Regression model for tuning the PID controller with

Ain Shams Engineering Journal (2014) 5, 1071–1081

Ain Shams University

Ain Shams Engineering Journal

www.elsevier.com/locate/asejwww.sciencedirect.com

ELECTRICAL ENGINEERING

Regression model for tuning the PID

controller with fractional order time delay system

* Corresponding author. Tel.: +91 7588306244.

E-mail address: [email protected] (S.P. Agnihotri).

Peer review under responsibility of Ain Shams University.

Production and hosting by Elsevier

2090-4479 � 2014 Production and hosting by Elsevier B.V. on behalf of Ain Shams University.

http://dx.doi.org/10.1016/j.asej.2014.04.007

S.P. Agnihotri *, Laxman Madhavrao Waghmare

SGGS Institute of Engineering and Technology, Vishnupuri, Nanded, India

Received 5 September 2013; revised 7 April 2014; accepted 16 April 2014

Available online 13 June 2014

KEYWORDS

Regression model;

PID controller;

Iterative algorithm;

Fractional order;

Time delay and system

Abstract In this paper a regression model based for tuning proportional integral derivative (PID)

controller with fractional order time delay system is proposed. The novelty of this paper is that tun-

ing parameters of the fractional order time delay system are optimally predicted using the regression

model. In the proposed method, the output parameters of the fractional order system are used to

derive the regression function. Here, the regression model depends on the weights of the exponential

function. By using the iterative algorithm, the best weight of the regression model is evaluated.

Using the regression technique, fractional order time delay systems are tuned and the stability

parameters of the system are maintained. The effectiveness and feasibility of the proposed technique

is demonstrated through the MATLAB/Simulink platform, as well as testing and comparison using

the classical PID controller, Ziegler–Nichols tuning method, Wang tuning method and curve fitting

technique base tuning method.� 2014 Production and hosting by Elsevier B.V. on behalf of Ain Shams University.

1. Introduction

In different regions, Time-Delay Systems (TDS) encounter

along with engineering, the field of biology, and also econom-ics [1,2]. A time delay is usually a footing regarding unsteadi-ness and also fluctuations within a process [3]. Two sorts of

time delay devices are there as follows: retarded and also fairlyneutral [4]. Throughout TDS, wherever time-delays existingbetween the features regarding input on the process and

also the ensuing result, could be suggested simply by delay

differential equations (DDEs) [5]. Programs along with delaysreveal any category in inexhaustible dimensions mostly

requested the actual modeling as well as the research regardingtransportation and also propagation phenomena [6]. Time-delays on top of things loops normally mortify process display

and confuse case study and also strategy regarding feedbackcontrollers [7].

The actual solidity of time-delay methods is often a prob-lem of chronic interest due to a number of functions of com-

munication systems in the field of biology in addition topopulation dynamics [8]. Generally, solidity review of time-delay methods could be classified straight into two varieties.

First is the particular delay-dependent stability review whichoften contains the data in the length of the particular delay,and one much more is the delay-independent stability review

[9,10]. The actual delay independent stabilization comes witha controller which will temporarily relieve the system in spiteof the length of the particular delay [11]. However, the delay

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1072 S.P. Agnihotri, L.M. Waghmare

centered stabilizing controller can be worried using the size ofthe delay in addition to routinely provide the upper bound ofthe delay [12].

Dead time is probably the motivated presentation in addi-tion to firmness involving time-delay devices [13]. Time delaycontinually subsists inside the measurement loop or control

loop, and therefore it is much more challenging to overpowerthis sort of method [14]. In order to enhance the control pre-sentation, a few novel control techniques, like predictive con-

trol and the neural type of an artificial neutral delay in acontrol loop were used [4]. The PID controller is used in anextensive number of difficulties like automotive, instrumenta-tion, motor drives and so forth. [15]. This specific controller

gifts feedback, the idea will be able to take out steady-stateoffsets by means of hooked up actions, and also it can certainlywait for the extracted actions [16]. Due to the simplicity of the

structure and potential to solve many control problems ofthe system [17]. PID controller offers sturdy and trustworthydemonstration pertaining to most of the devices in the event

the PID boundaries tend to be adjusted surely [15]. Manydelay-independent sufficient conditions for the asymptoticsteadiness involving basic delay differential devices are used

[18].As, this long-established PID compensator seemed to be

requested this monitoring and stabilization of the loopsdesign technique [19], considering that the conventional PID

controllers are not appropriate for nonlinear programs andhigher-ordered and time-delayed programs [20]. Below, thisstabilizing PID controller may reduce the working out occa-

sion also it keeps away from this time-consuming stablenessexamination [21] plus the reports of the PID controllersawfully be determined by the complete understanding of the

system time delay [6].Within this report, the regression model based proposed for

tuning proportional integral derivative (PID) controller along

with fractional order time delay system will be recommended.This novelty in this report will be which tuning parameterswith the fractional order time period delay process will be opti-mally expected when using the regression model. Within the

recommended method, this output parameter of the fractionalorder system is utilized to help derive this regression model sit-uation. In this paper, this regression model depends on the

loads with the exponential function. With the iterative criteria,the most beneficial weight to the regression model is decided.With all the regression process, fractional order time delay

system will be tuned plus the stability parameters with the pro-cess will be managed. This detailed justification with the rec-ommended hybrid process will be illustrated inside area 3.Previous those, the recent research works are described in

Section 2. The outcomes in addition to discussion referred inSections 4 and 5 end this report.

2. Recent research works: a brief review

Several associated works are previously accessible to the liter-ature which based on PID controller design for time delay

fractional order system. A few of them are assessed here. Atechnique to compute the entire set of stabilizing PID control-ler parameters for a random (including unstable) linear time

delay system has been offered by Hohenbichler [22]. To handlethe countless number of stability boundaries in the plane for a

permanent proportional gain kp was the most important con-tribution. It was illustrated that the steady area of the planecontains convex polygons for retarded open loops. A phenom-

enon was initiated concerning neutral loops. For definite sys-tems and certain kp, the precise, steady area in the planecould be explained by the limit of a sequence of polygons with

an endless number of vertices. This cycle might be fined fairlyaccurate by convex polygons. Moreover, they explained aneeded condition for kp-intervals potentially containing a sta-

ble area in the plane. As a result, after gridding kp in theseintervals, the set of stabilizing controller parameters could beplanned.

A partial order PIkDl controller of robust constancy areas

for interval plant with time delay has been suggested by Lianget al. [23]. They have explored the problem of computing therobust constancy area for interval plant with time delay. The

partial order interval quasi-polynomial was crumbling into anumber of vertex attribute quasi-polynomials by the lowerand upper bounds. To explain the constancy boundaries of

every vertex attributes quasi-polynomial in the space ofcontroller parameters, the D-decomposition method wasemployed. By overlapping the constancy area of each quasi-

polynomial, the constancy area of interval attribute quasi-polynomial was found out. By choosing the control parame-ters from the constancy area, the parameters of their suggestedcontroller were attained. The vigorous constancy was checked

by means of the value set together with the zero eliminationprinciple. Their suggested algorithm was constructive in exam-ining and planning the robust PIkDl controller for interval

plant.A particle swarm optimized I-PD controller of Second

Order Time Delayed System has been suggested by Suji Prasad

et al. [24]. Optimization was based on the presentation indiceslike settling time, rise time, peak overshoot, ISE (integralsquare error) and IAE (integral absolute error). PID control-

lers and its alternatives are most commonly used, althoughthere are important improvements in the control systems inindustrial processes. If the parameter of controller was notappropriately planned, next needed control output may not

succeed. Compared with Ziegler Nichols and Arvanitis tuning,they have confirmed that their simulation results with opti-mized I-PD controller to be specified enhanced presentations.

A PID controller for time delay systems has been explainedby Rama Reddy et al. [25]. Their suggested technique precisedthe stable areas of PID and a novel PID with cycle leading cor-

rection (SLC) for network control systems with time delay.The latest PID controller has a modification parameter ‘b’.They have obtained that relation of the parameters of the sys-tem. The outcome of plant parameters on constancy areas of

PID controllers and SLC-PID controllers in first-order andsecond-order systems with time delay is moreover precised.Finally, an open-loop zero was introduced into the plant-

unstable second order system with time delay so that the con-stancy areas of PID and SLC-PID controllers get competentlymade bigger.

Luo et al. [26] have suggested a part encloses in selecting twofeasible or achievable patterns, and a FOPI/IOPID controllersynthesis was applied for all the steady FOPTD systems. The

entire possible area of two patterns can be attained andpictured in the plane by means of their suggested plan.Every mixture of two patterns can be confirmed before thecontroller design, with those areas as the previous knowledge.

Regression model for tuning the PID controller with fractional order time delay system 1073

In particular, it was fascinating to compare the regions of thesetwo possible areas for the IOPID and FOPI controllers. A sim-ulation picture demonstrates that their suggested plan has

resulted and their presentation of the designed FOPI controlleris compared to the optimized integer order PI controller and theplanned IOPID controller.

Bouallegue et al. [27] have suggested to a novel PID-typefuzzy logic controller (FLC) tuning approaches from a particleswarm optimization (PSO) strategy. Two self-tuning methods

were inserted so as to develop more the presentation andtoughness properties of the suggested PID-fuzzy strategy.The scaling features tuning problem of these PID-type FLCconfigurations was created and steadily determined, by means

of a suggested limited PSO algorithm. To show the competenceand the supremacy of the suggested PSO-based fuzzy controlstrategies, the case of an electrical DC drive benchmark was

explored, inside an improved real-time framework.Shabib et al. [28] have explained about the power system

nonlinear with frequent changes in operating areas. In excita-

tion control of power systems, Analog proportional integralcopied PID controllers were extensively employed. Fuzzy logiccontrol was frequently out looked as a structure of nonlinear

PD, PI or PID control. They moreover explained the designprinciple, tracking presentation of a fuzzy proportional-integral PI plus derivative D controller. To integrate a fuzzylogic control mechanism into the alterations of the PID struc-

ture, this controller was improved by first explaining discretetime linear PID control law and subsequently more and moreobtaining the steps required. The bilinear transform (Tustin’s)

was applied to discretize the conventional PID controller. Inthat some presentations criteria were employed for comparisonbetween other PID controllers, such as settling times, over-

shoots and the amount of positive damping.Ozbay et al. [29] possess created some sort of traditional

appropriate PID controllers with regard to linear time period

invariant facilities whoever transfer operates were logical oper-ates connected with Sa, exactly where 0 < a < 1, and s is theLaplace transform variable. Effect connected with input–output time period delay about the range of allowed controller

details has been perused. This allowed PID controller detailswere identified from a small acquire style of argument utilizedsooner with regard to specific dimensional facilities.

Zhao et al. [30] proposed an Integral of Time Absolute Error(ITAE) zero-position-error optimal tuning and noise effectminimizing method for tuning two parameters in MD TDOF

PID control system to own sought after regulatory as well asdisturbance rejection overall performance. Your contrasttogether with Two-Degree-of-Freedom control program bymodified smith predictor (TDOF CS MSP) and also the made

MD TDOF PID tuned by the IMC tuning approach demon-strates the potency of the particular described tuning approach.

Feliu-Batlle et al. [31] proposed the latest technique for the

control of water distribution in an irrigation main canal poolseen as substantial time-varying time delays. Time delaysmay perhaps adjust greatly in an irrigation main canal pool

as a result of versions inside its hydraulic operations program.A classic system got its start to development fractional buy PIcontrollers coupled with Smith predictors that produce control

systems which can be robust for the modifications in the pro-cess time delay. The system was given to fix the situationregarding powerful water submission control in an irrigationmain canal pool.

Sahu et al. [32] have outlined around the design and styleas well as effectiveness evaluation regarding DifferentialEvolution (DE) algorithm based parallel 2-Degree Freedom

of Proportional-Integral-Derivative (2-DOF PID) controllerfor Load Frequency Control (LFC) of interconnected powersystem process. The planning issue has been formulated as

an optimization issue and DE has been currently employedto look for optimal controller parameters. Standard as wellas improved aim features have been used for the planning goal.

Standard aim features currently employed, which were Integralof Time multiplied by Squared Error (ITSE) and Integral ofSquared Error (ISE). To be able to additionally raise the effec-tiveness in the controller, some sort of improved aim operate is

derived making use of Integral Time multiply Absolute Error(ITAE), damping ratio of dominant eigenvalues, settling timesof frequency and peak overshoots with appropriate weight

coefficients. The particular fineness in the recommended tech-nique has become confirmed by simply contrasting the resultswith a lately published strategy, i.e. Craziness based Particle

Swarm Optimization (CPSO) for the similar interconnectedelectric power process. Further, level of sensitivity evaluationhas been executed by simply varying the machine details as

well as managing load conditions off their nominal valuations.It is really observed which the recommended controllers arequite powerful for many the system parameters as well as man-aging load conditions off their nominal valuations.

Debbarma et al. [33] have suggested a new two-Degree-of-Freedom-Fractional Order PID (2-DOF-FOPID) controllerended up being suggested intended for automatic generation

control (AGC) involving power systems. The controller endedup being screened intended for the first time using threeunequal area thermal systems considering reheat turbines

and appropriate generation rate constraints (GRCs). Thesimultaneous optimization of several parameters as well asspeed regulation parameter (R) in the governors ended up

being accomplished by the way of recently produced metaheu-ristic nature-inspired criteria known as Firefly Algorithm(FA). Study plainly reveals your fineness in the 2-DOF-FOPID controller regarding negotiating moment as well as

lowered oscillations. Found function furthermore exploresthe effectiveness of your Firefly criteria primarily based mar-keting technique in locating the perfect guidelines in the con-

troller as well as selection of R parameter. Moreover, theconvergence attributes in the FA are generally justify whencompared with its efficiency along with other more developed

marketing technique such as PSO, BFO and ABC. Sensitivityanalysis realizes your robustness in the 2-DOF-FOPID con-troller intended for distinct loading conditions as well as largeimprovements in inertia constant (H) parameter. Additionally,

the functionality involving suggested controller will bescreened next to better quantity perturbation as well as ran-domly load pattern.

Better performances of the closed-loop can be achieved byusing such kinds of controllers in fractional order time delaysystems. The PID controller is used due to the simplicity of

the operation, design and low cost in many industrial applica-tions. However, for making stability system the tuning processof PID controller is one of the complexes. Many tuning meth-

ods PID gains have been developed, but the Ziegler Nicholsmethod is one of the classical PID gain tuning technique.But, the Ziegler–Nichols method is still widely used fordetermining the parameters of PID controllers. In addition,


construction of a mathematical tuning model design becomessometimes costly and these tuning rules often do not give suit-able values because of modeling errors. The linear program-

ming method is efficiently for tuning the PID gains. But, it isan iterative feedback tuning; so, the computational time andthe difficulty of the tuning are high. Thus, the linear program-

ming method is suitable for the specific case of tuning that is alinear objective function. In this paper, iterative algorithm andcurve fitting technique proposed to tune the fractional order

time delay system with PID controller.

3. Fractional order PID controller

Fractional-order controller design has attracted considerableattention in the recent years due to a number of applications.Better performances of the closed-loop can be achieved by

using such kind of controllers. In many industrial applications,the PID controller is used due to the simplicity of the opera-tion, design and low cost. The PID controllers are describedby a fractional order mathematical model. The fractional order

system is designed on control theory based techniques. So theclosed loop control parameters are changed sensitively andtheir performance is enhanced. The fractional order PID con-

troller block diagram structure is given in the following Fig. 1.The above figure describes the combination of the PID con-

troller GC (s) and fractional order system GC(s) and e�hs. The

inputs, error and output of the present closed loop control sys-tem are r E and Y respectively. Here, the output of the frac-tional order PID controller can be described in the followingEq. (1).

YðsÞ ¼ EðsÞ � K � e�hs Kpsþ Ki þ Kds2

ðTs2 þ sÞ

� �ð1Þ

whereY(s) is the output equation,E(s) is the error of the system,

T is the time constant, h is the time delay andK is represented asthe steady state gain of the system, Kp, Ki and Kd are theproportional, integral and derivative gains respectively. The

better tuning parameters are achieved by the proposed tech-nique, which is briefly explained in the following Section 3.1.

3.1. Over view of the proposed method

In this paper, a regression analysis for tuning the PID control-ler with fractional order time delay system is proposed. The

regression analysis tuning is one of the statistical models,which are used to describe the relationship between two andmore variables. It identifies the best fit parameters from theavailable system dataset. Here, the tuning process of the

proposed model depends on the weight of the exponentialfunction. From the iterative algorithm best weights are deter-mined. It has been allowed to evaluate the best fit parameters

Figure 1 Structure of the fractional order PID controller.

of the system and it makes the exact system response. By usingthe evaluated parameters the fractional order system steadystate response is maintained and the best PID controller gains

were achieved at the time of system parameter variations.

3.1.1. Regression model

The proposed regression model is the widely used prediction

and forecasting technique, which is used to discover the bestfit parameters from the available system data points. Here, itforms the regression equation with the use of system output

parameters. In the regression equation the best values aredetermined with the required adjustments of the systemparameters. The general equation can be described [5,8] in

the following,

znðxÞn ¼ z0 þ z1x1 þ z2x

2 þ z3x3 þ � � � þ zn�1x

n�1 þ znxn ð2Þ

where zn(x)n is the required system data, z0, z1, z2 . . .zn�1

and zn are the system data points at various conditions. Thesystem data are depending on the response of Y(s), whichare varied from different conditions, i.e., 0ton values. Inregression analysis the system response at n value can be

described as the following,In regression analysis condition, xn ¼ 1

YðsÞ, zn ¼ 11þexpwn

Then the regression value zn(xn) is rewritten as follows,

znðxÞn ¼1

1þ expwn EðsÞ � K � e�hs KpsþKiþKds2

ðTs2þsÞ

� �� n ð3Þ

where wn is the weight of the exponential function, the equa-tion shows the system data at zn(x

n) value. By using the Eq.(3), the following equations are derived from different condi-

tions. Then the following equation can be described at the ini-tial data points and weight. If, xn = x0 and zn = z0, then theEq. (3) is written as follows:

znðxnÞ=n ¼ 0 ¼ z0 ð4Þ

If, xn = x1 and zn = z1 then Eq. (3) is written as follows:

Figure 2 Structure of the proposed method.

Figure 3 Performance of the system (a) PID controller (b) Ziegler–Nicholas method (c) curve fitting technique (d) Wang tuning

controller (e) regression method.


Figure 4 (a–c) Comparison of the tuning performance of the system at different time delay instants.


znðxnÞ=n ¼ 1

¼ 1

1þ expw1 EðsÞ � K � e�hs KpsþKiþKds2

ðTs2þsÞ

� �� 1 ð5Þ

If, xn = xn-1 and zn = zn�1 then Eq. (3) is written as follows:

ZnðxnÞ=n ¼ n� 1

¼ 1

1þ expwn�1 EðsÞ � K � e�hs KpsþKiþKds2

ðTs2þsÞ

� �� n�1ð6Þ

If, xn = xn and zn = zn then Eq. (3) is written as follows:

znðxnÞ=n ¼ n

¼ 1

1þ expwn EðsÞ � K � e�hs KpsþKiþKds2

ðTs2þsÞ

� �� n ð7Þ

The above mentioned equations at different conditions (4) to(7) are substituted in Eq. (2) and the regression based system

equation is derived. Finally, the data points are combinedwith the standard fractional order system which is derived interms of a regression equation, which is in the form of each

data point and the derived system equation is described asfollows:

znðxnÞ ¼ z0 þ 1

1þexpw1 EðsÞ � K � e�hs KpsþKiþKds2

ðTs2þsÞ

� �� 1þ � � �

þ 1

1þexpwn�1 EðsÞ � K � e�hs KpsþKiþKds2

ðTs2þsÞ

� �� n�1

þ 1

1þexpwn EðsÞ � K � e�hs KpsþKiþKds2

ðTs2þsÞ

� �� n

ð8Þ

The best fit data point of the system depends on the weight ofthe exponential function. The iterative algorithm is used to

determine the best weights; it means the certain weight con-tains reduced overshoot time, settling time and steady stateerror. The identification of the best weight using the iterativealgorithm is briefly explained in the following section.



3.1.2. Best weight determined by iterative algorithm

An iterative algorithm is the act to determine the desired goal,

target or result. In the process a mathematical function isapplied repeatedly, and the output of the one iteration is usedas the input of the next iteration. It can produce the approxi-

mate numerical solutions depending on the mathematical eval-uation. Here, the best weight is determined from certainevaluations. During the iteration process, the selected weight

checks for the convergence condition, i.e., the overshoot time,the settling time and the steady state error is reduced. If theresultant weight satisfies the convergence condition, then it

means that the steady state response of the system has beenmaintained.

wn ¼xn � l1

l2

ð9Þ

where xn is the data points of the fractional order system, l1and l2 are the scaling transformation l1 = mean(xn) andl2 = std(xn).

Steps to determine the best weight

Step 1: Initialize the system data points fromxnmin � xn � xn

max:Step 2: To determine the weight using the Eq. (9) and the

system data points.Step 3: The determined weights are applied into the Eq.(8) and check the output.

Step 4: If the convergence is satisfied, i.e., the overshoottime, the settling time and the steady state error isreduced. Then the selected weight is the best weight(wBF

n ) or else go to the next step 5.

Step 5: To adjust the weights as wn ± 1, which isachieved by changing the data points. Then repeat theprocess until the best weight is achieved (wBF

n ).

The final output of the iterative algorithm is the bestweight, which is used to develop the optimal system response.

The sequences of best weights are applied in the Eq. (1) and itcan be described in the following Eq. (10).



zBFn ðxÞn ¼ zBF0 þ zBF1

1

YðsÞ

� �1

þ zBF21

YðsÞ

� �2

þ zBF31

YðsÞ

� �3

þ � � � þ zBFn�11

YðsÞ

� �n�1

þ zBFn1

YðsÞ

� �n

ð10Þ

The above equation is the resultant regression equation. The

proposed method operational structure is described in the fol-lowing Fig. 2. The proposed regression model is implementedin the MATLAB platform and the effectiveness is analyzed by

comparing the classical PID controller, Ziegler–Nichols tuningmethod and iterative algorithm and curve fitting techniquebase tuning method.

4. Results and discussion

The proposed regression model is implemented on the MAT-

LAB 7.10.0 (R2010a) platform. The numerical results of the

proposed method are presented and discussed in this section.In the implementation process, the system parameters values

are set manually, i.e., the proportional gain (Kp), integral gain(Ki) and derivative gain (Kd) are 0.5, 0.05 and 3 respectively, timeconstant (T) is 360 s, time delay (h) is 1 s, steady state gain is (Tf)

14.9, the reference step is 10 and the simulated time is 1000 s.The effectiveness of the proposed method is tested and com-pared using the classical PID controller, Ziegler–Nichols tuning

method and curve fitting technique based tuning method. Thefractional order system with various time delays (h = 20, 40,60, 80 and 100) at PID controller, Ziegler–Nichols tuningmethod, curve fitting technique, Wang tuning controller and

regression method are analyzed in the following Fig. 3a–erespectively.

Then the fractional order time delay system of tuning per-

formance of the proposed regression method is compared withthe conventional PID controller, which is illustrated in theFig. 4a–c. It is demonstrated under various time delays such

as h = 20, 40 and 60. In Fig. 5a–c the regression method iscompared to the Ziegler–Nicholas method at time delays



h = 20, 40 and 60 respectively. The Wang tuning controller is

compared with the proposed method and it is explained in theFig. 6a–c respectively. The tuning performance of our methodeffectiveness is compared to the curve fitting technique at time

delay instants h = 20, 40 and 60, which is illustrated in theFig. 7a–c respectively. The bode diagram of the system is eval-uated and subsequently setting the described time delay values.The bode diagram of the system after setting time delay instant

h = 20 is illustrated in the Fig. 8a. Fig. 8b shows that bodediagram of the system after setting the time delay instanth = 40 and bode diagram after setting the time delay instant

h = 60, which is illustrated in the Fig. 8c.The proposed regression method’s effectiveness was dis-

cussed in this section. Here, the fractional order time delay

system is tested under the conventional PID controller,Ziegler–Nichols method, curve fitting technique, Wang tuningcontroller and our proposed method. These techniques areanalyzed with various time delay instants h = 20, 40, 60, 80

and 100. During the time delay occurrence in the fractional

order time delay system, the output performance was oscil-

lated. Therefore the rise time, overshoot time and settling timehave been increased. Then the output performance of the everytechnique is compared to the proposed technique. By using the

PID controller at different time delay instants h = 20, 40 and60. It takes more time to reach a low value to the highest value(rise time), the required output signal exceeds its target(overshoot time) and the settling time is also underprivileged.

For Ziegler–Nichols method, reaching the high value at the300 s at the time delay instant h = 20. The rise time getsincreased from 320 s and 340 s, due to the time delay becomes

increased at 40 and 60 respectively. The output of the Ziegler–Nichols method exceeds its target at increased time. Also theoutput requires more time to achieve the steady state or set-

tling time, i.e., takes more than 700 s at various time delayinstants h = 20, 40 and 60. Similar to the Ziegler–Nicholsmethod the Wang tuning controller is also inefficient to pro-duce better tuning performance. The curve fitting technique

also shows the following unfeasible solutions at various time

Figure 8 Bode diagram of the system after setting different time delay instants (a) h = 20 (b) h = 40 and (c) h = 60.


delay instants h = 20, 40 and 60. During the time delay occur-rence, the rise time is increased more than 80 s, a peak over-shoot time somewhat is reduced and the settling timebecomes above 100 s. The proposed regression method

achieves the rise time at less than 30 s, peak overshoot timegets reduced and the settling time has been less than 80 s.The comparative analysis shows that, the proposed technique

gets better for tuning the system response when comparedto curve fitting technique, Wang tuning controller, Ziegler–Nichols method and PID controller.

5. Conclusion

The proposed regression technique is used for tuning the frac-

tional order time delay system with PID controller. In theregression technique, fractional order system output parame-ters were utilized to derive the time delay system response in

the form of the regression function. Then, the best weightswere selected by an iterative algorithm for fitting the best sys-tem response. The best weight was applied to the regressionequation and the corresponding time delay system response

was analyzed. The results have been verified through varioustime delay responses and analyzed the stability of the PIDcontroller with fractional order time delay system. The effec-tiveness of the proposed method is analyzed via the compari-

son with the classical PID controller, Ziegler–Nichols tuningmethod and iterative algorithm and curve fitting techniquebase tuning method. The comparative analysis shows that,

the proposed hybrid technique is the best technique for tuningthe fractional order time delay system, which is competent overthe other tuning methods. In future, the proposed method can

be used in the higher order system tuning parameter optimiza-tion. Also the PID controller with fractional order time delaysystem tuning parameters will be predicted by using different

types of optimization techniques.

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Mr. S.P. Agnihotri (Santosh Prabhakar

Agnihotri) obtained his Bachelor’s degree in

Instrumentation and Control from University

of Pone. Then he obtained his Master’s degree

in Instrumentation Engineering and perusing

PhD from SGGS Institute of Engineering and

Technology, Vishnupuri, Nanded, Swami

Ramanand Teerth Marathwada University

his current research interests is time delay

system.

Dr. Laxman Madhavrao Waghmare Presently,

he is working as Director, SGGS Institute of

Engineering and Technology, Vishnupuri,

Nanded, completed B.E. (1986) and M.E.

(1990) from the SGGS Institute of Engineer-

ing and Technology, Nanded and Ph.D.

(2001) from Indian Institute of Technology

(IIT), Roorkee. His field of interest includes

intelligent control, process control and, image

processing. He is recipient of K.S. Krishnan

Memorial national award for the best system

oriented research paper (published in the IETE Research Journal).

Presently working for a research project sponsored by the NRB of

DRDO.

http://refhub.elsevier.com/S2090-4479(14)00049-5/h0010






















































































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