in [21] as given in eq.(9),but they are not only complex but many times could not deliver the optimal tuning. To reduce the effect of overshoot an index has proposed in [22] as in eq. (10). w

J = W1 e(t ) + W 2 u 2 (t )dt + W3 t u }K IF → e(t ) ≥ 0

∫ 0

(8)

else W

∫W

1

e(t ) + W 2 u 2 (t )dt + W 4 e(t ) + W3 t u

0

Where is the objective function, e(t ) is the error, u (t ) is the output of controller and t u is the rise time, W1 , W 2 , W3 , W 4 are the weights and W 4 ≥ W1 .

CX =

⎛ t ⎞ e − β ⎜⎜ s + αM O ⎟⎟ ⎝ max(t ) ⎠

α

(9)

where

(

)

α = 1− e − β 1 −

f MSE

T

2

∫ e(t ) dt

(5)

f ITAE = t e(t )dt

∫

(6)

0

T

2

f ITSE = te(t ) dt

∫ 0

(7)

(

f mp = t (e(t ))dt + W Max(Vt ) − V ref

∫

T

0

)

(10)

Where W is the weight factor which takes care of peak overshoot. To overcome issues faced by previously available indices, a different performance index has proposed in this paper which is a linear combination of IATE and weighted factor of performance parameters in the time domain includes overshoot (Mp), rise time (Tr), settling time (Ts) , steady state error (Ess) and difference of settling and rise time as given by eq. (11)

[

]

T Mx = ∫ t e(t ) dt + ⎛⎜1 − e − β ⎞⎟ M P + E SS + Tr + ⎝ ⎠ (11) 0 e − β T S − Tr Where β is the weighing factor and larger value will have smaller rise time and a little away from settling point and smaller value will have larger rise time but closer to settle point, a moderate value will try to make balance hence in this paper it is taken as 1.5.

[

0

T

tr max(t )

Where   is  the  weighing factor, M o →Overshoot, t s →Settling time, e ss →steady state error, t →Desired settling time.

0

1 = T

+ e ss

]

JCET Vol. 4 Iss. 3 July 2014 PP. 192-204 www.ijcet.org © American V-King Scientific Publish 193

Journal of Control Engineering and Technology

JCET

III. ADAPTIVE SOCIAL BEHAVIOR OPTIMIZATION (ASBO) ASBO is a very new heuristic and stochastic search method inspired by human social behavior to obtain the global solution, has developed by Singh [9].Social interactions enable individuals to adapt and improve faster than biological evolution based on the genetic inheritance alone. This is the driving concept behind the optimization algorithm that makes use of the competition and influence available within a formal society. Particle swarm optimization and ant colony algorithms are two very successful and established computing models already justifying the importance of the above statements. These two computing models are having the bias reference of social life activities with respect to species like bird, fish or specie like ants. In ASBO optimization process, behavior of entity to inspire automatically by various social elements has taken as fundamental operators to optimize the solution iteratively. This is a well known fact that, most of actions human take in his/her life are the result of social influences. The nature and characteristics of influence may be different from person to person and time to time. In ASBO, three macro social influence operators namely: inspiration by leader, inspiration by neighbours and self inspiration have taken. Level of influences is defined by corresponding adaptive constants. These constants play very important role to change the status of the individual, because influence is dynamic with time variable hence it can not be fixed for all life periods. The Adaptive characteristics of these constants have defined by self adaptive mutation strategy. Mathematical modelling for ASBO is given below. There are two populations; of one we can call solution population other can call influenced factor population. Each member of solution population represents the solution in a phenotype format (direct form i.e. not in coded form) and influence factor population contains the same number of members as solution population has with three parameters each corresponding to leader, neighbours and self influence. With respect to problem at hand using the fitness function a fitness value for each and every member defined. An Individual having the maximum value of fitness treated as leader at the present time. A group of individuals having next nearest higher value of fitness will be treated as neighbours for a particular individual. The change in existing status because of influence is innovated by each and every member of the population using (12) and the next location of status given by (13). ΔX (i + 1) = C g R g (Gbi − X i ) + C s R s (S bi − X i ) + C n R n (N ci − X i )

X (i + 1) = X i + ΔX (i + 1)

(12) (13)

Where ΔX(i+1) represents the new change in i’th dimension of an individual element. Cg, Cs, Cn are adaptive progress constants ≥ 0;Rg , Rs , Rn are uniformly distributed random number in range [0 1], Gb , global best individual at present population’s, Sb is the self best for an individual till present and Nc is the center position of a group formed by an

individual and its neighbours in present population, For a Ddimensional problem, Gb, Sb, & Nc represent vectors of D-dimension. Gb =[Gb1, Gb2, Gb3, Gb4 ... .... ... GbD]; Sb =[Sb1, Sb2, Sb3, Sb4 ... .... ... …SbD]; Nb =[Nb1, Nb2, Nb3, Nb4 ... .... ... NbD]; A. Evolution of New Set of Progress Constant A population of N initial random solution initialized. Each solution is taken as a pair of real valued vector called progress constant vector (pi) and strategy parameter vector (σi), with each vector there are three dimensions corresponding to the number of adaptive progress constant. The initial components of each pi, i∈ {1..... N},, were selected in accordance with a uniform distribution ranging over a presumed constant space. The values of σi i∈ {1..... N}, were initially set to some smaller value. A new solution ( p i , σ i ) generated from each previous solution '

'

( pi , σ i ) by eq. (14) and corresponding strategy parameters upgraded by using eq. (15).

pi' ( j ) = pi ( j ) + σ i ( j )N (0,1)

σ i' ( j ) = σ i ( j )e (τ

'

N (0,1) +τN J (0,1))

(14)

(15)   

j ∈ {1,2,3} Where p i ( j ), p i' ( j ), σ i ( j ), σ i' ( j ) denote the jth component of the vectors p i , p i' , σ i , σ i' respectively and N(0,1) is a random number from Gaussian distribution. Nj(0,1) is a new random number sampled for each value of the counter j using Gaussian distribution. ’ and are constants. There are two phases under which the whole process to get the global solution. (i) A PF number of different populations having same population size (PZ) initially are taken and ASBO method is applied independently up to a fix number of iterations say P. At the end, values of fitness and all progress constants are stored for each and every member from each final population. This phase will help to maintain the diversity and in result better exploration to localize the region of the solution. (ii) From all final population, depends upon the fitness, members who are having best PZ number of fitness values are selected to form new population and their existed progress constants are also taken to form the second stage single population. Over this newly generated population ASBO is applied to get the final solution. This phase will help to get the optimal solution in a faster manner. IV. NUMERICAL OPTIMIZATION USING ASBO Three different numeric benchmark problems have taken to analyse the capability of ASBO in delivering the global solution for minimization of functions. Details of benchmark problems are given in Table 1. Population size equal to 20 has taken for all the three cases with 10 different

JCET Vol. 4 Iss. 3 July 2014 PP. 192-204 www.ijcet.org © American V-King Scientific Publish 194

Journal of Control Engineering and Technology

JCET

TABLE I NUMERIC BENCHMARK PROBLEMS

Range [L U]

3

F1 (x) =

∑ i =1

(

[-5.12 5.12]

[0 0 0 ] & 0

[-2.048 2.047]

[1 1] & 0

x i2

)

2

F2 ( x) = 100 x12 − x 2

+ (1 − x1 ) 2

F3 (x ) = 20 + x 2 − 10 cos(2πx ) + y 2 − 10 cos(2πy )

Global solution& optimal value

0

0

[-5.0 5.0]

Obtained solution

Function value

F1 ( x)

[ 0.0393 0.1422 0.0540]*1e-161

0

F2 (x)

[1 1]

0

[0.1274 -0.1244]*1e-08

40 60 Iteration No.

80

100

-5

[0 0] & 0

Function

20

Fig. 3 Parameters convergence by best solution in population in first stage for F1 x 10

0.5

TABLE II .PERFORMANCES OBTAINED WITH ASBO FOR NUMERIC OPTIMIZATION

F3 (x )

x1 x2 x3

0.5

-0.5

0 Variables value

Function

1

Variable value

populations in the first stage. Each population in the first stage has iterated up to 100 iterations whereas termination in second stage is self termination with 200 last iterations had differences in their fitness less than a threshold value 10e-50.Performances for all the three cases have shown in Table 2.

x1 x2 x3

-0.5 -1 -1.5 -2 -2.5

0

500

1000

1500

Iteration No.

0

Fig. 4 Parameters convergence by best solution in population in second stage for F1 3 5

2.5

Obj.fun value

Obj.fun v alue

4

2 1.5 1 0.5 0

3

2

1

0

20

40 60 Iteration No.

80

100

Fig. 1 Objective function convergence by best solution in each population in first stage for F1

0

0

20

40 60 Iteration No.

80

100

Fig. 5 Objective function convergence by best solution in each population in first stage for F2

-9

x 10

-6

4

1.2

3.5

1

3 Obj.fun value

Obj.fun value

1.4

0.8 0.6 0.4

2.5 2 1.5 1

0.2 0 0

x 10

0.5 0

500

1000

1500

Iteration No.

Fig. 2 Objective function convergence by best solution in population in second stage for F1

0

500

1000

1500

Iteration No.

Fig. 6 Objective function convergence by best solution in population in second stage for F2

JCET Vol. 4 Iss. 3 July 2014 PP. 192-204 www.ijcet.org © American V-King Scientific Publish 195

Journal of Control Engineering and Technology

JCET

1

1.003 x1 x2

1.001 1 0.999 0.998

x y

0.5 Parameter Value

Variables Value

1.002

0 -0.5 -1

0.997 -1.5

0.996

0

500

1000

0

20

40 60 Iteration No.

1500

Iteration No.

Fig. 7 Parameters convergence by best solution in population in first stage for F2

80

100

Fig. 11 Parameters convergence by best solution in one population in first stage for F3 -9

2

x 10

1.1

Parameter value

1.05 Parameters Value

1

x1 x2

1

0.95

-1 -2 -3 -4

0.9

0.85

x y

0

0

20

40 60 Iteration No.

80

100

Fig. 8 Parameters convergence by best solution in population in second stage for F2

15

0

50

Obj.fun value

5

0

0

20

40 60 Iteration No.

80

100

Fig. 9 Objective function convergence by best solution in each population in first stage for F3 -15

3.5

x 10

3

Obj.fun value

2.5 2

200

250

300

Convergence characteristics for all the cases have shown in Fig.1 to Fig.12.ASBO have delivered the global solution for all the three test functions. PID AUTO TUNING USING ASBO

Tuning requirement of PID can be considered as an optimization problem and to achieve the global solution in this paper ASBO has applied. Parameters setting for all the different plants are same and have defined in Table 3. System performances have analysed by using the step response of the system in time domain. Time-domain analysis generally considers four different performance parameters for assessing the controller (a) rise-time [tr] :The time required to increase the value from 10% to 90% of final value,(b)settling-time [ts]: time required to damp out oscillations with 2% or 5% of final value. In this research work 2% of oscillations have been considered to calculate settling time.(c) overshoot [MP(%) ] : amount of system output response proceed beyond the desired response. Normally overshoot is given in percentage values and (d) steady-state-error [ess]: difference between output value and real output at final time. TABLE III . ASBO PARAMETERS VALUE FOR PID TUNING

1.5 1 0.5 0

150 Iteration No.

Fig. 12 Parameters convergence by best solution in population in second stage for F3

V. 10

100

0

50

100

150 200 Iteration No.

250

300

Fig. 10 Objective function convergence by best solution in population in second stage for F3

Parameter Name

Value

Population Size

20

First stage population density

10

Adaptive Progress constant range

[0 5]

No. of iteration in 1st stage

100

No. of iteration in 2

nd

stage

Initial strategy parameter

JCET Vol. 4 Iss. 3 July 2014 PP. 192-204 www.ijcet.org © American V-King Scientific Publish 196

100 0.000001

Journal of Control Engineering and Technology

JCET

A. ASBO Based Tuning for DC Motor With Various Performance Indices. The transfer function of the electric DC motor [16] is given in eq.(16).

θ (s )

V (s )

K

=

(

)

(16)

La Js + (R a J + BLa )s 2 + K 2 + R a B s 3

La = armature Inductance; Ra = armature resistance, K = motor constant; J = moment of inertia; B = mechanical friction. The parameters of the electric DC motor have the following value respectively, J=0.042, B=0.01625, K=0.9, La=0.025, Ra=5 as a nominal value. The transfer functions of the electric DC motor after applying the parameter value is defined as in eq. (17). G1 (s ) =

0.9

(17)

0.00105s 3 + 0.2104 s 2 + 0.8913s

To see the effect of performance index over performance parameters, we have applied several commonly used performance indices in literatures and in practice like ISE, IAE, IATE, ITSE, Cx as defined in eq.(2),eq.(3),eq.(6), eq.(7)and in eq.(9) correspondingly. A comparative analysis has given with respect to proposed performance index Mx. Step signal having sample interval of 0.01 for 2 sec has applied. Range for [ K p , K i , K d ] is taken as [0 100] to search the solution. All performance indices have applied with ASBO to tune the PID so that a proper comparison among indices can be justified. The minimization process of objective function Mx has shown in Fig.13. Phase2

Phase1 4

0.4

3.5

0.35

3

0.3

2.5 Mx

Mx

0.25 2

0.2 1.5 0.15

1 0.5

0.1

0

0.05

0

50 Iteration No.

100

0

50 Iteration No.

100

Fig13 Objective function convergence by best solution in each population in 1st and 2nd stage for DC motor

ISE IAE

1.15

A m p litu d e

IATE 1.1

ITSE

1.05

CX Mx

1 0.95

0.9

0.85 0.02

0.03

0.04

0.05

TABLE IV. PID TUNING FOR DC MOTOR WITH VARIOUS INDICES

(DC Motor)

ASBO (ISE)

ASBO (IAE)

ASBO (IATE)

ASBO (ITSE)

ASBO (Cx)

ASBO (Mx)

M p (%)

10.30

12.14

4.55

9.34

0

0

tr

0.0077

0.008

0.017

0.007

0.0230

0.0298

ts

0.0376

0.0384

0.043

0.037

0.0327

0.0466

e ss

0.002

0.0010

0.00

0.001

0.0009

0.0000

kp

100.00

99.999

99.34

100.0

50.07

57.5176

ki

37.881

18.027

0.0021

21.19

2.792

0.0160

kd

64.169

59.804

22.94

66.52

18.34

13.4903

B. Quadrotor Controller tuning using ASBO and CEDA Quadrotor is a type of rotorcraft that consists of four rotors and two pairs of counter rotating, fixed-pitch blades located at the four corners of the body. More recently quadrotor designs have become popular in unmanned aerial vehicle (UAV) research. These vehicles use an electronic control system and electronic sensors to stabilize the aircraft. With their small size and agile manoeuvrability, these quadrotor can be flown indoors as well as outdoors. However, quadrotor is dynamically unstable. In this experiment AR. Drone is taken which is a Wi-Fi-controlled quadrotor with cameras attached to it which is developed by Parrot Inc .Transfer function of quadrotor is taken from [17] is defined as in eq.(18). G 2 (s ) =

Step Response

0.01

For all indices, tuned value of PID parameters and obtained corresponding performance parameters are shown in Table 4. Step response in enlarged view has also presented in Fig.14, with rising and settling time indicators over their corresponding step response. With the observation of performance parameters it is clear that maximum overshoot has observed with IAE while the minimum value obtained with Cx and Mx. Rise time are lesser for ISE,IAE and ITSE and nearly same, whereas larger time taken for IATE, Cx and for Mx but settle time is nearly same for all performance indices. Steady error is zero for only IATE and Mx performance indices. From overall performances, it seems that Mx has delivered better tuning compared to other indices.

0.06

0.07

0.08

0.09

Time (sec)

Fig.14. Step response performances by ASBO with ISE, IAE, IATE, ITSE,Cx and Mx for DC motor

6226 s + 311330

(18) s 3 + 100 s 2 Estimation of distribution algorithms (EDAs) are stochastic optimization methods that explore the space of potential solutions by building and sampling explicit probabilistic models of promising candidate solutions. This explicit use of probabilistic models in optimization may offer some significant advantages over other types of metaheuristics. Here an attempt has given to determine the probability distribution that would give higher probabilities to solutions in the regions with the best solutions available. Once this was completed, sample this distribution to find new candidate solutions to the problem. Ideally, the repeated refinement of the probabilistic model based on representative samples of high quality solutions would keep increasing the probability of generating the global optimum and, after a reasonable number of iterations; the procedure

JCET Vol. 4 Iss. 3 July 2014 PP. 192-204 www.ijcet.org © American V-King Scientific Publish 197

Journal of Control Engineering and Technology

JCET

would locate the global optimum or its accurate approximation. EDA pseudo code Generate initial population, P(0) for first generation, say g = 1

While (Termination criteria does not satisfy) do • Obtain fitness of each solution, Fi • Apply selection operator to select population of promising solutions S (g ) from P(g ) . 

Develop the probabilistic model M (g ) Fig16. Step response performances by EDA and CEDA

• Incorporate N (g ) into P(g ) • g = g +1

End Chaotic estimation of distribution algorithm (CEDA) is a combination of chaos theory and basic EDA. The introduction of chaos theory into basic EDA tries to protect the solution to trap in local optimum. Chaotic search has applied around the best solution obtained in S (g ) by chaotic maps for e.g. logistic equation. Due to the non-repetition characteristics of chaos, it can carry out overall searches at higher speed than stochastic ergodic searches that depend on probabilities. Among the engendered series of solutions, the best one is selected and uses it to replace the former best solution. TABLE V. ASBO AND CEDA COMPARATIVE PERFORMANCES

For the transfer function in eq.(18) we have applied the ASBO with objective function Mx and step response has shown in Fig.15 with same scale as it presented in [17] as appear in Fig.16 for better comparison. Performance parameters for comparison purpose have given in Table 5.The proposed solution has outperformed in all aspects of performances given by CEDA. A range of search for kp,ki and kd have kept [0 2].With observation of obtained performance parameters values it seems that proposed tuning is the optimal choice for quadrotor control design. In Fig.17 objective function minimization with iterations has shown. Phase 2

Phase 1 1.167

1.166

1.1669 1.166

1.1668 1.1667

1.166

1.1666 Mx

• Apply sampling to M (g ) and generate new candidate solutions N (g ) . 

Mx

• from S (g ) . 

1.1665

1.166

1.1664

G1(Quadrotor)

CEDA (J)

ASBO (Mx)

M p (%)

2

0

1.1662

1.166

1.1661

tr

0.02

0.0008

ts

0.05

0.0049

e ss

0

0

Fig.17 Objective function convergence by best solution in each population

kp

0.00123

in 1st and 2nd stage for Quadrotor using ASBO

ki

1.49e-06

kd

1

0

Step Response ASBO 1.2 1 0.8 0.6 0.4 0.2 0

0

0.05

0.1

0.15

0.2

20

40 60 Iteration

80

100

1.166

0

20

40 60 Iteration

80

100

C. Comparison of ASBO with SOGA based tuning

1.4

Amplitude

1.166

1.1663

0.25

Time (sec)

Fig15. Step response performances by ASBO with Mx for Quadrotor

Based upon the natural evolution of mammals, a computing method called Genetic algorithm has developed by Holland.Crossover, mutation and selection are operators applied to develop the new generation from previous last generation. Various variations exist based upon how these operators have developed and applied. Self organizing genetic algorithm (SOGA) is an extension of genetic algorithm to increase the capability of global search and convergence speed [18]. Elitism based a selection method has defined to give more weight of dominant solutions. Based on biological evolution process a mutation operator called cyclic mutation operator has also introduced. SOGA has applied to tune the PID system using defined objective function as it given in eq. (8) for plant G3 and G4 as defined in eq. (19) and in eq. (20).

JCET Vol. 4 Iss. 3 July 2014 PP. 192-204 www.ijcet.org © American V-King Scientific Publish 198

Journal of Control Engineering and Technology

1.6

(19)

2

s + 2.584 s + 1.6

To have comparative performance between SOGA and ASBO a unit step signal with sample period of 0.01 for 10 seconds and a sample period of 0.1 for 100 seconds in case plant G3 and G4 correspondingly have applied. A range of search for getting the optimal tuning have defined as [0 20].Obtained optimal PID parameters have shown in Table 6 and Table 7 along with correspondingly delivered performance parameters. Comparative step response performances between the proposed solution and SOGA have shown in Fig.18 and in Fig.20. With observation of performance parameters, it is clear that ASBO has delivered no overshoot at all and very smaller rise and settle time, in result ASBO absolutely outperformed the SOGA in all aspects. Minimization of index Mx by ASBO for both plants has shown in Fig.19 and in Fig.21 for phase 1 and phase2.

e ss

0.0044

0.0000

kp

19.390

19.4653

ki

4.119

12.0528

kd

5.151

7.5330

G 4 (s ) =

15

(20)

3

50 s + 43s 2 + 3s + 1 Step Response

1.8 1.6

SOGA ASBO

1.4 1.2 A m p litu d e

G3 (s ) =

JCET

1 0.8 0.6 0.4

Step Response 1.4 SOGA

0.2

ASBO 1.2

0

0

10

20

30

40

50

60

70

80

90

100

Time (sec)

1

A m p litu d e

Fig.20. Step response performances by SOGA and ASBO for plant G4 0.8 Phase1

Phase2

800

120

0.6 700

0.2

500

115

Mx

600

Mx

0.4

110

400

0

0

1

2

3

4

5

6

7

8

9

10

Time (sec)

Fig18. Step response performances by SOGA and ASBO for plant G3

300

100 Phase2

Phase1

20

40 60 Iteration

80

100

100

0

20

40 60 Iteration

80

100

Fig.21 Objective function convergence by best solution in each population

1.337

3.5

in 1st and 2nd stage for plant G4 using ASBO 1.336

TABLE VII. ASBO AND SOGA COMPARATIVE PERFORMANCES FOR PLANT G4

3

Mx

1.335 Mx

0

1.338

4

2.5

1.334

Plant G4

SOGA (J)

ASBO (Mx)

1.333

M p (%)

62.9834

58.6744

2

1.5

1

105

200

1.332

0

20

40 60 Iteration

80

100

1.331

0

20

40 60 Iteration

80

100

Fig.19 Objective function convergence by best solution in each population in 1st and 2nd stage for plant G3 using ASBO TABLE VI. ASBO AND SOGA COMPARATIVE PERFORMANCES FOR PLANT G3

Plant G3

SOGA (J)

ASBO (Mx)

M p (%)

2.0753

0.0000

tr

0.2113

0.1823

ts

2.1348

0.3247

tr

0.5964

0.4920

ts

16.5541

9.6123

e ss

0.0007

0.0001

kp

2.98

1.1269

ki

0.096

0.4794

kd

12.7

18.9622

D. Comparison between ASBO, Differential evolution & Genetic algorithm based tuning Genetic algorithm and Differential evolution are two very powerful concepts available under evolutionary computations. They have extensively applied in number of

JCET Vol. 4 Iss. 3 July 2014 PP. 192-204 www.ijcet.org © American V-King Scientific Publish 199

Journal of Control Engineering and Technology

JCET

Fig.22 .Core stages in DE

1) High Order Plant: 25.2 s 2 + 21.2 s + 3

G5 (s ) =

(21)

s 5 + 16.58s 4 + 25.41s 3 + 17.18s 2 + 11.70 s + 1 Step Response

ki

10.9608

10.9941

11.1596

11.1719

8.1494

kd

18

18

18

18

12.8172

Phase1

Phase2

37

30.04

36

30.02

35

30

34

29.98

33

29.96

Mx

Mx

applications in science and engineering. An iteration of the classic DE and fundamentally all evolutionary algorithm consists of the four basic steps—initialization of a population of search variable vectors, mutation, crossover or recombination, and finally selection. Even though they share similarities in concept there are some remarkable differences in DE to perturb the present population members by with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used for generating the offspring. Block diagram for DE has shown in Fig.22 and detail survey is available in [23].In a paper [19] Saad and others have applied the DE and GA for number of plants to tune the associated PID parameters. We have taken their PID parameters to define the performance parameters and comparisons have made with proposed solution based on ASBO. Three different plants have taken as it given G5 in eq. (21), G6 in eq. (22) and G7 in eq.(23).Two different performance indices IAE and mean square MSE have applied in each case as it given in eq.(3) and in eq.(5).

32

29.94

31

29.92

30

29.9

29

0

20

40 60 Iteration

80

100

29.88

0

20

40 60 Iteration

80

100

Fig.24 Objective function convergence by best solution in 1st and 2nd stage for plant G5 using ASBO

A step input having sampled time of 0.01 for 4.5 sec has applied to get the response of performances. Search range of PID parameters in ASBO has taken in a range of [0 20].Step response for the high order system are shown in Fig.23 and performance parameters and PID parameters are shown in Table 8 and comparative studied has given.GA and DE based solution have delivered nearly the same performance. Step responses are overlapping with each other while ASBO based solution has delivered the much lesser overshoot whereas there are similar rising and settling time in comparison along with minimum steady error. Hence overall performance can be consider as superior for ASBO in association with Mx .Objective minimization curve using ASBO in phase 1 and phase 2 are also shown in Fig.24.

2) System with Delay: 1.2

This is a system with time delay with which controller has attached as defined in eq. (22).

A m p litu d e

1

G 6 (s ) =

0.8

0.6

DE(MSE) GA(MSE) DE(IAE) GA(IAE) ASBO(Mx)

0.4

0.2

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Time (sec)

Fig.23. Step response performance by DE, GA and ASBO for plant G5 with different indices. TABLE VIII. DE, GA &ASBO BASED COMPARATIVE PERFORMANCES FOR PLANT G5

Plant G5

DE (MSE)

GA (MSE)

DE (IAE)

GA (IAE)

ASBO (Mx)

M p (%)

27.1927

27.2598

28.4234

28.5395

20.9345

tr

0.0677

0.0677

0.0617

0.0617

0.0849

ts

0.4041

0.4038

0.3987

0.4763

0.4831

e ss

0.0008

0.0008

0.0003

0.0003

0.0003

kp

3.5563

3.7500

7.1578

7.5001

4.7663

10e −1.0 s (1 + 8s )(1 + 2s )

(22)

A search range of PID parameters has defined in a range of [0 2.5] for ASBO .With step input having sample period 0.05 for 50 seconds, responses deliver by DE and GA with MSE and IAE performance indices are shown in Fig.25,in same ASBO based response has also projected and performance parameters are shown in Table 9 .With observation it is clear that in IAE based performance are better in comparison of MSE for DE and GA, but ASBO outperformed others with good margin with nearly no oscillations in response curve. Minimization of performance index Mx by ASBO in different phases has also shown in Fig.26. 3) Non minimum Phase System: A Non minimum phase system G7 has defined as it given in eq. (23) G 7 (s ) =

(1 − 10s ) (1 + s )3

JCET Vol. 4 Iss. 3 July 2014 PP. 192-204 www.ijcet.org © American V-King Scientific Publish 200

(23)

Journal of Control Engineering and Technology

JCET

Step Response

Step Response 1.5

1.5

1 0.5 DE(MSE)

1 Am plitude

A m p litu d e

0

DE(MSE) GA(MSE)

DE(IAE) GA(IAE)

-0.5

ASBO(Mx) -1

DE(IAE) GA(IAE)

0.5

GA(MSE)

-1.5

ASBO(Mx)

-2 -2.5

0

0

5

10

15

20

25

30

35

40

45

0

20

40

60

50

80

100

120

Time (sec)

Time (sec)

FIG.25. STEP RESPONSE PERFORMANCE BY DE, GA AND ASBO FOR PLANT G6 WITH DIFFERENT INDICES TABLE IX. DE, GA &ASBO BASED COMPARATIVE PERFORMANCES FOR PLANT G6

Fig.27. Step response performance by DE, GA and ASBO for plant G7 with different indices TABLE X. DE, GA &ASBO BASED COMPARATIVE PERFORMANCES FOR PLANT G7

PlantG7

DE (MSE)

GA (MSE)

DE (IAE)

GA (IAE)

ASBO (Mx)

M p (%)

7.2742

-

2.9239

-

1.1148

Plant G6

DE (MSE)

GA (MSE)

DE (IAE)

GA (IAE)

ASBO (Mx)

M p (%)

42.9108

42.4999

21.1241

20.6872

14.9317

M u (%)

146.8

136.6

207.4

173.5

182.1

tr

0.6773

0.6832

1.0265

1.0235

1.3417

tr

2.4368

2.7308

1.8615

15.0071

2.3710

ts

21.9376

22.1526

6.8996

6.8808

5.5648

ts

20.5414

22.6791

11.9125

23.5982

8.5910

e ss

0.0004

0.0002

0.0000

0.0000

0.0000

e ss

0.0000

0.0000

0.0000

0.0000

0.0000

kp

0.6090

0.6250

0.6798

0.6718

0.6370

kp

0.1903

0.1884

0.2071

0.1875

0.2009

0.0624

0.0765

0.0624

0.0749

0.1048

0.0937

0.0671

0.0663

0.0638

ki

0.0695

ki

kd

0.1035

0.0662

0.1723

0.1875

0.1562

kd

2.1549

2.1289

1.3419

1.3526

1.0097 Phase2

Phase1

Phase1

Phase2

3500

105

2400

428.4

2200

428.2

2000

3000

428

1800

100

427.8

1600

95

1400

427.4 1200

Mx

Mx

2000 90 85

1000

800

427

600

426.8

400

80

500

0

50 Iteration

100

75

427.2

1000

1500

0

Mx

Mx

427.6

2500

0

50 Iteration

100

Fig.26 Objective function convergence by best solution in 1st and 2nd stage for plant G6 using ASBO

Step input having a sample period of 0.5 for 120 seconds has applied to get the comparative performances among DE, GA and ASBO. Step responses in all cases have shown in Fig.27.ASBO based solution has overall better performance in comparison of DE and GA based solution as it appears from Table 10. Minimization of Mx using ASBO has also shown in Fig.28

0

50 Iteration

100

426.6

0

50 Iteration

100

Fig.28 Objective function convergence by best solution in 1st and 2nd stage for plant G7 using ASBO

E. Comparison Between ASBO, Optimization Based Tuning

Convex-Concave

Convex programming is a powerful optimization technique, which has guaranteed convergence and efficient algorithms that have been packaged in easy-to-use tools. There is a modification called convex-concave optimization which admits nonconvex criteria and constraints. There is in general no guarantee of convergence to a global minimum but the algorithms converge to a saddle point or local

JCET Vol. 4 Iss. 3 July 2014 PP. 192-204 www.ijcet.org © American V-King Scientific Publish 201

Journal of Control Engineering and Technology

JCET

Phase1 21.5

34

21.4

G8 (s ) =

(24)

(s + 1)3

21.3 21.2

30 Mx

21.1 28

21 26 20.9 24

20.8

22 20

1

Phase2

36

32

Mx

minimum. In paper [20],convex-concave programming has applied to tune PID parameters of controller for the third order plant and in this paper it is taken G8 in eq.(24).Performance criteria’s are taken as IAE and IE in eq.(3) and in eq.(4).Step input with sample time 0.05 has applied for 30 seconds to get the responses by different methods and results of performance are available in Table 11 along with a response curve in Fig.29.It is observed that proposed solution using ASBO and Mx outperformed the solution given by Hast in [20 ] in terms of lesser overshoot and better settling time. Minimization of Mx using ASBO has also shown in Fig.30.

20.7

0

50 Iteration

100

20.6

0

50 Iteration

100

Fig.30 Objective function convergence by best solution in 1st and 2nd stage for plant G8 using ASBO

Step Response 1.4 ASBO(Mx) CC(IE) CC(ITE)

1.2

Am plitude

1

0.8

0.6

Fig.31.Automatic Voltage Regulator (AVR) system with Controller

0.4

0.2

0

0

5

10

15

20

25

30

Time (sec)

Fig.29. Step response performance by ASBO and Convex-Concave optimization for plant G8 with different indices TABLE XI. CONVEX-CONCAVE AND ASBO BASED COMPARATIVE PERFORMANCES FOR PLANT G8

Plant G8

ConvexConcave (IE)

Convex-Concave (ITE)

ASBO (Mx)

M p (%)

19.7569

17.5310

5.4529

tr

0.6679

0.8148

0.8868

ts

20.9926

8.3399

4.1585

e ss

0.0070

0.0000

0.0000

kp

3.3100

3.8100

3.9656

ki

6.6200

3.3300

1.4016

kd

6.2600

4.2500

4.0038

F. Comparison between ASBO, with BF-GA and Chaotic optimization based tuning of AVR system The role of an AVR is to keep constant the output voltage of the generator in a specified range. A simple AVR consists of amplifier, exciter, generator and sensor. The block diagram of AVR with PID controller is shown in Fig.31.Values of various parameters associated with amplifier, exciter, generator and sensor is given in eq.(25).

K A = 10, KE = KG = KR = 1,

τ A = 0.1,τ E = 0.4,τ G = 1,τ R = 0.01

(25)

Bacteria Foraging Optimization Algorithm (BFOA), proposed by Passino [24], is a new comer to the family of nature-inspired optimization algorithms. Bacteria search for nutrients in a manner to maximize energy obtained per unit time. Individual bacterium also communicates with others by sending signals. A bacterium takes foraging decisions after considering two previous factors. The process, in which a bacterium moves by taking small steps while searching for nutrients, is called chemotaxis and key idea of BFOA is mimicking the chemotactic movement of virtual bacteria in the problem search space. The four prime steps in BFOA.(i)Chemotaxis:,(ii) Swarming(iii) Reproduction(iv) Elimination and Dispersal. Researchers are trying to hybridize BFOA with different other algorithms in order to explore its local and global search properties separately .In [21] a hybrid approach involving genetic algorithms (GA) and bacterial foraging (BF) algorithms for function optimization problems proposed and has applied to tune the PID controller for AVR system. Objective function has defined as eq.(9). With the obtained parameters for controller, performance parameters are obtained and shown in Table12. In the present era of development Chaos theory has applied as a very useful method in many engineering and science applications. An important feature of chaotic systems is that even if there is a small change in the parameters or initialization values, this will generate very different future behaviors, such as stable fixed points, periodic oscillations, bifurcations, and ergodicity. These behaviors can be analysed based on Lyapunov exponents and the attractor theory. The application of chaotic sequences can be considered as an alternative to provide the search diversity in an optimization procedure. Due to the non-repetition of chaos, it can carry out overall searches at

JCET Vol. 4 Iss. 3 July 2014 PP. 192-204 www.ijcet.org © American V-King Scientific Publish 202

Journal of Control Engineering and Technology

JCET

higher speeds than stochastic ergodic searches that depend on probabilities. In [22], Coelho has applied the Lozi map to generate the chaotic sequence to define the optimization process called Chaotic optimization based tuning (COLM).Optimization process completed with two stages, first, region of global solution try to achieve later local exploration applied to get the optimal solution. Objective function given in eq.(10) has applied to define the performance criteria. Performance in PID tuning has shown in Table12.

ts

1.0037

0.9659

0.4587

e ss

0.0004

0.0003

0.0002

kp

0.6220

0.6728

0.6340

ki

0.4530

0.4787

0.4399

kd

0.2180

0.2299

0.2132

Step Response COLM 1.06

A practical high-order AVR system controlled by a PID controller as shown in Fig.31 has considered to verify the efficiency of the proposed ASBO and Mx in controller design. Step signal having sample interval of 0.01 for 5 sec has applied. Range for [ K p , K i , K d ] is taken as [0 1.5] to

1.04

A m p litu d e

1.02

System: ASBO Settling Time (sec): 0.458

System: BF-GA Settling Time (sec): 0.94

0.98 System: COLM Settling Time (sec): 0.99

0.96

0.94 0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Time (sec)

Fig.33. Step response performance in enlarge section to get details about rise and settle time for AVR system using ASBO, COLM and BF-GA Phase2

Phase1 18

5.75 5.74

16

5.73 14 5.72 12 Mx

5.71

10

5.7 5.69

8 5.68 6 4 0

Step Response

1

Mx

search the solution. Performance to minimize the objective function Mx has shown in Fig.34 for Phase1 and phase2.With obtained PID parameters value, performance parameters are shown in Table12 in comparison with performances shown by COLM and GA-BF. There is no much difference in the rise time for all the three methods but the significance difference in overshoot value and in settling time. There is minimum overshoot observed with COLM which is obvious because of extra pressure in the objective function but has taken maximum settling time. GA-BF based method has delivered the maximum overshoot compare to all but has minimum rise time and closer settling time to COLM but much higher than ASBO. Performance of ASBO is superior from other methods in terms of settling time and steady state error. Rise time is better compared to COLM but inferior in overshoot. Numeric value wise performance comparison have shown in Table 12 for all the three methods along with PID parameters. Step responses for all the three methods are also shown in Fig.32 and in Fig.33.

BF-GA ASBO

5.67 50 Iteration

100

5.66

0

50 Iteration

100

1.4

Fig.34 Objective function convergence by best solution in 1st and 2nd stage for AVR using ASBO

COLM BF-GA ASBO

1.2

VI. CONCLUSION

A m p litu d e

1

0.8

0.6

0.4

0.2

0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time (sec)

Fig.32. Step response performance by COLM, BF-GA and ASBO for AVR system TABLE XII. COLM, BF-GA AND ASBO BASED COMPARATIVE PERFORMANCES FOR AVR SYSTEM

Challenge to auto tune the PID controller in optimal manner has taken care in the proposed research work with proposing a new performance index Mx and global optimization of performance has achieved with the use of ASBO. The advantage of the new performance index has shown comparable with practically applied various performance indices. ASBO-Mx based auto-tuned system performances have shown superiority over other nature inspired algorithms in terms of time domain response behavior of the system. The proposed concept of auto tuning can be applied to get better optimal control with different types of systems in easy way hence having generalization applicability in application and cost effectiveness.

AVR System

COLM fmp

BF-GA Cx

ASBO Mx

ACKNOWLEDGMENT

M p (%)

0.3315

1.9377

0.9224

tr

0.3022

0.2799

0.3020

This research is completed in Manuro Tech Research, Bangalore, India. We express our thanks to associated members.

JCET Vol. 4 Iss. 3 July 2014 PP. 192-204 www.ijcet.org © American V-King Scientific Publish 203

Journal of Control Engineering and Technology

REFERENCES

Ziegler JG, Nichols NB.: “ Optimum settings for automatic controllers,” Trans ASME 1942;64:759–68. R.A. Krohling, J.P. Rey: “Design of optimal disturbance rejection PID controllers using genetic algorithm,” IEEE Trans.Evol.Comput. 5 (February) (2001) 78–82. Q.H. Wu, B.W. Hogg, G.W. Irwin: “A neural network regulator for turbogenerators,” IEEE Trans.Neural Networks 3 (1992) 95–100. A. Visioli.: “Tuning of PID controllers with fuzzy logic,”. Proc. Inst. Elect. Eng. Contr. Theory Applicant., vol. 148, no. 1, pp. 1–8, Jan. 2001. S.P. Ghoshal.: “Optimization of PID gains by particle swarm optimization in fuzzy based automatic generation control,” Electr. Power Syst. Res. 72 (2004)203–212. Z.L. Gaing: “A particle swarm optimization approach for optimum design of PID controller in AVR system,”IEEE Trans. Energy Convers. 19 (June(2)) (2004) 384–391. K.H.Ang,G.Chong, Yun Li.: “PID Control System Analysis, Design,and Technology,”.IEEE Transaction on control system technology, Vol. 13, No. 4 2005,PP:559-576 J. Kennedy, R.C. Eberhart: “Particle swarm optimization,” Proceedings of IEEE International Conference on Neural Networks, Perth, Australia,1995, pp. 1942–1948. Singh kr. Manoj: “A new optimization method based on adaptive social behavior: ASBO,” Springer, Proceedings of International Conference on Advances in Computing, Volume 174, 2012, pp 823-831. Chen, Ge, Almeida.: “Self-tuning PID Temperature Controller Based on Flexible Neural Network,” Advances ,springer,,LNCS Volume 4491, 2007, pp 138-147. Yanzhu Zhang, Jingjiao Li.: “Fractional-order PID controller tuning based on genetic algorithm,”.IEEE,BMEI, 2011, Volume: 3 ,PP: 764 – 767. Fabijanski, P. , Lagoda, R.: “On-line PID controller tuning using genetic algorithm and DSP PC board,” .IEEE. EPE-PEMC 2008. PP: 2087 - 2090 John Oyekan and Huosheng Hu.: “A Novel Bacterial Foraging Algorithm for Automated tuning of PID controllers of UAVs,”. Proceedings of the 2010 IEEE,International Conference on Information and Automation, Harbin, China,PP:693-698. Wonghong, T.: “Real-time PID controller tuning via unfalsified control,”. IEEE, (ECTI- CON), 2012 ,PP: 1 – 4. Zi Ye , Xiaoping Jiang ; Zhenchong Wang.: Self-tuning PID controller based on quantum evolution algorithm and neural network .IEEE,JEC-ECC, 2012,PP: 97 – 101. Hyung-soo Hwang, Jeong-Nae Choi, Won-Hyok Lee.: “A Tuning Algorithm for the PID controller Utilizing Fuzzy Theory,” IEEE Proceedings / Q1999 IEEE.PP:2210-2215. Pei Chu and Haibin Duan, “ Quadrotor Flight Control Parameters Optimization Based on Chaotic Estimation of Distribution Algorithm,” Springer, ISNN 2013, Part II, LNCS 7952, pp. 19–26, 2013. Zhang Jinhua,Zhaung Jian,Du Haifeng,Wang Sun’an, “Self – organizing genetic algorithm based tuning of PID controller,” Elsevier ,Information science 179(2009),pp.1007-1018 Saad, Darus, “Implementation of PID controller tuning differential evolution and genetic algorithm,” International journal of innovative computing, information and control, volume 8,number 11,2012,pp.7761-7779

JCET

M. Hast, K.J. Astrom, B. Bernhardsson, S. Boyd, “ PID Design by Convex-Concave Optimization,” 2013 European Control Conference (ECC)July 17-19, 2013, Zürich, Switzerland.pp.4460-4467. Dong Hwa Kim, “ Hybrid GA–BF based intelligent PID controller tuning for AVR system ,” Elsevier, Computing, Volume, January 2011, Pages 11–22. Leandro dos Santos Coelho, “ Tuning of PID controller for an automatic regulator voltage system using chaotic optimization approach,” Elsevier, Chaos, Solutions and Fractals 39 (2009) 1504–1514 S Das, and P N Suganthan, , “ Differential Evolution: A Survey of the State-of-the-Art”, IEEE transaction on evolutionary computation,Vol15,No.1,2011,pp:4-31 V. Gazi, K.M. Passino, “Stability analysis of social foraging swarms,” IEEE Transactions on Systems Man and Cybernetics Part B –Cybernetics 34 (1) (2004) 539–557. Sridhar N, is an Assistant Professor in the Department of Electronics & Communication Engineering, The Oxford College of Engineering, Bangalore, Karnataka, India. Currently he is pursuing his Ph.D. degree in Autonomous Control of Spacecraft power Systems. He obtained his Masters degree in Bio-Medical Instrumentation from VTU and BE in Electronics & Communication Engineering from Anna University. His research interest includes Non Linear Control Systems, Digital Signal Processing, Neural Networks & Fuzzy Logic.

Nagaraj Ramrao, is the Principal of The Oxford College of Engineering, Bangalore, Karnataka, India. He was the Director of R.V. Centre for Cognitive Technologies. He has obtained doctoral degree from the VTU for a thesis on Automatic Flight Control. His research interests are Aerospace Electronics, Industrial Electronics & Control and Digital Signal Processing. He has published several technical papers in International Refereed Journals & Conferences. He is a Senior Member, IEEE and also a life member of Indian Society for Technical Education, Institute of Electronics & Telecommunication Engineers. He has several ongoing research projects under his supervision, funded by various research labs in India. Manoj Kumar Singh is currently holding the post of director in Manuro Tech. research, Bangalore, India. He is actively involved with industry and academia as an expert in advanced intelligent technologies. He is having background of R&D in advanced intelligent computing and solution development in various fields. His field of research includes Nature inspired computation, Nano-computing, Soft computing, Machine learning, Optimization, etc. He has published several research papers in International Refereed Journals & Conferences and a member of IEEE.

JCET Vol. 4 Iss. 3 July 2014 PP. 192-204 www.ijcet.org © American V-King Scientific Publish 204