tuning of fuzzy pid

8/4/2019 Tuning of Fuzzy Pid

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ISA Transactions 50 (2011) 2836

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ISA Transactions

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Tuning of an optimal fuzzy PID controller with stochastic algorithms fornetworked control systems with random time delay

Indranil Pan a, Saptarshi Das a,b, Amitava Gupta a,b,

a Department of Power Engineering, Jadavpur University, Salt Lake Campus, LB-8, Sector 3, Kolkata-700098, Indiab School of Nuclear Studies and Applications (SNSA), Jadavpur University, Salt Lake Campus, LB-8, Sector 3, Kolkata-700098, India

a r t i c l e i n f o

Article history:

Received 12 August 2010

Received in revised form

11 October 2010

Accepted 19 October 2010Available online 11 November 2010

Keywords:

Fuzzy PID controller

Genetic Algorithm

Networked control system

Optimal tuning

Particle Swarm Optimization

Random network delay

a b s t r a c t

An optimal PID and an optimal fuzzy PID have been tuned by minimizing the Integral of Time multipliedAbsolute Error (ITAE) and squared controller output for a networked control system (NCS). The tuning is

attempted for a higher order and a time delay system using two stochastic algorithms viz. the GeneticAlgorithm (GA) andtwo variants of Particle Swarm Optimization(PSO) and theclosedloop performances

are compared. The paper shows that random variation in network delay can be handled efficiently withfuzzy logic based PID controllers over conventional PID controllers.

2010 ISA. Published by Elsevier Ltd. All rights reserved.

1. Introduction

Fuzzy logic controllers (FLC) have become more commonin recent control applications to handle complex nonlinearprocesses [1,2]. It has been shown by many contemporaryresearchers that application of FLC enhances the closed loopperformance of a PID controller in terms of handling change inan operating point for nonlinear processes by online updatingthe controller parameters [3,4]. FLCs generally work with a setof control rules, derived from experts knowledge. Various fuzzylogic controller structures which are analogousto the conventionalPID controllers are analyzed by Mann et al. [5] and Golob [6]

using single or multiple input conditions (viz. error, change of

error and rate of change of error). The universal approximationproperty as in [2] states that there is a way to implement fuzzycontrollers for almost all types of nonlinear processes but thereis no mathematical formulation to decide what would be theappropriate choice of fuzzy parameters in implementing them.Hence empirical rules are used for the choice of various fuzzyparameters as discussed in [7]. The fuzzy tuning parameters may

Corresponding author at: Department of Power Engineering, Jadavpur Univer-sity,Salt Lake Campus, LB-8,Sector3, Kolkata-700098, India. Tel.: +91 9830489108,

+91 33 2442 7700; fax: +91 33 2335 7254.

E-mail addresses: [email protected], [email protected](I. Pan),[email protected](S. Das), [email protected](A. Gupta).

be the choice of inputs, scaling factors, membership functions(number or type or both), rule base, fuzzificationdefuzzificationand inferencing techniques [7].

It has been shown in [24,8] that a change in inputoutputscaling factors (SF) affects the control performance of the FLC to agreater extent compared to the choice of the type of membershipfunctions (MF). Also, the output SFs act like the controller gainsand hence directly affect the stability of the closed loop system. So,the output SFs have greater importance than the input SFs on theclosed loop performance of a process and hence should be chosenvery carefully. The FLC tries to mimic the operators expertise byincorporating a nonlinear relationship between the error and thederivative of error and that of the output control signal [1,2]. Often,

fixed SFs and predefined MFs become insufficient for achievingan optimal performance and need to be tuned online. It has beenshown by Woo et al. [8] that a change in input and output scalingfactors (SF) affects the control performance to a higher extent thanvariation in overlap of the fuzzy membership functions. Hence, inthe present study, only inputoutput SFs are tuned to find out theoptimal parameters of a FLC based PIDcontroller to handle randomvariation in network delay.

In recent past, fuzzy logic based PID controllers have becomemore common to handle complex dynamic processes. Diverselinear and nonlinear plants have been tuned by Mudi and Pal[3,4] and Bhattacharya et al. [9] with a fuzzy gain tuningmechanism and implemented along with a two input-one outputFLC. Various improvements in conventional PID controllers using

0019-0578/$ see front matter 2010 ISA. Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.isatra.2010.10.005
http://dx.doi.org/10.1016/j.isatra.2010.10.005http://www.elsevier.com/locate/isatranshttp://www.elsevier.com/locate/isatransmailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.isatra.2010.10.005http://dx.doi.org/10.1016/j.isatra.2010.10.005mailto:[email protected]:[email protected]:[email protected]:[email protected]://www.elsevier.com/locate/isatranshttp://www.elsevier.com/locate/isatranshttp://dx.doi.org/10.1016/j.isatra.2010.10.005


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I. Pan et al. / ISA Transactions 50 (2011) 2836 29

Fig. 1. Optimal fuzzy PID structure with random network delays.

a fuzzy inferencing mechanism have been investigated in [1013].Various tuning methods have also been proposed for tuning thefuzzy controller parameters as in [14] and others involving theGenetic Algorithm etc. [10,1416]. Mathematical quantificationusing non symmetrical fuzzy sets for a generalized class ofcontrollers has been discussed by Mohan and Sinha [17] and theapplicability of various types of fuzzy controllers from controlperspectiveare analyzed. Performances of fuzzyPIDs are compared

with normal PIDs and model predictive control in [18]. In [18]the fuzzy parameters are tuned using the NelderMead downhillsimplex method. Also various performance indices [1820] forthe cost function are compared in [18]. PID controller parametershave been tuned by a fuzzy system by Kazemian [21]. Fuzzy logiccoupled with neural networks has also been used to tune PIDparameters in [19].

Due to quantum leaps in communication systems, in recentyears, it has become more normal to use a common commu-nication channel like Ethernet or CAN bus etc. for transmissionof the control signal and the measured output. This helps in re-ducing wiring costs and eliminates the necessity for maintain-ing dedicated communication channels for each control parameter[22,23]. However, this type of networked control system is not apanacea and has various unresolved issues like transmission delays

and packet dropouts [24] which can degrade control performance.Hence these finer nuances over conventional control systems needto be delved into before actually implementing it in a real plant.

In recent NCS applications, fuzzy logic based controllers havebeen proved to be efficient in handling packet drop-out [25,26] andnetwork induced delays [23]. Various improvisations over existingprotocols have been proposed using fuzzy logic in [2628] whichhelp in congestion control and reduce delays and packet losses inthe network. We,however intend to focus on existing transmissionprotocols and evaluate performances of various controllers forvarying levels of transmission delays. Different models basedon fuzzy logic have been proposed for the modelling of a NCSin [29,30]. Various nonlinear systems which can be represented byequivalent fuzzy models have beenimplemented over the network

in [3140] andtheir performance with respect to delaysand packetdropouts have been analyzed. A Matlab based co-simulation toolcalled TrueTime which helps in analyzing controller task executionin real time kernels along with network transmissions andcontinuous plant dynamics has been used in the analysis of fuzzyPID controllers implemented over the network in [4148]. Fuzzylogiccontrollers with their improvisations have been implementedto handle network induced delays and their performances overtheir conventional counterparts have been investigated in [4952].A fuzzy PID controller has been implemented for a network basedcascade control system in [53,54]. However no optimization of thefuzzy PID parameters has been done to check for the optimumvalues of these parameters. Also time domain error indices likeITAE, Integral of Absolute Error (IAE) etc. based optimization have

not been included in the analysis, and the saturation of controlleroutput for these controllers has not been investigated. In the

present work, we implement a fuzzy PID controller for a higherorder plant and also a plant with time delay and optimize the fuzzyparameters with stochastic algorithms like the Genetic Algorithmand Particle Swarm Optimization, taking the random delays inthe network into account. Also the effectiveness of the variousstochastic algorithms and their variants for tuning are comparedin the present study. Our cost function not only includes ITAE butalso hasthe controller outputtakeninto account to avoid controllersaturation.

A practical networked control loop generally consists of adeterministic inherent system delay and two stochastic delays [23]viz. the controller to actuator delay (CA) and the sensor tocontroller delay (SC) as shown in Fig. 1. Under these conditions,the process to be controlled over a network can be considered asrandomly varying with time. It has been suggested by Mudi andPal [3,4] that FLCs have a higher capability of enforcing optimalperformance in a control loop over conventional optimal PIDs fornonlinear and time-varying systems. In this paper, an optimalfuzzy PID controller has been tuned by minimizing the sum ofITAE and squared value of control signal considering randomvariationin network delay andthe performance is compared with aconventional optimal PID controller, tuned with the same criteria.

The performance of the optimal controllers also depends on

the choice of a suitable optimization algorithm, used for controllertuning. Many stochastic optimization algorithms have come up incontrol applications, especially in controller tuning [5557]. Inthispaper, a PID and fuzzy-PID controller have been tuned with twostochastic optimization algorithms, namely the Genetic Algorithmand Particle Swarm Optimization with its two variants viz. gbestand lbest PSO [58,59].

The rest of thepaper is organized as follows. Section 2 discussesthe structure of the optimal fuzzy PID. A brief description of thetwo stochastic optimization methods used for controller tuning isdiscussed in Section 3. Section 4 presents the simulation results oftwotest plants with andwithout randomnetwork delay. Thepaperends with the conclusion as Section 5 followed by the references.

2. Structure of the fuzzy PID controller and its optimal tuning

2.1. Fuzzy PID controller to handle random network delay

The fuzzy PID structure (Fig. 1) used in this paper is acombination of fuzzy PI and fuzzy PD controllers with Ke, Kd asinput SFs and , as output SFs as discussed by Woo et al. [8],Yesil et al. [60], Qiao and Mizumoto [61], Li et al. [62], Mohanand Sinha [63] and Mann et al. [64]. This uses two-dimensionallinear rule base (Fig. 2) for error (e), error derivative (e) and FLCoutput (uFLC) with standard triangular MFs (Fig. 3) and Mamdani-type inferencing.

In Figs. 2 and 3, the fuzzy linguistic variables NL, NM, NS, ZR,PS, PM, PL represent Negative Large, Negative Medium, NegativeSmall, Zero, Positive Small, Positive Medium and Positive Large

respectively. The FLC output (uFLC) is determined by using thecenter of gravity method by defuzzification.


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30 I. Pan et al. / ISA Transactions 50 (2011) 2836

Fig. 2. Rule base for error, error derivative and FLC output.

Fig. 3. Membership functions for error, error derivative and FLC output.

2.2. Formulation of the objective function for time domain optimal

tuning

The controller output of a conventional PID is a weighted sumof error, its derivative and integral values, i.e.

u(t) = Kp [e(t)] + Ki

[e(t)dt

]+ Kd

[de(t)

dt

]. (1)

The simple error minimization criteria can be modified byintroducing a suitable time domain performance index like ITAEor Integral of Time multiplied Squared Error (ITSE) to have a bettercontrol action. Also for a sudden change in set-point, ITSE basedtuning produces a larger controller output than ITAE, hence in thepresent study only ITAE has been considered as a suitable timedomain performance index [55] and not other performance indices

having higher powers of error and time.The objective function, used for controller tuning has been

taken as a weighted sum of the ITAE and squared control signalsimilar to that of [56,57], i.e.

J=

0w1t|e(t)| + w2u

2(t) dt. (2)It is worth mentioning that the weights w1 and w2 have beenintroduced in the objective function (2) with a provision ofbalancing the impact of the error and control signal. In the presentsimulation study we have considered equal weights for the twoobjectives to be met by the controller as such the minimizationof the error index is as equally important as the control signal is.The objective function J in (2) is now minimized to find out the

optimal set of controller parameterswhich simultaneously reducesthe ITAE and control signal u(t). The time multiplication term inerror index ITAE minimizes the chance of oscillation at later stages,thus effectively reducing the settling time (ts) of the closed loopsystem and the absolute value of error minimizes the percentageof overshoot (%Mp). The minimization of the squared control signal

reduces the chance of actuator saturation and also reduces the sizeof the actuator and thus the cost involved.

It has been seen that classical optimization problems oftenget trapped in local minima. This limitation can be overcomeby the introduction of stochastic optimization methods likeParticle Swarm Optimization or the Genetic Algorithm[5557].Butoptimal performance cannot be guaranteed if there are randomdelays in the network, i.e. CA and SC (Fig. 1). To overcome theproblem of random variation in network delay, the controllerperformance can be further enhanced by introducing a FLC based

PID over a simple PID structure. Thus Fuzzy PIDs are expected toproduce satisfactory closed loop response for random variationin system parameters i.e. network delays in this case. Thus ourproposed scheme combines both the time domain optimality aswell as required robustness against random delay variation inthe closed loop system (due to the network in the loop) with anoptimal Fuzzy PID controller.

3. Stochastic optimization algorithms used for controller

tuning

The tuning of the parameters of the Fuzzy PID controller(i.e. input and output SFs) has been carried out by two popularstochastic optimization methods, namely the GA and PSO which

are described briefly in the following subsections.

3.1. Particle Swarm Optimization (PSO)

In PSO the particles are initially distributed randomly in thesearch space. The particles move towards a global minima in eachiteration depending on the best value found so far (global best or

gbest) among all the particles and the individual particles bestposition (pbest). The objective function which is to be minimizedis used to evaluate the fitness of the particle for a particularposition. For each particle (i) the velocity in each dimension inthe consecutive iteration is updated by the following velocity andposition update equation, given by

vi(t+ 1) = vi(t) + c11(pi(t) xi(t)) + c22(pg(t) xi(t))xi(t+ 1) = xi(t) + vi(t+ 1).

(3)


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Each particles position (xi) in the next iteration depends onits velocity (vi) in the present equation multiplied by an inertiafactor () which is generally kept large so as to prevent randommovement of the particles in the search space and to deviate the

velocity of the particles by a smaller amount in each iteration.The other two positive constants c1, c2 are the cognitive learningrate and the social learning rate respectively. The weights c1, c2represent the relative importance of the learning of the particlesfrom its own best position (pi) and the global best position (pg),and both have been chosen as 1.49 for the present study, similarto [55]. In (3), {1, 2} [0, 1] are two uniformly distributedrandom numbers.

The inertia factor () in our case has also been reduced linearlyfrom 0.9 to 0.4 over the iterations [55]. This is an improvisationover the conventional PSO algorithm and incorporates a velocitycontrol mechanism which ensures more effective searching ata fine grain [56]. A velocity clamping is also introduced in thealgorithm and the maximum value of the velocity is set to 15% ofthe range in each dimension [65]. This ensures that the velocitydoes not explode to large values and helps in controlling the global

exploration of the particles. However, a judicious choice of thePSO parameters should be made so as to reduce thecomputational

effort and at the same time prevent pre-convergence of theoptimum solutions. Maiti et al. [55] dealt with a similar kind ofcontroller tuning and hence this has been chosen as a base casefor the PSO parameter values.

As a rule of thumb in the PSO algorithm, the minimum numberof particles must be at least greater than the number of solutionvariables. Increasing the number of particles gives better resultsat the cost of an increase in computational time and complexity.Hence there is a tradeoff between the two. In our case 20 particlesgive satisfactory results in terms of the convergence criterion aswell as the time taken. For the sake of effective comparison ofboth the gbest and lbest PSO algorithms the population is chosenas same.

In the gbest PSO a star topology is considered for the social

network as opposed to a ring topology in lbest PSO [58,59] and inboth cases the number of particles has been considered to be 20.

The same velocity and position update equations are used in boththese PSO variants but in gbest PSO, Pg in (3) represents the globalbest of all the particles till the current iteration, whereas in lbestPSO it represents the neighbourhood best of the particles till thecurrent iteration for each cluster. The lbest PSO has an overlappingneighbourhood, to facilitate information exchange. This is basedon adjacent indices of the population array rather than on spatialpositions to reduce computational complexity.In general, thegbestPSO converges faster than the lbest PSO due to larger particleinterconnectivity. However lbestPSOhas largerdiversityand is lesssusceptible to being trapped in local minima.

3.2. Genetic Algorithm (GA)

The genetic algorithm is another stochastic optimization pro-cess inspired by natural evolution and can be used to minimizea suitable objective function for tuning the controller parame-ters [57]. Initially, a population of solution vectors is created ran-domly over the whole solution domain. Each solution vector in thepresent population undergoes reproduction, crossover and muta-tion, in each iteration, to give rise to a better population of solutionvectors in the next iteration.

Reproduction implies that solution vectors with higher fitnessvalues can produce more copies of themselves in the nextgeneration. Usually a parametercalled theelite count is used whichrepresents the number of fittest individuals (solution vectors) that

will definitely go to the next generation. Increasing the elite countmay result in domination of the fitter individuals obtained earlier

in the simulation process and as such will result in less effectivesolutions. Hence this parameter is generally a small fraction ofthe total population size. In the present study, population size isconsidered to be 20 and elite count as 2.

Crossover refersto informationexchange based on probabilisticdecisions between solution vectors. Here the child vector of thenext generation is formed by combining the solution vectors oftwo parent individuals in the current population. The crossover

fraction dictates how many children other than the elite childrenare formed by crossover. The remaining children are formed bymutation. In mutation a small randomly selected part of a solutionvector is occasionally altered, with a very small probability ofcreating a child in the next generation. This way the solution isrefined iteratively until the objective function is minimized belowa certain tolerance level or the maximum number of iterations isexceeded.

If we have a crossover fraction of 1, which implies that thereis no mutation, then the genetic algorithm initially progresses tominimize the objective function until it forms the best individualfrom theavailable gene pool. After this thebest individual is carriedforward and replicated in successive generations and no newbetter individuals are obtained due to lack of mutation. Hence theproblem stagnates and the program terminates with this fitness

value after the maximum number of iterations is reached.However if we set crossover fraction as 0, implying that the

whole population evolves through mutation, then it does notimprove the fitness of the best individual at the first generation.It improves the fitness of the other individuals in the population,but since these are never combined with the genes of the bestindividual due to lack of crossover, the best fitness value levelsoff at a certain time and the program is terminated when themaximum number of iterations are reached.

Hence, a judiciouschoiceof the crossoverand mutation fractionneeds to be used. In our simulation we have used the crossoverfraction to be 0.8 and mutation fraction to be 0.2 which has givensatisfactory results for a wide variety of problems [66].

4. Results and discussions

The closed loop performance of some representative plantsin Zhuang and Atherton [67] (with and without network delays)have been compared with a conventional PID and a Fuzzy PID,both of which have been tuned with three stochastic optimizationmethods, namely the GA, gbest PSO and lbest PSO.

P1(s) =1

(s + 1)5(4)

P2(s) =2 (0.5s + 1) e0.1s

(s + 1) (4s + 1). (5)

The performance of the above plants has been compared on thebasis of optimal tracking for a unit change in set point as well assuppression of unit load disturbance [67]. Also, comparisons aremade for control signals in each case which is a cause of actuatorsaturation [56,57].

4.1. Simulation without network delay

The stochastic optimization based tuning results for test plants(4) and (5) with conventional PID and Fuzzy PID are reported inTables 1 and 2.

Here, the controller parameters in Tables 1 and 2 are calculatedwith minimization of the objective function in (2) for unit changein set point. Additionally the load disturbance is compared laterto evaluate the performance of the controllers, tuned via differentintelligent optimization algorithms. The closed loop responsefor plant P1 and P2 and the respective controller outputs for

unit change in set-point and load disturbance are shown inFigs. 48.


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Table 1

Tuning results of PID controller without network delay.

Plant Optimization algorithm Jmin Kp Ki Kd

P1

GA 53.0824 0.96 0.2273 1.0704

gbest-PSO 52.6866 1.1 0.2462 1.4367

lbest-PSO 52.6866 1.101 0.239 1.4364

P2

GA 14.46459 1.423 0.3162 0.195

gbest-PSO 14.4294 1.799 0.4025 1.0026

lbest-PSO 14.43 1.715 0.3816 0.4755

1.2

1

0.8

0.6

Amplitude

0.4

0.2

010 20 30 40 50 600

Time (sec)

70

Time Response of Plant P1 with Unit Set-Point Change & Load Disturbance

Fig. 4. Output of plant P1 with step change in set-point & load disturbance.

A

mplitude

10 20 30 40 50 60

Time (sec)

0 70

2.2

2

1.8

1.6

1.4

1.2

1

0.8

Controller Output for Plant P2

Fig. 5. Controller output for plant P1.

4.2. Simulations with network induced delay

Since FLC works on instantaneous values ofe and e, rather thana predefined model structure, its performance is expected to be

better over a simple PID for handling stochastic delays due to thenetwork, and the tuning results for the test plants are reported inTables 3 and 4. For the simulation of network delays in the forwardand the feedback path in Fig. 1, a random number in the interval of[00.2] seconds is generated at each time step.

The hybrid system comprising of the discrete time network andcontroller with Zero Order Hold (ZOH) along with the continuoustime plant can be considered as a continuous time system withrandom delay if the sampling time (Ts) is very small as shown byTipsuwan and Chow [68] and Fang et al. [69]. In the present studyTs = 0.01 s has been considered.

The corresponding closed loop response and controller outputsfor plant P1 and P2 are shown in Figs. 811, considering networkdelays.

It is evident from Figs. 8 and 10 that fuzzy PIDs have a nicecapability to suppress the effect of random delay variation in a

1.2

1

0.8

0.6

Am

plitude

0.4

0.2

0

Time Response of Plant P2 with Unit Set-Point Change & Load Disturbance

10 20 30 40 50

Time (sec)

0 60

Fig. 6. Output of plant P2 with step change in set-point & load disturbance.

20

Controller Output for Plant P2

2.2

2

1.8

1.6

1.4

1.2

1

0.6

0.8

Amplitude

2.4

0.410 30 40 50

Time (sec)

600

Fig. 7. Controller output for plant P2.

1.2

1

0.8

0.6

Amplitude

0.4

0.2

0

Time Response of Plant P1 with Unit Set-Point Change & Load Disturbance ConsideringRandom Network Delays

10 20 30 40 50

Time (sec)

0 60

Fig. 8. Output of plant P1 with random network delay.

networked control system. Also, the load disturbance suppression

is faster and deviation from the set-point is less with fuzzy PIDs

compared to a conventional PID controller. The controller output

becomes oscillatory with high amplitude in case of simple PID. The

fuzzy PID controller outputs are also oscillatory but the amplitudes

are less (Figs. 9, 11). To ensure that a large control signal does not

saturate the actuator, the control signal u(t) is also minimized as a

part of the objective function (2), in the proposed technique.

It is worth mentioning that the introduction of randomnetwork delays would lead to such a variation of controller


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Table 2

Tuning results of fuzzy PID controller without network delay.

Plant Optimization algorithm Jmin Ke Kd

P1

GA 55.2846 0.4506 0.6335 1.4428 0.6494

gbest-PSO 55.3445 0.4487 0.6113 1.4952 0.6512

lbest-PSO 55.2535 0.4369 0.5525 1.5043 0.6334

P2

GA 14.5233 0.8528 0.5305 3.0839 0.7747

gbest-PSO 14.1719 0.2947 0.372 4.1761 10.487

lbest-PSO 14.1732 0.3522 0.4726 3.2474 7.9644

20

Controller Output for Plant P1 Considering Random Network Delays

10 30 40 50

Time (sec)

600

4

3

2

1

0

1

2

Amplitude

5

3

Fig. 9. Controller output for plant P1 with random network delay.

Time Response of Plant P2 with Unit Set-Point & Load DisturbanceConsidering Random Network Delays

10 20 30 40 50

Time (sec)

0 60

1

0.8

0.6

0.4

0.2

Amplitud

e

1.2

0

Fig. 10. Output of plant P2 with random network delay.

20

Controller Output for Plant P2 Considering Random Network Delays

10 30 40 50

Time (sec)

600

2.5

2

1.5

1

0.5

0

0.5

1

Amplitude

3

1.5

Fig. 11. Controller output for plant P2 with random network delay.

Table 3

Tuning results of PID with network delay.

Plant Optimization algorithm Jmin Kp Ki Kd

P1

GA 54.4237 0.978 0.2217 0.9524

gbest-PSO 54.4947 0.946 0.2207 0.9018

lbest-PSO 54.684 0.943 0.2267 1.1464

P2

GA 14.5265 1.618 0.3636 0.1876

gbest-PSO 14.677 1.588 0.3059 0.2344

lbest-PSO 14.6801 1.158 0.3136 0.4203

output. Introducing network prediction schemes can ameliorate

the adverse effects to a certain degree. Other alternative can be to

design effective transmission protocols so that the random delaysare handled adequately by the network protocol itself. Also, the

presence of the control signal in the performance index effectively

reduces the band of oscillation in the controller output. With

only a simple error minimizing criteria, the band of oscillation in

control signal would have been more. This is a particular problem

introduced by the randomness of the communication network.

Since the primary objective of the controller is to maintain time

domain optimality which is evident from the time responses, the

control signal suffers to some extent (as it has been optimized and

not been allowed to be arbitrarily high) so as to suppress the effect

of random delay in the time responses and yield a smooth closed

loop dynamics. From the presented figures and tables, it is also

evident that the PSO variants perform better than the GA for the

optimization process.

4.3. Effect of gradual increase in random network delay

The best tuned controllers ofTables 3 and 4 (having the lowest

Jmin) are now tested with increased network delay (CAmax =

SCmax =

{0.2, 0.4, 0.5}) to see how efficiently they handle relatively

large random delays with the same tuning parameters. Simulated

results of the system and controller outputs for plants (4)(5) are

presented in Figs. 1215 respectively.

It is clear from Figs. 13 and 15 that the controller output

for the PID controller becomes larger than the Fuzzy PID when

the network induced delay is increased, which may saturate the

actuator in practical NCS applications. Also, Fuzzy PIDs give lowerovershoot than simple PIDs for increased network delay (Figs. 12

and 14).

It is also worth mentioning that all issues in networked control

applications are not essentially process control delays (which

might be large but are generally constant). Stochastic delays are

much harder to deal with and even a small amount of random

stochastic delay in each sampling time can result in system

instability even if the system might be stable due to the same

amount of constant time delay which is not stochastic in nature as

shown by Hirai and Satoh [70]. This implies that a control system

designed for the worst case scenario does not necessarily ensure

system stability when the delay varies stochastically between the

upper and lower bounds. The simulated Figs. 1215 show that the

fuzzy logic controller has higher capability of suppressing randomvariation in network delay in the forward and feedback path.


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Table 4

Tuning results of fuzzy PID with network delay.

Plant Optimization algorithm Jmin Ke Kd

P1

GA 56.09 0.4165 0.3617 1.6922 0.6183

gbest-PSO 55.6603 0.3487 0.486 1.8778 0.895

lbest-PSO 56.325 0.5709 0.8484 1.1915 0.5034

P2

GA 14.92 1.9299 1.08 1.9199 0.7337

gbest-PSO 14.6336 0.6815 1.0369 0.9233 3.2445

lbest-PSO 14.7689 0.6049 0.8688 1.0554 4.6765

1.2

1

0.8

0.6

Amplitude

0.4

0.2

0

Time Response of Plant P1 with Gradual Increase in Random Network Delay

10 20 30 40 50

Time (sec)

0 60

Fig. 12. Output of plant P1 with gradual increase in random network delay.

20

Controller Output of Plant P1 with Gradual Increase in Random Network Delay

10 30 40 50

Time (sec)

600

8

6

4

2

0

2

4

6

8

A

mplitude

10

10

Fig. 13. Controller output for P1 with gradual increase in random network delay.

1.2

1

0.8

0.6

Amplitude

0.4

0.2

0

Time Response of Plant P1 with Gradual Increase in Random Network Delay

10 20 30 40 50

Time (sec)

0 60

Fig. 14. Output of plant P2 with gradual increase in random network delay.

Also the controller tuning algorithm presented in this paper isoffline andis independent of thechoiceof sampling time. However,

20

Controller Output of Plant P2 with Gradual Increase in Random Network Delay

10 30 40 50

Time (sec)

600

3

2

1

0

1

2

Amplitude

4

3

Fig. 15. Controller output for P2 with gradual increase in random network delay.

the controller performance will deteriorate as the sampling time is

increased, as it deviates from the continuous time case to a larger

extent. In NCS applications however the sampling time is a design

input variable based on the network conditions, since decreasing

the sampling time would result in a large number of packets being

sent through the network which would result in more network

congestion and increase delays. Real time implementation of

such controllers in NCS for process control applications has been

reported in [23,71].

5. Conclusion

The effect of random delays in NCS has been handled in this

paper by using fuzzy PID controllers. Tuning of controllers is

done by minimizing ITAE and the squared control signal with

three stochastic algorithms viz. the GA, gbest PSO and lbest PSO.

Simulation results indicate that load disturbance suppression with

Fuzzy PID tuned by gbest and lbest PSO is better than that with

the GA. Also, to nullify the effect of random variation network

delay in the controlled output, the control action with simple

PIDs becomes much larger than that with Fuzzy PIDs. The random

network induced delay is then gradually increased and the FuzzyPID controller again shows better performance than a simple

PID controller, especially in load disturbance suppression. Further

works on the proposed scheme can be directed towards stability

analysis of such controllers in NCS applications. Other future

investigations may include a performance study of the fuzzy

controller to handle nonlinear processes and considering sensor

noise and packet drop-outs in the network.

Acknowledgement

This work has been supported by the Board of Research in

Nuclear Sciences (BRNS) of the Department of Atomic Energy

(DAE), India, sanction no. 2009/36/62-BRNS, dated November2009.


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References

[1] Driankov Dimiter, Hellendoorn Hans, Reinfrank Michael. An introduction tofuzzy control. Berlin: Springer-Verlag; 1993.

[2] Passino Kevin M, Yurkovich Stephen. Fuzzy control. Reading, (MA): Addison-Wesley Longman Inc.; 1998.

[3] Mudi Rajani K, Pal Nikhil R. A robust self-tuning scheme for PI-and PD-typefuzzy controllers. IEEE Transactions on Fuzzy Systems 1999;7(1):216.

[4] Mudi Rajani K, Pal Nikhil R. A self-tuning fuzzy PI controller. Fuzzy Sets andSystems 2000;115(2):32738.

[5] Mann George KI, Hu Bao-Hang, Gosine Raymond G. Analysis of direct actionfuzzy PID controller structures. IEEE Transactions on Systems, Man andCybernetics, Part B (Cybernetics) 1999;29(3):37188.

[6] Golob Marjan. Decomposed fuzzy proportional-integral-derivative con-trollers. Applied Soft Computing 2001;1(3):20114.

[7] Reznik Leonid, Ghanayem Omar, Bourmistrov Anna. PID plus fuzzy controllerstructures as a design base for industrial applications. Engineering Applica-tions of Artificial Intelligence 2000;13(4):41930.

[8] Woo Zhi-Wei, Chung Hung-Yuan, Lin Jin-Jye. A PID type fuzzy controller withself-tuning scaling factors. Fuzzy Sets and Systems 2000;115(2):3216.

[9] Bhattacharya S, Chatterjee A, Munshi S. A new self-tuned PID-type fuzzycontroller as a combination of two-term controllers. ISA Transactions 2004;43(3):41326.

[10] Bandyopadhyay R, Chakraborty UK, Patranabis D. Autotuning a PID controller:a fuzzy-geneticapproach. Journal of SystemsArchitecture 2001;47(7):66373.

[11] Bandyopadhyay R, Patranabis D. A new autotuning algorithm for PIDcontrollers using dead-beat format. ISA Transactions 2001;40(3):25566.

[12] Bandyopadhyay R, Patranabis D. A fuzzy logic based PI autotuner. ISA

Transactions 1998;37(3):22735.[13] Blanchett TP, Kember GC, Dubay R. PID gain scheduling using fuzzy logic. ISA

Transactions 2000;39(3):31725.[14] Boubertakh Hamid, Tadjine Mohamed, Glorennec Pierre-Yves, Labiod Salim.

Tuning fuzzy PD and PI controllers using reinforcement learning. ISATransactions 2010;49(4):54351.

[15] Hu Baogang, Mann George KI, Gosine Raymond G. New methodology foranalytical and optimal design of fuzzy PID controllers. IEEE Transactions onFuzzy Systems 1999;7(5):52139.

[16] Visioli A. Tuning of PID controllers with fuzzy logic. IEE ProceedingsControlTheory and Applications 2001;148(1):18.

[17] Mohan BM, Sinha Arpita. Mathematical models of the simplest fuzzy PI/PDcontrollers with skewed input and output fuzzy sets. ISA Transactions 2008;47(3):30010.

[18] Mansour SE, Kember GC, Dubay R, Robertson B. Online optimization of fuzzy-PID control of a thermal process. ISA Transactions 2005;44(2):30514.

[19] Lee Ching-Hung, Teng Ching-Cheng. Calculation of PID controller parametersby using a fuzzy neural network. ISA Transactions 2003;42(3):391400.

[20] Xu Jian-Xin, Liu Chen, Hang Chang Chieh. Tuning of fuzzy PI controllers based

on gain/phase margin specifications and ITAE index. ISA Transactions 1996;35(1):7991.

[21] Kazemian Hassan B. Comparative study of a learning fuzzy PID controller anda self-tuning controller. ISA Transactions 2001;40(3):24553.

[22] Das M, Banerjee A, Ghosh R, Goswami B, Balasubramanian R, Chandra AK,Gupta A. A study on multivariable process control using message passingacross embedded controllers. ISA Transactions 2007;46(2):24753.

[23] Das M, Ghosh R, Goswami B, Chandra AK, Balasubramanian R, Luksch P,Gupta A. Multi-loop networked process control: a synchronized approach. ISATransactions 2009;48(1):12231.

[24] Zhang Wei, Branicky Michael S, Phillips Stephen M. Stability of networkedcontrol system. IEEE Control Systems Magazine 2001;21(1):8499.

[25] Dong Hongli, Wang Zidong, Gao Huijun. H fuzzy control for systems withrepeated scalar nonlinearitiesand random packet losses. IEEETransactions onFuzzy Systems 2009;17(2):44050.

[26] Li JianGuo, YuanJing Qi,Lu JunGuo. Observer-basedH controlfor networkednonlinear systems with random packet losses. ISA Transactions 2010;49(1):3946.

[27] Jammeh Emmanuel A, Fleury Martin, Wagner Christian, Hagras Hani,GhanbariMohammed. Interval type-2 fuzzylogic congestion control for videostreamingacross IP networks. IEEETransactions onFuzzy Systems2009;17(5):112342.

[28] Siripongwutikorn Peerapon, Banerjee Sujata, Tipper David. Fuzzy-basedadaptive bandwidth control for loss guarantees. IEEE Transactions on NeuralNetworks 2005;16(5):114762.

[29] Ren F-C, Chang C-J, Cheng R-G. QoS-guaranteed fuzzy transmission controllerfor dynamic TDMA protocol in multimedia communication systems. IEEProceedingsCommunications 2002;149(56):2928.

[30] Zheng Ying, Fang Huajing, Wang Hua O. TakagiSugeno fuzzy-model-basedfault detection for networked control systems with Markov delays. IEEETransactions on Systems, Man and Cybernetics, Part B (Cybernetics) 2006;36(4):9249.

[31] Jiang Bin, Mao Zehui, Shi Peng. H-filter design for a class of networkedcontrol systems via TS fuzzy-model approach. IEEE Transactions on FuzzySystems 2010;18(1):2018.

[32] Jia Xinchun, Zhang Dawei, Hao Xinghua, Zheng Nanning. Fuzzy H trackingcontrol for nonlinear networked control systems in TS fuzzy model. IEEE

Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 2009;39(4):10739.

[33] Zhang Huaguang, Yang Dedong, Chai Tianyou. Guaranteed cost networkedcontrol forTS fuzzy systems with time delays. IEEE Transactions on Systems,Man, and CyberneticsPart C: Applications and Reviews 2007;37(2):16072.

[34] Zhang Huaguang, Yang Jun, Su Chun-Yi. TS fuzzy-model-based robust Hdesign for networked control systems with uncertainties. IEEE Transactionson Industrial Informatics 2007;3(4):289301.

[35] Jiang Xiefu, Han Qing-Long. On designing fuzzy controllers for a class ofnonlinear networked control systems. IEEE Transactions on Fuzzy Systems2008;16(4):105060.

[36] Gao Huijun, Zhao Yan, Chen Tongwen. H fuzzy control of nonlinear systems

under unreliable communication links. IEEE Transactions on Fuzzy Systems2009;17(2):26578.

[37] Peng Chen, Yang Tai Cheng. Communication-delay-distribution-dependentnetworkedcontrolfor a class of TSfuzzy systems.IEEE Transactionson FuzzySystems 2010;18(2):32635.

[38] Zhang Huaguang, Li Ming, Yang Jun, Yang Dedong. Fuzzy model-based robustnetworked control for a class of nonlinear systems. IEEE Transactions onSystems, Man and Cybernetics, Part A (Systems and Humans) 2009;39(2):43747.

[39] YangDe-Dong, Zhang Hua-Guang. Robust H networkedcontrol foruncertainfuzzy systems with time-delay. Acta Automatica Sinica 2007;33(7):72630.

[40] Tian Engang, Yue Dong, Gu Zhou. Robust H control for nonlinear systemsover network: a piecewise analysis method. Fuzzy Sets and Systems 2010;161(21):273145.

[41] ZhangWenjuan, WangLian-Ming, DengYufen,Zhang Hongwei.Studieson thefuzzyPID control method for networked control systems withrandom delays.In: 7th world congress on intelligent control and automation. WCICA 2008.2008. p. 331620.

[42] Dezong Zhao, Chunwen Li, Jun Ren. Fuzzy speed control and stability analysisof a networked inductionmotor system withtime delays and packet dropouts.Nonlinear Analysis: Real World Applications 2011;12(1):27387.

[43] ZhangQian, GuoXi-Jin,Wang Zhen, TianXi-Ian.Application of improvedfuzzycontroller in networkedcontrol systems.Journalof China University of Miningand Technology 2006;16(4):5004.

[44] Huang Congzhi, Bai Yan, Liu Xingjie. Fuzzy PID control method for a class ofnetworked cascade control systems. In: The 2nd international conference oncomputer and automation engineering. ICCAE, 2010. vol. 1. 2010. p. 1404.

[45] Huang Congzhi, Bai Yan, Li Xinli. Simulation for a class of networked cascadecontrol systems by PID control. In: International conference on networking,sensing and control. ICNSC 2010. 2010. p. 45863.

[46] Zhang Wen-Juan, Deng Yu-Fen, Wang Lian-Ming, Zhang Hong-Wei. FuzzyPID control method for networked control system with constant delays. In:International conference on machine learning and cybernetics, 2008. vol. 4.2008. p. 196873.

[47] Du F, Qian QQ. Fuzzy immune self-regulating PID control based on modifiedSmith predictor for networked control systems. In: IEEE internationalconference on networking, sensing and control. ICNSC 2008. 2008. p. 4248.

[48] Du F, Qian QQ. Fuzzy immune self-regulating PID control for wirelessnetworked control system. In: IET conference on wireless, mobile and sensornetworks. CCWMSN07. 2007. p. 1081-4.

[49] Lee Kyung Chang, Lee Suk, Lee Man Hyung. Remote fuzzy logic control ofnetworked control system via profibus-DP. IEEE Transactions on IndustrialElectronics 2003;50(4):78492.

[50] Almutairi NaifB, Chow Mo-Yuen. PI parameterization using adaptive fuzzymodulation (AFM) for networked control systems-part I: partial adaptation.In: 28thannual conference of the industrial electronics society. IECON 02. vol.4. 2002. p. 31527.

[51] Almutairi NaifB, Chow Mo-Yuen. PI parameterization using adaptive fuzzymodulation (AFM) for networked control systems-part II: full adaptation. In:28th annual conference of the industrial electronics society. IECON 02. vol. 4.2002. p. 315863.

[52] Almutairi NaifB, Chow Mo-Yuen, Tipsuwan Yodyium. Network-based con-trolled dc motor with fuzzy compensation. In: 27th annual conference of theindustrial electronics society. IECON 01. vol. 3. 2001. p. 18449.

[53] Fadaei A, Salahshoor K. Design and implementation of a new fuzzy PID

controller for networked control systems. ISA Transactions 2008;47(4):35161.[54] Fadaei A, Salahshoor K. Improving the control performance of networked

control systems using a new fuzzy PID. In: IEEE international symposium onindustrial electronics. ISIE 2008. 2008. p. 206671.

[55] Maiti Deepyaman, Acharya Ayan, Chakraborty Mithun, Konar Amit, Ja-narthanan Ramdoss. Tuning PID and PID controllers using the integral timeabsoluteerror criteria.In: 4thinternationalconferenceon information and au-tomation for sustainability. ICIAFS 2008. 2008. p. 45762.

[56] Cao Jun-Yi, Cao Bing-Gang. Design of fractional order controllers basedon particle swarm optimization. In: 1st IEEE industrial electronics andapplications. 2006. p. 16.

[57] Cao Jun-Yi, Liang Jin, Cao Bing-Gang. Optimization of fractional orderPID controllers based on Genetic Algorithms. In: Proceedings of the 2005international conference on machine learning and cybernetics. vol. 9. p.56869.

[58] Kennedy James, Mandes Rui. Population structure and particle swarm perfor-mance. In: Proceedings of the 2002 congress on evolutionary computation.CEC02. vol. 2. p. 16716.

[59] Ghosh Sayan, KunduDebarati, Suresh Kaushik, Das Swagatam,AbrahamAjith,Panigrahi BijayaK, Snase Vaclav. On some properties of the lbest topology


9/9


in particle swarm optimization. In: Ninth international conference on hybridintelligent systems. HIS09. vol. 3. p. 3705.

[60] Yesil E, Guzelkaya M, Eksin I. Self tuning fuzzy PID type load and frequencycontroller. Energy Conversion and Management 2004;45(3):37790.

[61] Qiao Wu Zhi, Mizumoto Masaharu. PID type fuzzy controller and parametersadaptive method. Fuzzy Sets and Systems 1996;78(1):2335.

[62] Li Han-Xiong, Zhang Lei, Cai Kai-Yuan, Chen Guanrong. An improved robustfuzzy PID controller with optimal fuzzy reasoning. IEEE Transactions onSystems, Man and Cybernetics, Part B (Cybernetics) 2005;35(6):128394.

[63] Mohan BM, Sinha Arpita. Analytical structure and stability analysis of a fuzzy

PID controller. Applied Soft Computing 2008;8(1):74958.[64] Mann George KI, Hu Bao-Gang, Gosine RaymondG. Two-level tuning of fuzzy

PID controllers. IEEE Transactions on Systems, Man and Cybernetics, Part B(Cybernetics) 2001;31(2):2639.

[65] Liu Bo, Wang Ling, Jin Yi-Hui, Tang Fang, Huang De-Xian. Improved particleswarm optimization combined with chaos. Chaos, Solitons & Fractals 2005;25(5):126171.

[66] Global optimization toolbox: users guide. Mathworks, Inc. 2010.[67] Zhuang M, Atherton DP. Automatic tuning of optimum PID controllers.

IEE ProceedingsD: Control Theory and Applications 1993;140(3):21624.[68] Tipsuwan Yodyium, Chow Mo-Yuen. Control methodologies in networked

control systems. Control Engineering Practice 2003;11(10):1099111.[69] Fang Laihua, Wu Zhongzhi, Wu Aiguo, Zheng Aihong. Fuzzy immune self-

regulating PID control of networked control system. In: International confer-ence on computational intelligence for modelling, control and automation,2006 and internationalconferenceon intelligent agents,web technologiesand

internet commerce. CIMCA-IAWTIC06. 2006. p. 748.[70] HiraiKazumasa,Satoh Yoshiaki. Stabilityof a system withvariabletime delay.IEEE Transactions on Automatic Control 1980;25(3):5524.

[71] Das Monotosh, Ghosh Ratna, Goswami Bhaswati, Gupta Amitava, Tiwari AP,Balasubramanian R, Chandra AK. Network control system applied to a largepressurized heavy water reactor. IEEE Transactions on Nuclear Science 2006;53(5):294856.

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