Real Time Implementation of Improved PSO Tuning for a ... · classical PID controller tuning methods, heuristic method such as Particle Swarm Optimization (PSO) and an improved particle

Real Time Implementation of Improved PSO Tuning for a Conical Tank

Process used in Biodiesel Production

D.Mercy1 and S.M.Girirajkumar

2

1Department of EEE, St.Joseph’s College of Engineering & Technology, Thanjavur, India

2Department of ICE, Saranathan College of Engineering, Tiruchirappalli, India

Abstract:

The particle swarm optimization is a stochastic optimization technique for finding

optimal regions of nonlinear continuous functions through the interaction of individuals in the

swarm. An improved particle swarm optimization (IPSO) algorithm is proposed in this study

in all applications. The usefulness of this method is verified through a comparative study with

classical PID controller tuning methods, heuristic method such as Particle Swarm

Optimization (PSO) and an improved particle swarm optimization (IPSO). A real time

implementation of the proposed method is carried on a nonlinear conical tank process using

LabVIEW module; this design can be applicable for biodiesel production plant and it is

evident that the IPSO algorithm executes fine on a nonlinear unstable process models. The

IPSO tuned controller offers improved process characteristics such as better time domain

specifications, smooth reference tracking, supply disturbance rejection, and error

minimization compared to other controller tuning methods.

Keywords: PID Controller, PSO, IPSO, Nonlinear Process, Conical tank process, LabVIEW.

1. Introduction

A stand alone control algorithm used to tune

the linear process in a classical way, usually called

as PID (Proportional Integral Derivative)

controller. PID controller is one of the earliest and

most popular controllers. The advanced PID

controllers and classical PID controllers have been

associated with different types of industries so the

tuning methods are still developing. The PID

controller was proposed by Norm Minorsky in

1922. Now days the researchers are mainly

concentrating on the adaptive and optimized

controller which deals with more complicated

process. Now a day researchers are developing

various algorithms for the tuning the PID controller

although Zeigler Nichols PID tuning method is the

base for all tuning methods. Bhawana Singh and

Neelu Joshi discussed about the various classical

and optimized tuning methods . Marshiana et al

proposes the controller design for nonlinear

systems using Fractional order PI controller

(FOPIC) technique which offers victory as a result

of valuable methods in differentiation and

integration and they offer additional flexibly in the

controller design [13]. Suji Prasad et al proposed

the particle swarm optimization based PID

controller[14] tuning used for the performance

analysis. S.Nithya et al proposed the model based

tuning methods of PID controller for a real time

systems[28].

Based on the literature review, the proposed

system includes classical PID tuning and improved

optimized PID tuning for a conical tank process.

Classical PID tuning method is applicable for the

linear process and for a nonlinear process improved

optimized PID tuning is proposed. Conical tank

system is a difficult and important criterion due to

its nature of the shape which can increases the

nonlinearity of the process. To overcome the

nonlinearity of the conical tank process improved

optimized control techniques are widely used. In

the proposed system mathematical modeling of a

conical tank system is derived and the final transfer

function is obtained. The obtained transfer function

is used to get the simulation and the real time

response for various tuning methods. The response

curves are plotted for each tuning values.

Comparative study is performed to analyze the

response curves based on the time domain

International Journal of Pure and Applied MathematicsVolume 118 No. 18 2018, 2051-2062ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

2051

specifications and error criteria. From the results

IPSO based PID tuning method provides better

results.

2. Mathematical modeling of a conical

tank system

Mathematical modeling of conical tank system

is derived based on the structure and the output

transfer function is obtained. The output equations

are well formulated and assumed as a process

model structure with optimization. Optimized PID

tuning is an effective tool for tuning of a controller.

To derive the mathematical modeling of a conical

tank, the input of the process should be initialized

and the input and output relations should be known

and should be properly defined. The primary task is

to understand the system and the system need to be

investigated to realize the incident of nonlinearity

present in the system dynamics. Now days, the

utility of Improved Particle Swarm Optimization

Algorithm is extensively increasing because of its

high accurate, fast and optimal responses compared

with conventional techniques [4]. The proposed

conical tank system, identified as a nonlinear

complex structure is shown in Fig. 1.

Fig:1 Structure of conical tank system

Where,

H = Total height of the conical tank

Fin = Input flow rate of conical tank

Fout = Output flow rate of conical tank

R = Top radius of conical tank

r = Radius of nominal level of the tank

Mass balance Equation is given by

Fin-Fout = A1dh/dt ------------------- (1)

Fout = b √h ------------------ (2)

Where, b = a √(2g)

a = Outlet area of the tank

g = Acceleration due to gravity

By substituting the Equation and considering the

cross sectional area of the tank at level H is given

by,

Tanθ = r/H, A=пr2 ------------- (3)

r = R2h2/H2

A = пR2h2/H2 ------------- (4)

The nonlinear dynamics of the system is expressed

by the FOPDT (first order process with delay time).

The standard transfer function of nonlinear conical

tank system is obtained and is written as,

H(S) /Q1(S) = Re−θs / τS+1 ----- (5)

Where,

R = Gain constant

θ = Time delay

τ = Time constant.

The standard transfer function is modelled

with standard step input to obtain the response

curve. The timing corresponds to the 35.3% and

85.3% the value of t1 and t2 are calculated. The

parameters τ and θ are calculated as follows [1].

τ = 0.67(t2 −t1) ----------------- (6)

θ = 1.3t1 −0.29t2 ----------------- (7)

The input and output flow rate of the conical

tank process is kept constant to approach the

equilibrium state and the output is noted for each

increment. Different readings are observed until the

conical tank process reaches the stable state. By

International Journal of Pure and Applied Mathematics Special Issue

2052

substituting the gain constant, time delay, time

constant in the transfer function equation (5) and it

is approximated as FOPDT model. The derived

process model of a conical tank process is given by,

G(s) = 14.62 e – 5.8s /134.6 S+1 ----------- (8)

where, Gain constant, R = 14.62

Time delay, θ = 5.8 sec

Time constant τ = 134.6

Equation (8) describes about the transfer

function of a real time conical tank process used in

biodiesel production plant. The obtained transfer

function is tuned with different tuning methods and

the response curve is plotted. The plotted results

are compared based on the time domain

specifications and error values. The best tuning

method is concluded based on the plotted results.

3. Classical PID tuning methods

―PID‖ is a short form for Proportional

Integral Derivative controller that includes

elements with three functions. The PID controller is

a conventional controller combines the three error

functions that is control error, integration of the

error value, and derivation of the error value. The

PID controller is helpful to control the output

results, if three terms of controllers are constructed

with inclusion of nonlinear function [30]. There are

widespread papers present distinct methods to

layout nonlinear PID controller. Including all

nonlinear controllers some of the nonlinear

controllers are mostly used in engineering

applications. The reason for that is the linear

controller is converted as a nonlinear based on

simple specifications. Controller tuning is a process

of adjusting the control parameters Kp, Ki and Kd

to reach the optimum values and to obtain the

desired control response. Tuning of the controller is

essential for maintaining the system stability. The

following tuning rules are effectively used to tune

the PID controller of a conical tank system in a

classical way.

1. Ziegler–Nichols (Z–N) method (1942):

Controller tuning is based on the value ultimate

gain and the value of ultimate period.

2. Cohen–Coon (C–C) method (1953): Tuning of

the controller is Based on Process reaction curve.

3. Shinskey tuning method (1990):

Kc = , Ti = , Td=

4. Maclaurin tuning method (1990):

Kc= , Ti = , Td =

5. Connel tuning method (1987): Tuning of the

controller is Based on Process reaction .

Kc = , Ti = , Td =

6. K.J.Astrom and T.Hagglund tuning

method(1984): Integral gains of PID controller.

Kc = , Ti = 2 d , Td= 0.5 d

4. PSO tuning for a conical tank system

Particle Swarm Optimization is a strong

random functional technique is initiated by the

scattering of particles in the search space and

swarm intelligence. PSO is a concept related to the

problem solving based on public interaction.

Particle Swarm Optimization method was invented

by James Kennedy and Russell Eberhart. This

method exploits a numerous representatives that

compose a flock scattering around in the search

space and come across for the high quality solution.

Each particle in the search space is treated as a

point which fine-tunes its airborne terminology

according to its personal practice and the airborne

information of the additional particles present in

the system. The PSO algorithm has to follow three

steps and it has to repeat the steps still reaching the

stopping condition.

Calculate the fitness of each particle.

Revise individual and global best fitness

and positions.

Revise the velocity and location of each

particle.

Every particle in the search space sustain

the track of records and are related with the high

efficient result that have been recognized by the

particles. This is known as personal best, pBest.

The obtained new finest value is tracked using the

PSO technique is the finest value accomplished up

to now through every particle in the locality of that

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particle. It is known as gBest. The fundamental

idea of PSO lies on the speeding up of each particle

in the pathway of its pBest and the gBest positions,

by means of a subjective biased speeding up at

each time step [11]. Pseudo Code is a basic code

for implementing the PSO algorithm. The basic

code for executing the algorithm is given below,

Start the process

For each and every particle

Initiate each particle in the search space

Stop the process

Repeat the process


Calculate the fitness value

If calculated value is better than the best value

Set the present current value as new pBest

Stop the process

Choose the particle with the best fitness value

from all the particles (gBest)


Estimate the particle velocity

Renew the particle location

Stop the process

Fig. 2: Flow diagram of PSO

Fig. 3: Vector diagram of PSO


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In the proposed system optimized tuning

values are identified based on iteration values.

From the classical PID tuning methods best Kp, Ki,

Kd values are obtained. The obtained values are

used to initialize the PSO tuning method and

initialization of PSO tuning includes the parameter

initialization process. To introduce PSO, numerous

parameters want to be described. Parameter

initialization is a process of initiating the dimension

of the search space, number of iterations and

velocity constants. The dimension of the flock

satisfies the necessity of global optimization and

working out cost. Initial inputting of the parameters

are as per the table. After the completion of the

iteration global best and local best values are

obtained.

Table.1 PARAMETER INITIALIZATION

The most significant method of applying the

PSO algorithm is to choose the objective function

which is used to estimate the fitness of each

Particle.Most of the process uses performance

indices as an objective function. The objective

functions are Mean of the Squared Error, Integral

of Time Absolute Error, Integral of Absolute Error,

and Integral of the Squared Error. Based on the

above objective function various error criteria were

calculated for each tuning methods and the error

values are compared. The PID controller is

employed to reduce the error value and it will be

defined more thoroughly based on the error

criterion. If the performance indices values are

smaller it gives the best results and for higher

values it will not provide good results [3].

5. Improved PSO tuning for a conical tank

system

PSO algorithm has the advantages of simple

structure, less parameters and fast convergence, it

is easy to fall into local extreme value, and it

cannot obtain globally optimal solution. There are

two main reasons for this phenomenon:

The character of optimization function.

Due to the inappropriate parameter design and

population size of algorithm in the operation

process.

The two reasons will rapidly disappear the diversity

of particles in the process of calculation, and cause

the premature phenomenon. The inertia weight and

learning factor are improved and the parameters of

PSO algorithm are initialized by using chaotic

characteristic in order to the global optimization

ability in this paper. The basic code for executing

the IPSO algorithm is given below,

Begin the process

Initialize the parameters including

population size, the dimension size and the

maximum iteration number.

Generate the initial population and initial

velocity.

Calculate the fitness value of each particle

and record best fitness and its

corresponding position.

Calculate the population’s best fitness and

its corresponding position.

Compute population centroid with the

weighted coefficient.

Update the velocity and weight values.

Calculate the best fitness values.

End

In the classical PSO algorithm, the moving

speed of particles is fast, but the regulations of

cognition component and social component make

particles move around global point. Based on the

velocity and position regeneration formula, once

the finest individual in the swarm is trapped into a

local optimum, the information sharing mechanism

in PSO will attract other particles to approach this

local optimum steadily, and the whole swarm

converged at this position. When the number of

iteration increase, the velocity of particles will

become zero at the end, then the whole swarm is

hard to jump out of the local optimum and has no

way to attain the global optimum. At this time, the

whole swarm will be converged at one point in the

solution space, if gbest particles haven't found

gbest, the whole swarm will be trapped into a local

optimum; and the capacity of swarm jump out of a

local optimum is rather feeble. In order to get

through this disadvantage, in this paper we presents

a new algorithm based on PSO. In order to avoid

being trapped into a local optimum, this will surely

enlarge the global searching space of particles and

enable them to avoid being trapped into a local

Population Dimension 50

Iteration Count 150

Constant Velocity ,c1 2

Constant Velocity ,c2 2


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optimum too early, in the same time, it will

improve the possibility of finding gbest in the

searching space. Based on the following tabulation

best fitness values are calculated using the IPSO

algorithm.

Table.2 FUNCTIONS OF IPSO

Fig. 4: Block diagram of IPSO

Table.3 PID TUNING PARAMETERS

Tuning Methods Kp Ki Kd

Z-N 1.55 0.36 3.42

Cohen & Coon 1.42 0.32 3.15

Shinskey 1.36 0.29 3.05

Maclaurin 1.14 0.26 2.54

Connel 0.98 0.24 2.18

Astrom & Hagglund 0.91 0.19 2.01

PSO 0.52 0.11 1.35

IPSO 0.21 0.08 0.14


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The block diagram of IPSO is shown in figure.4.

Based on the block diagram by using the improved

particle swam optimization method the PID

controller is tuned using various tuning

methods.PID parameters are calculated using

various tuning methods and the Kp, Ki, Kd values are tabulated and best tuning values are analysed.

5. Uses of Conical Tank in Biodiesel Production

Conical bottom tanks are the ideal solution

for getting every last drop out of the tank. The

conical bottoms facilitate quick and complete

drainage. Conical bottom tanks are also referred to

as sloped bottom tanks, conical tanks and full drain

tanks, fermenter tanks, brewing tanks, and mixing

tanks.

They are commonly used in the industrial,

agricultural, commercial, manufacturing, and water

treatment sectors. Now a day farmers from corner

to corner of the country are switching to make their

own biodiesel with the help of conical bottom tanks

easily. Using waste vegetable oils from farming

and catering sources biodiesel are produced with

three relatively simple stages includes;

pre-treatment, reactions and product purification.

The concluding of which relies on impurities and

sediments falling to the bottom of the conical tanks

where it can be drained away completely. The

block diagram shown in fig.5 is the biodiesel

production plant. Conical bottom tank plays a vital

role in all stages of the process in biodiesel

production plant.

Fig. 5: Block diagram of a biodiesel production plant using cone bottom tank

Fig. 6: Real Time

Experimental setup


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6. Real Time Experimental Setup

The non-linear behaviour of the conical tank

system is identified by constant input flow rate.

The maximum height of the tank is 150 cm. Input

to the tank is incremented stepwise, the current to

the system is maintained at 4-20 mA and passes all

the way through the serial port RS - 232 along

DAQ interface unit. Through manual control

method, specified transform at input value the

output response of the process is documented.

Using controller tuning methods the time constant

and delay time of a FOPTD process is constructed

using tangent method based on its point of

inflection. The experimental real time setup of the

proposed system consists of conical tank process,

water reservoir, centrifugal pump, rotameter, an

electro pneumatic converter and pneumatic control

valve. The output signal from the process is

interfaced with a computer using compact DAQ

through RS-232 serial port. Thus the coding were

developed using LabVIEW software and interfaced

using DAQ module. The Fig.5 above shows the

experimental setup of the automated process.

In Fig. 5 water reservoir is used as a storage

tank. Centrifugal pump is used to pump the water

from the reservoir and circulates the water

throughout the plant. The rotameter is a type of

flow meter used to compute the flow rate of liquids

and gases in industries. An electro pneumatic

converter converts a 4 to 20 mA input signal to a

directly proportional (3 to 15 psi) pneumatic output

signal. Pneumatic control valve is used to control

the flow rate. The pneumatic valve used here is

―air to close valve‖ which is used to adjust the

water flow in the conical tank system. The height

of the conical tank process is obtained through

computational method and broadcasted in the form

of current range between (4–20) mA. Hardware and

software of the system are interfaced by means of

DAQ system. The input to the system is regulated

and tuned using optimal tuning method. The

control action is performed by executing LabVIEW

coding, based on the hardware interface. The

control signal controls the valve position thus

controls the level of the conical tank.

7. Results and Discussion

The output reaction of conical tank system

using PID controller is determined and the results

are recorded. The response of the controllers are

estimated and evaluated in the form of rise time,

overshoot and settling time with existence of

measurement noise. The controller output is

evaluated based on the performance index, if the

error values are lesser than the controller is

consider as a best controller. PSO tuning

terminology provides an iteration based analysis

were we can get the optimized local best and global

best values. This value can be used to get quick

steady state response [5].

The real time LabVIEW software is used to

analyse the results based on controller tuning

method and controls the actions automatically. The

various PID tuning methods like Astrom and

Huggland, CC Method, ZN method, Shinskey

method, PSO, IPSO method are compared using

the LabVIEW coding shown in Fig.7.

Fig. 7: LabVIEW coding

Fig. 8: LabVIEW Response


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Table:4 describes the different types of error values

for various tuning methods. This error analysis can

be done for the identification of best tuning

method. From the above table the error values of

IPSO tuning method is very much reduced. This

shows that IPSO tuning is the best tuning method.

Table:4 ERROR VALUES

Methods IAE ITAE MSE ISE

Astrom

& Hagglund 53.4 143.7 87.3 134.1

Connel 76.5 178.2 81.2 121.7

Shinskey 76.2 179.2 78.9 123.4

Maclaurin 67.8 187.2 76.4 125.7

Ziegler &

Nichols 67.5 156.2 89.3 136.7

PSO 24.6 101.8 44.6 87.3

IPSO 22.1 98.1 41.4 77.4

Table:5 includes the time domain specifications of

the various tuning method. From the analysis IPSO

tuning method provides better performance based

on increased rise time, smooth response without

overshoot and fast settling time.

Table:5 TIME DOMAIN SPECIFICATIONS

8. Conclusion

Optimized Improved PSO based PID

controller is able to provide an effective closed-

loop performance over the standard PSO and

traditionally tuned PID controller parameters for a

conical tank process. The IPSO controller results

are evaluated and analyzed with the standard PSO

and conventional PID tuning methods. The

proposed improved optimized tuning method

provides more efficient results in terms of

improved step response such as reduced error, fast

response time and rapid settling time in the

application of level control for conical tank based

biodiesel production plant. Comparison graph of

the output response with respect to time is shown in

Fig.8. Based on the response curve overshoot of

IPSO controller is reduced to zero and in the error

criteria IAE value is very much reduced.

Concluding that the IPSO tuning is preferred as the

best tuning technique that can be proposed for

biodiesel production plant for separation of

biodiesel products and for storage applications. The

entire concept has been configured to implement in

the biodiesel production plant, where, the conical

tank plays a major role.

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Methods

Rise

Time

(Sec)

Overshoot

(%)

Settling

Time

(Sec)

Astrom&Hagglund 15 82 45

Cohen & Coon 18 76 54

Shinskey 19 81 58

Ziegler & Nichols 16 92 68

Connel 18 89 65

Maclaurin 17 76 53

PSO 14 21 28

IPSO 10 16.3 25


2059

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Authors Details

Mrs.D.Mercy received her Bachelor’s

degree in Electronics and Instrumentation

Engineering from Jayaram College of

Engineering and Technology, Trichy and

her Post Graduate degree in Control

Systems &Instrumentation Engineering from SASTRA

University, Thanjavur. She is currently doing her PhD under the

Faculty of Electrical Engineering in the area of Process Control

in Anna University Chennai. She has around 11 years of

teaching experience in various engineering colleges. Presently

she is serving as an Assistant Professor and Head in the

Department of Electrical and Electronics Engineering at

St.Joseph’s College of Engineering and Technology, Elupatti,

Thanjavur. She has published more than 15 research papers in

various International Journals and Conference Proceedings. Her

area of interest includes Control systems, Process Modeling,

Fuzzy Logic, Genetic Algorithm and optimization techniques

etc.

Dr. S.M Girirajkumar received his

Bachelor’s degree in Electronics and

Instrumentation Engineering from

Annamalai University and his M.Tech +

Integrated Ph.D (M.Tech-Control System

Based, Ph.D-Electrical Engineering) from

SASTRA University, Thanjavur. He has

around 18 years of teaching experience in

various engineering colleges and around 3 years of Industrial

experience. Presently he is serving as a Professor and Head in

the Department of Instrumentation and Control Engineering at

Saranathan College of Engineering, Trichy. He has published

more than 80 research papers in various International, National

Journals and Conference Proceedings. He has obtained various

grants from Government of Tamilnadu and completed the

funded projects. He is a recognized research supervisor for Anna

University of Technology, Tiruchirappalli, and Chennai

associated with EEE department. He is Guiding 4 scholars for

their PhD work, through Anna University of Technology,

Tiruchirappalli and Guiding 6 scholars for their PhD work,

through Anna University of Technology, Chennai. His area of


2060

interest includes Control systems, Process Control, Industrial

Automations and Programmable Logic Controller.


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Documents

Real Time Implementation of Improved PSO Tuning for a ... · classical PID controller tuning methods, heuristic method such as Particle Swarm Optimization (PSO) and an improved particle