Self-Tuning PI Control Using Adaptive PSO of a Web Transport System withOverlapping Decentralized Control

TAKESHI NISHIDA,1 TETSUZO SAKAMOTO,1 and NICOLA IVAN GIANNOCCARO21Kyushu Institute of Technology, Japan

2University of Salento, Japan

SUMMARY

Web transport systems for transporting films, textilematerial, paper, etc., are usually large-scale systems. Thevelocity and the tension of the web are controlled bydividing the systems into several subsystems in whichstrong coupling exists between the velocity and tensioncontrol. A self-tuning PI (STPI) controller with an estimatorbased on a novel adaptive particle swarm optimizationmethod is constructed, and it is applied for controlling anactual web transport system. The controllers are designedon the basis of the methodology of the overlapping decen-tralized control by taking into consideration online execu-tions performed by a general computer. The effectivenessof the constructed control system is verified on the basis ofseveral experimental results obtained by using an actualexperimental web transport system. © 2013 Wiley Peri-odicals, Inc. Electr Eng Jpn, 184(1): 56–65, 2013; Publishedonline in Wiley Online Library (wileyonlinelibrary.com). DOI10.1002/eej.22366

Key words: web transport system; overlapping de-centralized control; self-tuning PI control; adaptive particleswarm optimization.

1. Introduction

Web is a collective term for paper, films, and othermaterials. The equipment used in processing of such mate-rials is usually called web transport. Raw web materials aredischarged from unwinders, processed (e.g., printed) whilepassing over multiple rollers, and finally wound up bymotor-driven winders. A change of web transport speed inthe course of processing may result in nonuniform process-ing; furthermore, abnormal tension leads to buckling andbreaks. Thus, advanced control is required in order to

synchronize all parts of a web for appropriate speed andtension.

Usually, web transport is a large system includingnumerous driving rollers, and hence decentralized controlis often applied to improve maintenance and simplify theconfiguration of the control system [1]. When designingdecentralized control, a system is divided into multiplesubsystems. The problem is how to deal with mutual inter-ference among the subsystems. Overlapping decentralizedcontrol was proposed as a solution to this problem [2].Specifically, strongly coupled components were arrangedin one subsystem, and shared by neighbor subsystems. Inreal life, however, the parameters of a web transport systemvary with time and the environment, and high-order dynam-ics is difficult to model; thus, adaptivity remains an issue tobe solved. Recently, an STPID (Self-Tuning PID) controldesign was proposed to solve this problem by providingadaptation to parameter fluctuations [3]. In particular, theproposed control system for web transport has the follow-ing features: (1) a system is divided into subsystems usingoverlapping decentralized control design, (2) using noise-robust GMVC (Generalized Minimum Variance Control)[4], explicit self-tuning control [5] is configured, (3) PSO(Particle Swarm Optimization) is employed for systemparameter identification, (4) GMVC control rules are re-placed with PID control rules [5, 7, 8]. The effectiveness ofthe previously proposed control method [3] was verified bysimulations, and its robustness to the system’s nonlinearcharacteristics and observation noise was demonstrated.However, actual web transport systems involve dynamicsand observation noise that cannot be fully reproduced insimulations, and therefore real-machine verification re-mained an issue. In addition, the computational complexityin real systems is restricted by the necessity of real-timeexecution, and hence the control algorithm must be imple-mented for online execution. In the present study, we con-sider the improvements required in order to apply thepreviously proposed method [3] to actual web transport

© 2013 Wiley Periodicals, Inc.

Electrical Engineering in Japan, Vol. 184, No. 1, 2013Translated from Denki Gakkai Ronbunshi, Vol. 131-D, No. 12, December 2011, pp. 1442–1450

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systems. Specifically, we present a method for online esti-mation of the system parameters based on adaptive PSO(OPSO: Online PSO) that offers good calculation effi-ciency, and a particular configuration of a self-adjusting PIcontroller based on the estimated parameters. We also dem-onstrate the effectiveness of the proposed methods using aweb transport system.

The paper is organized as follows. First, related stud-ies are reviewed in Section 2. Then the considered webtransport system and control system design are explainedin Section 3. Experimental results are presented in Section4, and conclusions are drawn in Section 5.

2. Related Research

2.1 Research on web transport systems

As regards decentralized control proposed so far forweb transport systems, there are methods based on H∞control [2, 10, 11], two-DOF H∞ control [12, 13], and atwo-DOF gain-scheduled controller [14]. The effectivenessof these methods was verified in experiments with a three-motor experimental system [12, 14] and in simulations witha relatively large nine-motor system model [13]. In addi-tion, the design parameters were adjusted in advance usingdetailed models, and were implemented in real machines(simulation-based control design).

Research on model-reference web tension controlsystems includes feedforward control [15] and adaptive PIcontrol [16]. In such methods, one needs relatively detailedmodels of the controlled plants, while providing robustnessto modeling errors is an important issue of controller de-sign. The effectiveness of these methods has been provenin simulations.

The previously proposed methods were verifiedmainly by simulations. Even experimental studies havedealt with minimum configurations of the web transportsystems; to our knowledge, the real-machine verification inthe present study is the first of this scale.

2.2 Research on controller self-tuning basedon PSO

There are many methods for PSO-based search ofPID gain sets. The most typical are those that select the PIDparameters so as to minimize a response waveform indexby offline simulations using an identification model [17–22]. Direct search is performed in a space configured ofthree PID parameters, using a combination of criteria suchas IAE (Integral Absolute Error), ISE (Integral SquareError), ITSE (Integral-of-Time multiplied Square Error), orITAE (Integral-of-Time multiplied Absolute Error). How-ever, when using such criteria to evaluate the performance

of a PID controller, one must comprehensively examine thecontrol waveforms, from transient states to steady state,which means that online search for the PID parameters isimpracticable.

In addition, there have been attempts to combine PSOand PID with other algorithms. For example, a method wasproposed in which the PID parameters are predeterminedby PSO search under various credible conditions, and thensynthesized dynamically by fuzzy rules in system control[23]. In addition, a method for online design of an H∞controller was proposed using PSO, intended for optimiza-tion of constrained problems (ALPSO: Augmented La-grangian PSO) [24]. However, these methods employconventional PSO algorithms that do not provide adaptivesearch for time-varying systems, and hence the search forcontrol parameters must be applied to static models.

As regards online PSO implementation, there is amethod of adjusting the PID parameters by minimizationof the errors between a reference model and the outputwhen identification is difficult [25]. Another method hasbeen proposed for tuning of PID control rules using offlineand online PSO [26]. However, these methods do not con-sider adaptation to the system’s time variation; PSO searchand PID parameter tuning converge over time, which makesit difficult to use these methods for time-varying systems.

On the other hand, there is a method called MPC-PSOin which PSO is used in online control to determine theinput sequence of model predictive control (MPC) [27]. Inthis method, the predictive control input is selected usingconventional PSO. The effectiveness of such an approachwas verified for both linear and nonlinear systems. How-ever, this usage of PSO is different from the online parame-ter identification in the present study; in MPC-PSO, aseparate means is needed to acquire a plant model. Inaddition, here too, adaptation to time-varying systems is notconsidered.

3. Experimental Web Transport System and ControlSystem Design

The experimental web transport system is shown inFig. 1. The system includes 12 rollers, of which 4 areprovided with servo motors and 2 are provided with tensionsensors. The rollers driven by motors are called drivingrollers. In addition, the first roller that discharges the webis called the unwinder, and the last roller that winds the webup is called the winder. The present study aims at control tomaintain the desired values of the tension T1(t) and T2(t) attwo points as well as the speeds v2(t) and v4(t) of the webon the second and fourth rollers (driving rollers) as shownin Fig. 1(b). Here t denotes time. Other symbols used in thisstudy are explained in Table 1.

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3.1 Overlapping decentralized control

In the system shown in Fig. 1, the tension and speedat every roller are related in terms of the viscoelasticity ofthe web as follows:

where the characteristic transfer function P(s) is expressedby the Voigt model as

The input/output relations of the experimental system areshown in Fig. 2. Thus, the transfer functions for the webspeed are

Considering Eq. (1), the transfer functions from U1(s) andU2(s) to T1(s), or from U3(s) and U4(s) to T3(s), can beexpressed as follows:

where

(i = 1, 3). Now the transfer function from U2 to V2(s), orfrom U4 and V4(s), can be expressed as follows:

where

(1)

Fig. 1. Experimental web transport system. [Colorfigure can be viewed in the online issue, which is

available at wileyonlinelibrary.com.]

(2)

(3)

(4)

(5)

(6)

(10)

(8)

(9)

(11)

(7)

Fig. 2. Block diagram of system.

Table 1. Conventional symbols

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(i = 2, 4). Thus, the experimental system can be divided intofour overlapping subsystems in Eqs. (7) and (10). Let themanipulated variable of every subsystem be expressed as

Then the input of every motor is

Here u(t) ≡ (u1(t) u2(t) u3(t) u4(t))T and the following is the

transformation matrix of the manipulated variables:

3.2 Discrete-time model

In order to implement a control algorithm in theexperimental system, every subsystem is represented by adiscrete-time model as follows:

Here yj(k) denotes the output at discrete time point k, andkm denotes the minimum dead time. In this study, weassume km = 1 and consider only the dead time of zero hold.In addition, j is the subsystem number; below this index isomitted because the control system is configured in thesame way for each subsystem.

In this study, we configure a mechanism to sequen-tially identify A(z–1) and B(z–1) for a response within about1 s from the current instant* using adaptive PSO (to beexplained below). Thus, in this study the response (9) isapproximated by a sequentially updated first-order delaysystem, and the transfer functions of all subsystems aresynthesized from first-order delay elements G(s) =K/(Tas + 1) and zero-hold elements (1 – exp(–Tss))/s, andapproximated by the z-transform:

Here Ts is the sampling time; Ta and K are the time constantand gain, respectively. From the above, the following poly-nomials are obtained for the system parameters:

3.3 Online identification of system parametersby OPSO

PSO is a method of search for statistically optimalsolutions. The method imitates swarm intelligence andproves effective for nonlinear programming problems [6].The robustness and high speed of PSO in optimal solutionsearch have been proved by numerous studies dealing withnonlinear, nondifferentiable, multimodal, and other prob-lems, and this method is now applied in a wide range offields [28, 29]. PSO was first proposed for solving staticoptimization problems. Recently, the method was modifiedto deal with real dynamical systems, and new PSO algo-rithms can adapt to environmental changes caused by meas-urement noise or the system’s time variation, that is, to avarying search space [30–32]. In addition, the authors haveproposed an adaptive OPSO featuring high calculationefficiency in online identification of time-varying systems[9]. In the present study, this algorithm is used to configurea mechanism for online identification of system parameters.

3.3.1 Algorithm

The position and velocity of particles in the searchspace are expressed by xm(k) ≡ (a1m(k)b0m(k))T and vm(k) ∈R2, respectively. Here m = [1, M] ∈ N+ is the particle’snumber, and a1m(k) and b0m(k) are system parameters esti-mated by the m-th particle. OPSO is used to seek theoptimal solution to the following problem with objectivefunction fk : R2 → R:

First, the best solution xm(k − 1) of every particle obtainedat the previous time point is reevaluated using the evalu-ation function at the present time point, and the minimumvalue is found:

Then the position and velocity of each particle are updatedas follows:

Here ω, c1, and c2 are configuration parameters; the initialvalues xm(0) = xm(0) and vm(0) are set using random num-bers. Then the position of every particle offering the mini-mum evaluation value and its value fk(x(m)(k)) are found:

(12)

(13)

(14)

(15)

(16)

*We set this time period assuming it to be sufficient for estimation of thedominant mode in every subsystem.

(18)

(19)

(17)

(20)

(21)

(22)

(23)

(24)

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Finally, the best solution for the entire swarm, that is, theOPSO estimate at time point k, is found:

OPSO is different from conventional PSO algorithmsas follows: (1) due to the use of a time-varying evaluationfunction, the values xm(k) (usually referred to as pbest) andxg(k) (usually referred to as gbest) do not decrease mono-tonically, (2) no new design parameters are added, (3) thecalculation procedure is simple, (4) a strong adaptive abilityis obtained while the only additional calculation is Eq. (21).

3.3.2 Particle evaluation

The following evaluation function is used to estimatethe system parameters by OPSO:

where

I is the number of estimation steps. Because of the con-straint on the stability of the system parameters to beestimated, search is not performed in the regions wherea1m(k) > 0 or b0m(k) < 0. The greater the value of I that isset, the more effectively the influence of measurement noisecan be suppressed; however, the computational complexityincreases directly with I, which results in a longer delaytime in order to reflect the changes of the system parametersin the control rules. In this study, the sampling time of theexperimental system is Ts = 10 ms, and I is set to 100. Thismeans that the parameters representing the system’s dy-namics are calculated using response waveforms within 1s at most.

3.4 Self-tuning of PID controller based onGMVC

The control systems of every subsystem of the webtransport system considered in this study are configuredusing a method that couples minimization of the perform-ance index and PID control rules [7]. Transformation intoPID control rules has the following advantages: (1) easyimplementation on PID-controlled equipment, (2) easy ex-amination of system behavior in the frequency domain, (3)the behavior and implications of the self-tuned controlinputs are easy to understand for specialists experienced inPID control. In the framework of the present study, points(2) and (3) are especially beneficial. Namely, the experi-mental system is susceptible to mutual interference amongthe subsystems and the influence of measurement noise,

and hence it is important to select PI parameters for efficientcontrol in the low-frequency region. In this context, therepresentation of control rules by means of PID parametersis very convenient to evaluate the validity of self-tuningcontrollers. Below we explain briefly how this method isapplied to the control system in this study.

First consider the minimization of the following per-formance index based on GMVC:

The generalized output φ(k + km + 1) is specified as follows:

Here ω(k) is the target value and λ is a design parameterthat weights the control input. In addition, ∆ = 1 – z–1. Thecontrol rule u(k) is expressed as follows:

Here E(z–1) and F(z–1) are found from the following Dio-phantine equation:

where

In addition, P(z – 1) is defined as the following designpolynomial to adjust the rise time and damped oscillationcharacteristics:

where

The quantities δ and σ can be used to adjust the systemresponse characteristics. In the present study, δ = 0 is fixedto prevent overshoot, and therefore the above expressionscan be simplified as follows, with σ being the only parame-ter that defines P(z–1):

(25)

(26)

(27)

(28)

(29)

(30)

(31)

(34)

(35)

(36)

(37)

(38)

(32)

(33)

(39)

(40)

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On the other hand, the control rules of a digital PID con-troller can be expressed as follows:

Here e(k) ≡ ω(k) – y(k). This can be rewritten as follows:

where

Now, placing the emphasis on the steady-state response andapproximating E(z–1)B(z–1) ≈ E(1)B(1), Eq. (30) can bedescribed as follows:

where

Therefore, as follows from a comparison with Eq. (42),GMVC and PID control can be considered approximatelyequivalent with the following design:

Therefore, the PID parameters can be derived as followsusing the system parameters a1(k) and b0(k) estimated byOPSO:

However, the system dynamics in this study is approxi-mated by low-order polynomials, and TD cannot be calcu-lated. Using Eq. (31) and the system parameters estimatedby Eq. (40), the following can be obtained:

Figure 3 shows the control system configured by applyingthis method to the web transport system.

The design parameters of such STPI control based onGMVC are λ and σ. All subsystems of the web transportsystem should be controlled synchronously, and hencethese parameters should be designed the same for all sub-systems. Thus, we adjust the four subsystems using the

common parameters λ and σ. The physical meaning ofthese parameters is obvious, which makes their settingrelatively easy.

In the previous study [3], we repeated PSO search 40or more times at each discrete optimization step, and inaddition we sought five system parameters assuming asecond-order estimation model. On the other hand, in thepresent study, the processing time is reduced by a factor ofabout 100 due to the introduction of OPSO and the use ofan estimation model of lower order, which makes possiblereal-time implementation of the control algorithm.

4. Experiments

4.1 Response to step input

Here we present the results of experiments with theabove control method applied to the web transport system.The number of particles in PSO was 100, and the numberof evaluation steps for the function in Eq. (26) was I = 100.The design parameters of GMVC were λ = 10 and σ = 1.The target values were set to ω1 = ω4 = 0.3 m/s, ω2 = 2 N,ω3 = 10 N. The initial values of the sought parameters werea1j(k) = 0 and b0j(k) = 0. Here j = 1, 2, 3, 4 is the number ofthe subsystem.

The time evolution of the output values and inputtorque is illustrated in Fig. 4. As indicated by the diagram,the controlled variables converge to the respective target

(41)

(42)

(43)

(44)

(45)

(46)

(47)

(48)

(49)

(50)

(51)

(52)

(53)

Fig. 3. Block diagram of control system.

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values without overshoot, while the steady-state responsechanges smoothly. The time evolution of the estimatedparameters a1j and b0j is shown in Fig. 5. The time evolutionof the PI parameters tuned online is shown in Fig. 6. As canbe seen from these results, the estimated system parametersvary adaptively over time, and the PI parameters are tunedaccordingly. The estimated parameters fluctuate because ofmeasurement noise and other disturbances, which is re-flected in oscillatory fluctuations of the PI parameters;however, kp is adjusted within a relatively narrow range of0 to 0.2, except for the initial part,* thus not exerting a strongeffect on input variation and the control results.

4.2 Variation of response characteristics withsystem parameters

In the proposed method, there are two configurationparameters, λ, which imposes a constraint on input vari-ation, and σ, which adjusts the response time. Here wepresent experimental results pertaining to the influence ofthese parameters on the system’s response.

Experimental results obtained for various λ areshown in Fig. 7. As can be seen from the graphs, greatervariation of the input is allowed when λ is set smaller, andconvergence to the target becomes faster. However, at λ <3, the proportional gain becomes too high, which results ininstability.

Experimental results obtained for various σ areshown in Fig. 8. As can be seen from the graphs, theconvergence worsens when σ is set small. However, at σ =0.3 a strong fluctuation of v2 was observed for about 1 s;that is, an anomalous web speed may occur when theparameter is set too small. When σ is set above 1, the secondand third terms on the right-hand side of Eq. (34) becomevery small, and the effect of σ on the system’s responseweakens.

According to the above results, first σ should be setsufficiently large unless there is a need to provide a slowresponse; then λ should be set as small as possible whileassuring the system’s stability.

*In Fig. 6, kp of subsystems 2 and 4 goes beyond this range in some places;in particular, 0.977 at 0.06 s and 0.501 at 0.07 s in the former case, and0.259 at 0.08 s and 0.220 at 0.30 s in the latter case. These deviations werevery brief and were not so large as to degrade the system’s stability.

Fig. 4. Experimental results. [Color figure can beviewed in the online issue, which is available at

wileyonlinelibrary.com.]

Fig. 5. Time evolution of estimated system parametersof each subsystem. [Color figure can be viewed in the

online issue, which is available atwileyonlinelibrary.com.]

Fig. 6. Time evolution of calculated PI parameters ofeach subsystem. [Color figure can be viewed in the

online issue, which is available atwileyonlinelibrary.com.]

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4.3 Comparison in performance with othermethods of PI parameter tuning

Here we demonstrate the effectiveness of the pro-posed method by experimental comparison with other set-tings of PI parameters.

First, in preliminary tests we confirmed that the webcannot be transported without breakage by using conven-tional methods such as PI or CHR. In such adjustmentalgorithms, the proportional gains in subsystems 2 and 4(speed adjustment systems) tended to be set large; thus, weadjusted the PI parameters of subsystems 1 and 3 (tensioncontrol system) using the CHR algorithm and then tunedthe PI parameters of subsystems 2 and 4 by trial and error.The obtained PI parameters are listed in Table 2, and theexperimental results obtained using these parameters areshown in Fig. 9. In order to evaluate the response withrespect to variation of the target values, the initial targetvalues ω1 = ω4 = 0.3 m/s, ω2 = 2 N, ω3 = 10 N were changedto ω1 = ω4 = 0.7 m/s, ω2 = 4 N, ω3 = 13 N after 10 s. Theother conditions were the same as in the previous experi-ments. As can be concluded from these results, the proposedmethod provides fast adaptation to variation of the targetvalues and is more efficient than conventional PI controllerswith complicated adjustment procedures.

Fig. 7. Experimental results using various λ. [Colorfigure can be viewed in the online issue, which is

available at wileyonlinelibrary.com.]

Fig. 8. Experimental results using various σ. [Colorfigure can be viewed in the online issue, which is

available at wileyonlinelibrary.com.]

Fig. 9. Experimental results by using fixed PIparameters and using proposed method. [Color figure can

be viewed in the online issue, which is available atwileyonlinelibrary.com.]

Table 2. PI parameters for each subsystem

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5. Conclusions

In this study, we configured an experimental webtransport system, and designed a control system based onoverlapping decentralized control. The controller for eachsubsystem was designed using STPI control based onGMVC, and a mechanism was provided for online estima-tion of the system parameters required for control usingOPSO. In addition, we performed experiments with theproposed method, which demonstrated that the controlsystem designed in this study was capable of simultaneouscontrol of web speed and tension.

The proposed method has the following features:

• Real-time processing can be implemented on ageneral-purpose computer.

• Only two parameters, λ and σ, are used to adjustthe control characteristics of the overlapping sub-systems.

• The adjustment parameters have clear physicalmeanings, which makes adjustment easy.

• The system parameters of the controlled plant areestimated online, so that there is no need fordetailed models, and greater versatility is achievedthan in conventional methods.

Topics for further research include comparative ex-periments with previously proposed H∞ control algorithms,which requires the development of an accurate emulator. Inaddition, the control performance should be verified on alarge-scale real system.

REFERENCES

1. Sakamoto T. Analysis and control of web tensioncontrol system. Trans IEE Jpn 1997;117-D:274–280.(in Japanese)

2. Sakamoto T, Tanaka S. Overlapping decentralizedcontroller design for web tension control system.Trans IEE Jpn 1998;118-D:1272–1278. (in Japanese)

3. Mizoguchi K, Sakamoto T. Self-tuning decentralizedcontroller design of web tension control system. Procof EUROSIM Congress on Modeling and Simula-tion, 2010.

4. Wellstead PE, Zarrop MB. Self-tuning systems: con-trol and signal processing. Wiley; 1991.

5. Omatsu S, Yamamoto T. Self-tuning control. Corona;1996. (in Japanese)

6. Kennedy J, Eberhart RC. Particle swarm optimiza-tion. Proc of IEEE Int Conf on Neural Network IV, p1942–1948, 1995.

7. Yamamoto T, Kaneda M. A design of self-tuning PIDcontrollers based on the generalized minimum vari-

ance control law. Trans ISCIE 1998;11:1–9. (in Japa-nese)

8. Yamamoto T, Mitsukura Y, Kaneda M. A design ofPID controllers using a genetic algorithm. TransSICE 1999;35:531–537. (in Japanese)

9. Nishida T, Giannoccaro NI, Sakamoto T. Onlineidentification of time-varying nonlinear systems byparticle swarm optimization. Record of 2010 JointConference of Electrical and Electronics Engineersin Kyushu, CD-ROM 06-2A-03. (in Japanese)

10. Knittel D, Gigan D, Laroche E. Robust decentralizedoverlapping control of large scale winding systems.Proc of American Control Conf Anchorage, p 1805–1810, 2002.

11. Yulin X. Modeling and LPV control of web windingsystem with sinusoidal tension disturbance. Proc ofChinese Control and Decision Conference, p 3815–3820, 2009.

12. Knittel D, Laroche E, Gigan D, Koc H. Tensioncontrol for winding systems with two-degree-of-free-dom H∞ controllers. IEEE Trans Ind Appl2003;39:113–120.

13. Benlatreche A, Knittel D, Ostertag E. Robust decen-tralised control strategies for large-scale web han-dling systems. Control Eng Pract 2008;16:736–750.

14. Claveau F, Chevrel P, Knittel K. A 2DOF gain-sched-uled controller design methodology for a multi-mo-tor web transport system. Control Eng Pract2008;6:609–622.

15. Knittel D, Arbogast A, Vedrines M, Pagilla P. Decen-tralized robust control strategies with model basedfeedforward for elastic web winding systems. Proc ofAmerican Control Conf, p 1968–1974, 2006.

16. Wang B, Zuo J, Wang M, Hao H. Model referenceadaptive tension control of web packaging material.Proc of IEEE Int Conf on Intelligent ComputationTechnology and Automation, p 395–398, 2008.

17. Gaing Z. A particle swarm optimization approach foroptimum design of PID controller in AVR system.IEEE Trans Energy Convers 2004;19:384–391.

18. Kaneko T, Matsumoto H, Mie H, Nishida H,Nakayama T. Offline tuning of positioning controlsystem using particle swarm optimization consider-ing speed controller. IEE Japan 2007;127-D:52–59.(in Japanese)

19. El-Telbany ME. Employing particle swarm optimizerand genetic algorithms for optimal tuning of PIDcontrollers: A comparative study. ICGST-ACSE J2007;7:49–54.

20. Oi A et al. Development of a PID parameter tuningmethod by PSO. Papers of Technical Meeting on IIC,IEEJ, p 52–59, 2008. (in Japanese)

21. Allaoua B, Gasbaoui B, Mebarki B. Setting up. DCmotor speed control alteration parameters using par-

64

ticle swarm optimization strategy. Leonardo ElectronJ Pract Technol 2009;14:19–32.

22. GirirajKumar SM, Jayaraj D, Kishan AR. PSO basedtuning of a PID controller for a high performancedrilling machine. Int J Comput Appl 2010;1(19):12–18.

23. Kao C, Chuang C, Fung R. The self-tuning PIDcontrol in a slider-crank mechanism system by apply-ing particle swarm optimization approach. Mecha-tronics 2006;16:513–522.

24. Kim T, Maruta I, Sugie T. Robust PID controllertuning based on the constrained particle swarm opti-mization. Automatica 2008;44:1104–1110.

25. Tanaka K, Murata Y, Nishimura Y, Rahman FA, OkaM, Uchibori A. Variable gain type PID control usingPSO for ultrasonic motor. J JSAEM 2010;18:294–299. (in Japanese)

26. Pillay N, Govender P. Particle swarm optimization ofPID tuning parameters. LAP LAMBERT AcademicPublishing; 2010.

27. Yousuf MS. Nonlinear predictive control using par-ticle swarm optimization. VDM Verlag Dr. Müller;2010.

28. Ishigame A. Particle swarm optimization: global op-timization technique. J SICE 2008;47:459–465. (inJapanese)

29. Martínes JLF, Gonzalo EG. The PSO family: deduc-tion, stochastic analysis and comparison. Swarm In-tell 2009;3:332–344.

30. Blackwell TM. Swarms in dynamic environments.LNCS 2003;2723:1–12.

31. Cui X, Potok TE. Distributed adaptive particle swarmoptimizer in dynamic environment. Proc of IEEE IntParallel and Distributed Processing Symposium, p244–250, 2007.

32. Zhang X, Qin YDZ, Qin G, Lu J. A modified particleswarm optimizer for tracking dynamic system.LNCS 2005;3612:592–601.

AUTHORS (from left to right)

Takeshi Nishida (member) received a bachelor’s degree from Kyushu Institute of Technology (School of Engineering) in1998, completed the doctoral program in 2002, and became a research associate. He has been an associate professor since 2007.His research interests are outdoor mobile robots. He holds a D.Eng. degree, and is a member of RSJ, SICE, JNNS, and othersocieties.

Tetsuzo Sakamoto (senior member) completed the doctoral program at Kyushu University in 1984 and joined the facultyas a research associate. He became a research associate at Kyushu Institute of Technology in 1985, then a lecturer and an associateprofessor; professor since 2002. His research interests are linear drives, maglev and web tension systems. He holds a D.Eng.degree, and is a member of SICE and other societies.

Nicola Ivan Giannoccaro (nonmember) received a bachelor’s degree from Polytechnic University of Bari (Italy) in 1996and completed the doctoral program in 2001. He is now a researcher at University of Salento. He was a visiting researcher atKyushu Institute of Technology in 2006 and 2010. His research interest is mechatronics. He holds a Ph.D. degree.

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