Estimation of Valve Stiction Using Particle Swarm Optimization

Sensors & Transducers Volume 129, Issue 6, June 2011

www.sensorsportal.com

ISSN 1726-5479

Editors-in-Chief: professor Sergey Y. Yurish, tel.: +34 696067716, e-mail: [email protected] Editors for Western Europe Meijer, Gerard C.M., Delft University of Technology, The Netherlands Ferrari, Vittorio, Universitá di Brescia, Italy Editor South America Costa-Felix, Rodrigo, Inmetro, Brazil

Editors for North America Datskos, Panos G., Oak Ridge National Laboratory, USA Fabien, J. Josse, Marquette University, USA Katz, Evgeny, Clarkson University, USA Editor for Asia Ohyama, Shinji, Tokyo Institute of Technology, Japan

Editor for Eastern Europe Sachenko, Anatoly, Ternopil State Economic University, Ukraine

Editor for Asia-Pacific Mukhopadhyay, Subhas, Massey University, New Zealand

Editorial Advisory Board Abdul Rahim, Ruzairi, Universiti Teknologi, Malaysia Ahmad, Mohd Noor, Nothern University of Engineering, Malaysia Annamalai, Karthigeyan, National Institute of Advanced Industrial Science and Technology, Japan Arcega, Francisco, University of Zaragoza, Spain Arguel, Philippe, CNRS, France Ahn, Jae-Pyoung, Korea Institute of Science and Technology, Korea Arndt, Michael, Robert Bosch GmbH, Germany Ascoli, Giorgio, George Mason University, USA Atalay, Selcuk, Inonu University, Turkey Atghiaee, Ahmad, University of Tehran, Iran Augutis, Vygantas, Kaunas University of Technology, Lithuania Avachit, Patil Lalchand, North Maharashtra University, India Ayesh, Aladdin, De Montfort University, UK Azamimi, Azian binti Abdullah, Universiti Malaysia Perlis, Malaysia Bahreyni, Behraad, University of Manitoba, Canada Baliga, Shankar, B., General Monitors Transnational, USA Baoxian, Ye, Zhengzhou University, China Barford, Lee, Agilent Laboratories, USA Barlingay, Ravindra, RF Arrays Systems, India Basu, Sukumar, Jadavpur University, India Beck, Stephen, University of Sheffield, UK Ben Bouzid, Sihem, Institut National de Recherche Scientifique, Tunisia Benachaiba, Chellali, Universitaire de Bechar, Algeria Binnie, T. David, Napier University, UK Bischoff, Gerlinde, Inst. Analytical Chemistry, Germany Bodas, Dhananjay, IMTEK, Germany Borges Carval, Nuno, Universidade de Aveiro, Portugal Bousbia-Salah, Mounir, University of Annaba, Algeria Bouvet, Marcel, CNRS – UPMC, France Brudzewski, Kazimierz, Warsaw University of Technology, Poland Cai, Chenxin, Nanjing Normal University, China Cai, Qingyun, Hunan University, China Campanella, Luigi, University La Sapienza, Italy Carvalho, Vitor, Minho University, Portugal Cecelja, Franjo, Brunel University, London, UK Cerda Belmonte, Judith, Imperial College London, UK Chakrabarty, Chandan Kumar, Universiti Tenaga Nasional, Malaysia Chakravorty, Dipankar, Association for the Cultivation of Science, India Changhai, Ru, Harbin Engineering University, China Chaudhari, Gajanan, Shri Shivaji Science College, India Chavali, Murthy, N.I. Center for Higher Education, (N.I. University), India Chen, Jiming, Zhejiang University, China Chen, Rongshun, National Tsing Hua University, Taiwan Cheng, Kuo-Sheng, National Cheng Kung University, Taiwan Chiang, Jeffrey (Cheng-Ta), Industrial Technol. Research Institute, Taiwan Chiriac, Horia, National Institute of Research and Development, Romania Chowdhuri, Arijit, University of Delhi, India Chung, Wen-Yaw, Chung Yuan Christian University, Taiwan Corres, Jesus, Universidad Publica de Navarra, Spain Cortes, Camilo A., Universidad Nacional de Colombia, Colombia Courtois, Christian, Universite de Valenciennes, France Cusano, Andrea, University of Sannio, Italy D'Amico, Arnaldo, Università di Tor Vergata, Italy De Stefano, Luca, Institute for Microelectronics and Microsystem, Italy Deshmukh, Kiran, Shri Shivaji Mahavidyalaya, Barshi, India Dickert, Franz L., Vienna University, Austria Dieguez, Angel, University of Barcelona, Spain Dighavkar, C. G., M.G. Vidyamandir’s L. V.H. College, India Dimitropoulos, Panos, University of Thessaly, Greece Ding, Jianning, Jiangsu Polytechnic University, China Djordjevich, Alexandar, City University of Hong Kong, Hong Kong

Donato, Nicola, University of Messina, Italy Donato, Patricio, Universidad de Mar del Plata, Argentina Dong, Feng, Tianjin University, China Drljaca, Predrag, Instersema Sensoric SA, Switzerland Dubey, Venketesh, Bournemouth University, UK Enderle, Stefan, Univ.of Ulm and KTB Mechatronics GmbH, Germany Erdem, Gursan K. Arzum, Ege University, Turkey Erkmen, Aydan M., Middle East Technical University, Turkey Estelle, Patrice, Insa Rennes, France Estrada, Horacio, University of North Carolina, USA Faiz, Adil, INSA Lyon, France Fericean, Sorin, Balluff GmbH, Germany Fernandes, Joana M., University of Porto, Portugal Francioso, Luca, CNR-IMM Institute for Microelectronics and Microsystems, Italy Francis, Laurent, University Catholique de Louvain, Belgium Fu, Weiling, South-Western Hospital, Chongqing, China Gaura, Elena, Coventry University, UK Geng, Yanfeng, China University of Petroleum, China Gole, James, Georgia Institute of Technology, USA Gong, Hao, National University of Singapore, Singapore Gonzalez de la Rosa, Juan Jose, University of Cadiz, Spain Granel, Annette, Goteborg University, Sweden Graff, Mason, The University of Texas at Arlington, USA Guan, Shan, Eastman Kodak, USA Guillet, Bruno, University of Caen, France Guo, Zhen, New Jersey Institute of Technology, USA Gupta, Narendra Kumar, Napier University, UK Hadjiloucas, Sillas, The University of Reading, UK Haider, Mohammad R., Sonoma State University, USA Hashsham, Syed, Michigan State University, USA Hasni, Abdelhafid, Bechar University, Algeria Hernandez, Alvaro, University of Alcala, Spain Hernandez, Wilmar, Universidad Politecnica de Madrid, Spain Homentcovschi, Dorel, SUNY Binghamton, USA Horstman, Tom, U.S. Automation Group, LLC, USA Hsiai, Tzung (John), University of Southern California, USA Huang, Jeng-Sheng, Chung Yuan Christian University, Taiwan Huang, Star, National Tsing Hua University, Taiwan Huang, Wei, PSG Design Center, USA Hui, David, University of New Orleans, USA Jaffrezic-Renault, Nicole, Ecole Centrale de Lyon, France Jaime Calvo-Galleg, Jaime, Universidad de Salamanca, Spain James, Daniel, Griffith University, Australia Janting, Jakob, DELTA Danish Electronics, Denmark Jiang, Liudi, University of Southampton, UK Jiang, Wei, University of Virginia, USA Jiao, Zheng, Shanghai University, China John, Joachim, IMEC, Belgium Kalach, Andrew, Voronezh Institute of Ministry of Interior, Russia Kang, Moonho, Sunmoon University, Korea South Kaniusas, Eugenijus, Vienna University of Technology, Austria Katake, Anup, Texas A&M University, USA Kausel, Wilfried, University of Music, Vienna, Austria Kavasoglu, Nese, Mugla University, Turkey Ke, Cathy, Tyndall National Institute, Ireland Khelfaoui, Rachid, Université de Bechar, Algeria Khan, Asif, Aligarh Muslim University, Aligarh, India Kim, Min Young, Kyungpook National University, Korea South Ko, Sang Choon, Electronics. and Telecom. Research Inst., Korea South Kotulska, Malgorzata, Wroclaw University of Technology, Poland Kratz, Henrik, Uppsala University, Sweden Kockar, Hakan, Balikesir University, Turkey

Kong, Ing, RMIT University, Australia Kumar, Arun, University of South Florida, USA Kumar, Subodh, National Physical Laboratory, India Kung, Chih-Hsien, Chang-Jung Christian University, Taiwan Lacnjevac, Caslav, University of Belgrade, Serbia Lay-Ekuakille, Aime, University of Lecce, Italy Lee, Jang Myung, Pusan National University, Korea South Lee, Jun Su, Amkor Technology, Inc. South Korea Lei, Hua, National Starch and Chemical Company, USA Li, Genxi, Nanjing University, China Li, Hui, Shanghai Jiaotong University, China Li, Xian-Fang, Central South University, China Li, Yuefa, Wayne State University, USA Liang, Yuanchang, University of Washington, USA Liawruangrath, Saisunee, Chiang Mai University, Thailand Liew, Kim Meow, City University of Hong Kong, Hong Kong Lin, Hermann, National Kaohsiung University, Taiwan Lin, Paul, Cleveland State University, USA Linderholm, Pontus, EPFL - Microsystems Laboratory, Switzerland Liu, Aihua, University of Oklahoma, USA Liu Changgeng, Louisiana State University, USA Liu, Cheng-Hsien, National Tsing Hua University, Taiwan Liu, Songqin, Southeast University, China Lodeiro, Carlos, University of Vigo, Spain Lorenzo, Maria Encarnacio, Universidad Autonoma de Madrid, Spain Lukaszewicz, Jerzy Pawel, Nicholas Copernicus University, Poland Ma, Zhanfang, Northeast Normal University, China Majstorovic, Vidosav, University of Belgrade, Serbia Malyshev, V.V., National Research Centre ‘Kurchatov Institute’, Russia Marquez, Alfredo, Centro de Investigacion en Materiales Avanzados, Mexico Matay, Ladislav, Slovak Academy of Sciences, Slovakia Mathur, Prafull, National Physical Laboratory, India Maurya, D.K., Institute of Materials Research and Engineering, Singapore Mekid, Samir, University of Manchester, UK Melnyk, Ivan, Photon Control Inc., Canada Mendes, Paulo, University of Minho, Portugal Mennell, Julie, Northumbria University, UK Mi, Bin, Boston Scientific Corporation, USA Minas, Graca, University of Minho, Portugal Moghavvemi, Mahmoud, University of Malaya, Malaysia Mohammadi, Mohammad-Reza, University of Cambridge, UK Molina Flores, Esteban, Benemérita Universidad Autónoma de Puebla, Mexico Moradi, Majid, University of Kerman, Iran Morello, Rosario, University "Mediterranea" of Reggio Calabria, Italy Mounir, Ben Ali, University of Sousse, Tunisia Mulla, Imtiaz Sirajuddin, National Chemical Laboratory, Pune, India Nabok, Aleksey, Sheffield Hallam University, UK Neelamegam, Periasamy, Sastra Deemed University, India Neshkova, Milka, Bulgarian Academy of Sciences, Bulgaria Oberhammer, Joachim, Royal Institute of Technology, Sweden Ould Lahoucine, Cherif, University of Guelma, Algeria Pamidighanta, Sayanu, Bharat Electronics Limited (BEL), India Pan, Jisheng, Institute of Materials Research & Engineering, Singapore Park, Joon-Shik, Korea Electronics Technology Institute, Korea South Penza, Michele, ENEA C.R., Italy Pereira, Jose Miguel, Instituto Politecnico de Setebal, Portugal Petsev, Dimiter, University of New Mexico, USA Pogacnik, Lea, University of Ljubljana, Slovenia Post, Michael, National Research Council, Canada Prance, Robert, University of Sussex, UK Prasad, Ambika, Gulbarga University, India Prateepasen, Asa, Kingmoungut's University of Technology, Thailand Pullini, Daniele, Centro Ricerche FIAT, Italy Pumera, Martin, National Institute for Materials Science, Japan Radhakrishnan, S. National Chemical Laboratory, Pune, India Rajanna, K., Indian Institute of Science, India Ramadan, Qasem, Institute of Microelectronics, Singapore Rao, Basuthkar, Tata Inst. of Fundamental Research, India Raoof, Kosai, Joseph Fourier University of Grenoble, France Rastogi Shiva, K. University of Idaho, USA Reig, Candid, University of Valencia, Spain Restivo, Maria Teresa, University of Porto, Portugal Robert, Michel, University Henri Poincare, France Rezazadeh, Ghader, Urmia University, Iran Royo, Santiago, Universitat Politecnica de Catalunya, Spain Rodriguez, Angel, Universidad Politecnica de Cataluna, Spain Rothberg, Steve, Loughborough University, UK Sadana, Ajit, University of Mississippi, USA Sadeghian Marnani, Hamed, TU Delft, The Netherlands Sandacci, Serghei, Sensor Technology Ltd., UK Sapozhnikova, Ksenia, D.I.Mendeleyev Institute for Metrology, Russia Saxena, Vibha, Bhbha Atomic Research Centre, Mumbai, India

Schneider, John K., Ultra-Scan Corporation, USA Sengupta, Deepak, Advance Bio-Photonics, India Seif, Selemani, Alabama A & M University, USA Seifter, Achim, Los Alamos National Laboratory, USA Shah, Kriyang, La Trobe University, Australia Silva Girao, Pedro, Technical University of Lisbon, Portugal Singh, V. R., National Physical Laboratory, India Slomovitz, Daniel, UTE, Uruguay Smith, Martin, Open University, UK Soleymanpour, Ahmad, Damghan Basic Science University, Iran Somani, Prakash R., Centre for Materials for Electronics Technol., India Srinivas, Talabattula, Indian Institute of Science, Bangalore, India Srivastava, Arvind K., NanoSonix Inc., USA Stefan-van Staden, Raluca-Ioana, University of Pretoria, South Africa Sumriddetchka, Sarun, National Electronics and Computer Technology Center, Thailand Sun, Chengliang, Polytechnic University, Hong-Kong Sun, Dongming, Jilin University, China Sun, Junhua, Beijing University of Aeronautics and Astronautics, China Sun, Zhiqiang, Central South University, China Suri, C. Raman, Institute of Microbial Technology, India Sysoev, Victor, Saratov State Technical University, Russia Szewczyk, Roman, Industrial Research Inst. for Automation and Measurement, Poland Tan, Ooi Kiang, Nanyang Technological University, Singapore, Tang, Dianping, Southwest University, China Tang, Jaw-Luen, National Chung Cheng University, Taiwan Teker, Kasif, Frostburg State University, USA Thirunavukkarasu, I., Manipal University Karnataka, India Thumbavanam Pad, Kartik, Carnegie Mellon University, USA Tian, Gui Yun, University of Newcastle, UK Tsiantos, Vassilios, Technological Educational Institute of Kaval, Greece Tsigara, Anna, National Hellenic Research Foundation, Greece Twomey, Karen, University College Cork, Ireland Valente, Antonio, University, Vila Real, - U.T.A.D., Portugal Vanga, Raghav Rao, Summit Technology Services, Inc., USA Vaseashta, Ashok, Marshall University, USA Vazquez, Carmen, Carlos III University in Madrid, Spain Vieira, Manuela, Instituto Superior de Engenharia de Lisboa, Portugal Vigna, Benedetto, STMicroelectronics, Italy Vrba, Radimir, Brno University of Technology, Czech Republic Wandelt, Barbara, Technical University of Lodz, Poland Wang, Jiangping, Xi'an Shiyou University, China Wang, Kedong, Beihang University, China Wang, Liang, Pacific Northwest National Laboratory, USA Wang, Mi, University of Leeds, UK Wang, Shinn-Fwu, Ching Yun University, Taiwan Wang, Wei-Chih, University of Washington, USA Wang, Wensheng, University of Pennsylvania, USA Watson, Steven, Center for NanoSpace Technologies Inc., USA Weiping, Yan, Dalian University of Technology, China Wells, Stephen, Southern Company Services, USA Wolkenberg, Andrzej, Institute of Electron Technology, Poland Woods, R. Clive, Louisiana State University, USA Wu, DerHo, National Pingtung Univ. of Science and Technology, Taiwan Wu, Zhaoyang, Hunan University, China Xiu Tao, Ge, Chuzhou University, China Xu, Lisheng, The Chinese University of Hong Kong, Hong Kong Xu, Sen, Drexel University, USA Xu, Tao, University of California, Irvine, USA Yang, Dongfang, National Research Council, Canada Yang, Shuang-Hua, Loughborough University, UK Yang, Wuqiang, The University of Manchester, UK Yang, Xiaoling, University of Georgia, Athens, GA, USA Yaping Dan, Harvard University, USA Ymeti, Aurel, University of Twente, Netherland Yong Zhao, Northeastern University, China Yu, Haihu, Wuhan University of Technology, China Yuan, Yong, Massey University, New Zealand Yufera Garcia, Alberto, Seville University, Spain Zakaria, Zulkarnay, University Malaysia Perlis, Malaysia Zagnoni, Michele, University of Southampton, UK Zamani, Cyrus, Universitat de Barcelona, Spain Zeni, Luigi, Second University of Naples, Italy Zhang, Minglong, Shanghai University, China Zhang, Qintao, University of California at Berkeley, USA Zhang, Weiping, Shanghai Jiao Tong University, China Zhang, Wenming, Shanghai Jiao Tong University, China Zhang, Xueji, World Precision Instruments, Inc., USA Zhong, Haoxiang, Henan Normal University, China Zhu, Qing, Fujifilm Dimatix, Inc., USA Zorzano, Luis, Universidad de La Rioja, Spain Zourob, Mohammed, University of Cambridge, UK

Sensors & Transducers Journal (ISSN 1726-5479) is a peer review international journal published monthly online by International Frequency Sensor Association (IFSA). Available in electronic and on CD. Copyright © 2011 by International Frequency Sensor Association. All rights reserved.

Sensors & Transducers Journal

Contents Volume 129 Issue 6 June 2011

www.sensorsportal.com

ISSN 1726-5479

Research Articles A Review of Concept of Force Measurements between the Past and Today Ebtisam H. Hasan...............................................................................................................................

1

Design, Development and Testing of a Semicircular Type Capacitive Angular Position Sensor Nikhil Gaurav, Sagarika Pal................................................................................................................

16

Design, Development and Calibration of a Portable Capacitive Moisture Meter Mahmoud Soltani, Reza Alimardani ...................................................................................................

24

Laser Power Measurement Using Commercial MEMS Pressure Sensor along with PSoC Embedded Read-out J. Jayapandian and K. Prabakar ........................................................................................................

33

Design and Development of Embedded System for the Measurement of Thermal Conductivity of Liquids by Transient Hot Wire Method Nagamani Gosala, Raghavendra Rao Kanchi. ..................................................................................

42

Performance Assessment of PCA, MF and SVD Methods for Denoising in Chemical Sensor Array Based Electronic Nose System S. K. Jha and R. D. S. Yadava ...........................................................................................................

57

Simple Design of a PID Controller and Tuning of Its Parameters Using LabVIEW Software Subrata Chattopadhyay, Ganesh Roy and Mrutyunjaya Panda ........................................................

69

The DC Motor Speed Controller Using AT89S52 Microcontroller to rotate Stepper Motor attached into Potentiometer in Variable Regulated Power Supply Marhaposan Situmorang ....................................................................................................................

86

Use of Polythiophene as a Temperature Sensor D. S. Kelkar, A. B. Chourasia, V. Balasubrmanian.............................................................................

97

Modeling of a Non-invasive Electromagnetic Sensor for the Measurement Glycaemia A. Rouane, D. Kourtiche, S. M. Alavi .................................................................................................

105

CdO Doped Indium Oxide Thick Film as a Low Temperature H2S Gas Sensor D. N. Chavan, V. B. Gaikwad, Ganesh E. Patil, D. D. Kajale, G. H. Jain...........................................

122

Design and Simulation of Double-spiral Shape Micro-heater for Gas Sensing Applications Mahanth Prasad, R. P. Yadav, V. Sahula and V. K. Khanna.............................................................

115

Glucose Concentration Sensor Based on Long Period Grating Fabricated from Hydrogen Loaded Photosensitive Fiber T. M. Libish, J. Linesh, M. C. Bobby, B. Nithyaja, 1S. Mathew, C. Pradeep and P. Radhakrishnan.

142

Estimation of Valve Stiction Using Particle Swarm Optimization S. Sivagamasundari, D. Sivakumar....................................................................................................

Authors are encouraged to submit article in MS Word (doc) and Acrobat (pdf) formats by e-mail: [email protected] Please visit journal’s webpage with preparation instructions: http://www.sensorsportal.com/HTML/DIGEST/Submition.htm International Frequency Sensor Association (IFSA).

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Sensors & Transducers Journal, Vol. 129, Issue 6, June 2011, pp. 149-162

Sensors & Transducers ISSN 1726-5479 © 2011 by IFSA http://www.sensorsportal.com

Estimation of Valve Stiction Using Particle Swarm Optimization 1

S. Sivagamasundari, 2D. Sivakumar

Dept. of Instrumentation Engineering, Annamalai University, Annamalainagar – 608002, India Tel.: 1 9444160969, 2 9443238642 E mail: [email protected], [email protected] Received: 6 May 2011 /Accepted: 20 June 2011 /Published: 30 June 2011 Abstract: This paper presents a procedure for quantifying valve stiction in control loops based on particle swarm optimization. Measurements of the Process Variable (PV) and Controller Output (OP) are used to estimate the parameters of a Hammerstein system, consisting of connection of a non linear control valve stiction model and a linear process model. The parameters of the Hammerstein model are estimated using particle swarm optimization, from the input-output data by minimizing the error between the true model output and the identified model output. Using particle swarm optimization, Hammerstein models with known nonlinear structure and unknown parameters can be identified. A cost-effective optimization technique is adopted to find the best valve stiction models representing a more realistic valve behavior in the oscillating loop. Simulation and practical laboratory control system results are included, which demonstrates the effectiveness and robustness of the identification scheme. Copyright © 2011 IFSA. Keywords: Control valve stiction, Nonlinear system identification, Hammerstein model, Particle swarm optimization.

1. Introduction Stiction in control valves and inadequate controller tuning are two of the major sources of control loop performance degradation. While process models play an essential role in controller design, friction models are needed to diagnose abnormal valve operation or to compensate such undesirable effects. Hence, methods for valve stiction quantification and process model identification arise as important tools to treat loop performance problems. Choudhury et al. [2] dealt with friction quantification by fitting an ellipse to PV vs. OP data, but the results produced by this technique depend on the controller 149

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tuning. In a method proposed by Srinivasan et al. [3, 4], an optimization approach is used to jointly estimate the process dynamics and the friction model parameters. This method can be seen as Hammerstein model identification, since the valve stiction is treated as a nonlinear block followed by a linear dynamic block that represents the process. As the process dynamics is also estimated, the joint procedure previously mentioned can be used for controller retuning. However, as inappropriate friction model structure is employed reproducing important sticky valve characteristics becomes difficult. Choudhury et al. [6, 7] eliminated this drawback by adopting a two-parameter friction model structure. Different nonparametric approaches have been used for the Hammerstein model identification [5]. Recently, neural networks have also been used to model the nonlinearity in the Hammerstein model for single-input single-output (SISO) systems. Recently, particle swarm optimization (PSO) has been used extensively in solving many optimization searching problems [8-10]. PSO is a population-based stochastic optimization technique, inspired by social behavior of bird flocking or fish schooling. PSO shares many similarities with the genetic algorithm (GA), such as initialization of population of random solutions and search for the optimal by updating generations. However, unlike GA, PSO has no evolution operators, such as crossover and mutation. One of the most promising advantages of PSO over the GA is that, PSO uses only a few parameters and is easy to implement. Also PSO does not require linearity in the parameters which is needed in iterative searching optimization techniques. This property of PSO makes it suitable to the identification of Hammerstein model with nonlinearities of known structure and unknown parameters in the parameters estimation problem. In the present work, a PSO-based scheme for the identification of the nonlinear Hammerstein model of the valve stiction is proposed. This is accomplished by formulating the identification of the Hammerstein model as an optimization problem and the PSO is used in the optimization process.

2. Valve Stiction Model Fig. 1 shows the general structure of a pneumatic control valve. Stiction occurs when the smooth movement of the valve stem is hindered by excessive static friction at the packing area. The sudden slip of the stem after the controller output sufficiently overcomes the static friction caused undesirable effect to the control loop.

Fig. 1. Structure of pneumatic control valve.

Fig. 2 illustrates the input-output behaviour for control valve with stiction. The dash-dotted line represents the ideal control valve without any friction. Stiction consists of dead band, stick band, slip jump and the moving phase [2]. For control valve under stiction resting at point a, the valve position remains unchanged even when the controller output increases due to the dead band caused by the static 150

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friction. When the controller output exceeds the maximum static frictional force fS, the valve starts to respond. A slip jump of magnitude J is incurred when the valve starts to move at point b when the frictional forces fS convert to kinetic force fD. From c to d, the valve position varies linearly. The same scenario happens when the valve stops at point d, and when the controller output changes direction. Parameter S represents the dead band plus stick band regions.

Fig. 2. Typical Stiction Behaviour.

Fig. 3 shows the flowchart of He’s two parameter stiction model [11]. The variable ur is the residual force acting on the valve that has not materialized a valve move.

Fig. 3. Flowchart of He’s two parameter stiction model.

He’s two parameter model naturally handles both deterministic and stochastic signals, and is flexible in simulating different types of stiction by tuning fS and fD. It is worth noting that He’s two-parameter model assumes that the valve stops at each sampling interval, that is why the total force applied on the valve is always compared to the static friction band fS to determine whether the valve moves or not. 151

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3. Identification of Model Structure The dynamic behaviour of many chemical processes can be approximated by a non-linear block in series with a linear block as shown in Fig. 4. This structure is known as the Hammerstein model which has been successfully used to model a large class of nonlinear systems. Many approaches have been developed for identifying Hammerstein models. The Hammerstein model is represented by the following equations. The process dynamics, including the valve dynamics (linear block) are represented by an ARMAX model A ( q 1 ) y ( k )  B ( q 1 )u v ( k )  v ( k )

(1)

,

where q−i is the backward shift operator such that q−iu(k) = u(k−i) and v(k) is the measurement noise. A(q−1) and B(q−1) are polynomials in q−1 of specified order n and m respectively:

A ( q  1 )  1  a 1 q  1  ...  a n q  n

(2)

B ( q  1 )  b 0  b1 q  1  ...  b m q  m

(3)

  MV 

OP 

Stiction  u(k)  Non‐linear block 

uv(k)

Valve  dynamics 

Process 

PV 

y(k)

Linear block

Fig. 4. Process control loop with Hammerstein Model Structure.

It is assumed that the model order is known a priori. The non measured intermediate variable uv(k) is the output of the static nonlinearity, given as:

u v ( k )  f ( u ( k ), f S , f D )

(4)

Thus, the problem of Hammerstein model identification is to estimate the unknown parameters a1…an, bo…bm, fS and fD using input-output data. The basic principle of parameter estimation is to minimize the error between measured output and the estimated output. However, the objective function for nonlinear parameter estimation is more complex, and the traditional gradient based optimization method would trap into local optima. Then some intelligent global optimization algorithms such as genetic algorithm are proposed for nonlinear parameter estimation [1]. The framework of PSO based parameter estimation of the Hammerstein model is illustrated in Fig. 5. Here y(k) and yˆ (k ) are the measured output and the estimated output, respectively; u(k) is the system input signal and v(k) is the measurement noises. The use of PSO in the estimation of the unknown parameters requires an objective function (fitness function) to be specified. The following objective function can be defined so as to determine how well the estimates fit the system.

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F 

M

 ( y (k ) 

yˆ ( k )) 2

(5)

k 1

 

v(k)

y(k)

u(k)  Hammerstein  Model 

+

+

Estimation

Performance  evaluator 

yˆ (k )  

Model 

Identified  Parameter 

fˆS , fˆD  

PSO Based  Identifier 

Fig. 5. PSO based Parameter estimation procedure.

yˆ ( k ) 

Bˆ ( q  1 ) uˆ v ( k ) Aˆ ( q 1 )

(6)

with

Aˆ ( q  1 )  1  aˆ 1 q  1  ...  aˆ n q  n

(7)

Bˆ ( q  1 )  bˆ0  bˆ1 q  1  ...  bˆm q  m

(8)

uˆ v ( k )  f ( u ( k ), fˆS , fˆD )

(9)

Here M is the number of input-output data points used in the identification, and the parameters estimates aˆ1 … aˆ n , bˆ0 … bˆm and fˆS , fˆD are found by minimizing the fitness function given by equation (5). Due to the nonlinear property of control valve, it is hard to estimate all unknown variables precisely. Traditional methods, especially gradient decent based approaches, can easily be trapped in local optima. Therefore, many intelligent global optimization techniques such as evolutionary algorithm are introduced recently. PSO (Particle Swarm Optimization) is a population based searching technique, an alternative to genetic algorithm. Compared with GA, PSO has some attractive characteristics. PSO has memory, so that the knowledge of good solutions is retained by all particles, whereas in GA, previous knowledge of the problem is destroyed once the population changes. Also, PSO has constructive cooperation between particles, that is, particles in a swarm share their information.

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4. Particle Swarm Optimization PSO is a population-based optimization method first proposed by Eberhart and Colleagues. Some of the attractive features of PSO include the ease of implementation and the fact that no gradient information is required. It can be used to solve a wide array of different optimization problems. Like evolutionary algorithms, PSO technique conducts search using a population of particles, corresponding to individuals. Each particle represents a candidate solution to the problem at hand. In a PSO system, particles change their positions by flying around in a multidimensional search space until computational limitations are exceeded. The PSO technique is an evolutionary computation technique, but it differs from other well-known evolutionary computation algorithms such as the genetic algorithm. Although a population is used for searching the search space, there are no operators inspired by the human DNA procedures applied on the population. Instead, in PSO, the population dynamics simulates a ‘bird flock’s’ behavior, where social sharing of information takes place and individuals can profit from the discoveries and previous experience of all the other companions during the search for food. Thus, each companion, called particle, in the population, which is called swarm, is assumed to ‘fly’ over the search space in order to find promising regions of the landscape. For example, in the minimization case, such regions possess lower function values than other, visited previously. In this context, each particle is treated as a point in a d-dimensional space, which adjusts its own ‘flying’ according to its flying experience as well as the flying experience of other particles (companions). In PSO, a particle is defined as a moving point in hyperspace. For each particle, at the current time step, a record is kept of the position, velocity, and the best position found in the search space so far. The assumption is a basic concept of PSO [9]. In the PSO algorithm, instead of using evolutionary operators such as mutation and crossover, to manipulate algorithms, for a variable optimization problem, a flock of particles are put into the d-dimensional search space with randomly chosen velocities and positions knowing their best values (Pbest) so far and the position in the d-dimensional space. The velocity of each particle, adjusted according to its own flying experience and the other particle’s flying experience. For example, the i-th particle is represented as

X i  ( x i1  x i 2  ...  x id )

(10)

in the d-dimensional space. The best previous position of the i-th particle is recorded and represented as:

Pbesti  ( pbesti,1  pbesti, 2  ...  pbesti,d )

(11)

The index of best particle among all of the particles in the group is gbestd. The velocity for particle i is represented as

V i  ( v i1  v i 2  ...  v id )

(12)

The modified velocity and position of each particle can be calculated using the current velocity and the distance from Pbesti,d to gbestd as shown in the following formulae

V i ,tm1  w .v it, m  c1 ( rand ())( Pbesti , m  X it, m )  c 2 ( rand ())( g besti , m  X it, m )

(13)

X it,m1  x it, m  x (V i ,tm1 )

(14)

with, i = 1, 2 …n, ; m=1,2…d 154

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where, N - Number of particles in the group; d – Dimension; t - Pointer of iterations (generations); V i t, m - Velocity of particle i at iteration t; w - Inertia weight factor; c1, c2 - Acceleration constant; rand () - Random number between 0 and 1; X it, m - Current position of particle i at iterations; Pbesti - Best previous position of the i-th particle; gbestd - Best particle among all the particles in the population.

5. PSO Based Identification Algorithm The PSO based identification algorithm can be summarized in the following steps: i. M input-output data points are generated from the system to be identified. ii. Random initial values for parameters a1…an, bo…bm, of the linear block and the parameters of the nonlinearities fS and fD in the appropriate range are generated. iii. Initial searching velocities are generated randomly. iv. The objective function for each particle in the initial population is evaluated. Pbest is set to each initial searching point. The initial best evaluated value among Pbest values is set to gbest v. Velocity updating: Using the global best and individual best of each particle, particle velocity is updated according to equation (13) vi. Position Updating: Based on the updated velocities, each particle changes its position according to equation (14). vii. The objective function to the new searching points and the evaluation values are calculated. If the evaluation value of each agent is better than the previous Pbest value, the value is set to Pbest. If the best Pbest is better than gbest, the value is set to gbest. All of gbest values are stored as candidates for the final control strategy. viii. Step (v) is repeated until predetermined number of iteration has been produced.

6. Implementation of the Identification Algorithm In this section, the PSO based identification approach is applied to the discrete linear process represented by the following transfer function (equation (15)) and a discrete PI controller (KC=1,KI=0.5) with a sampling period of 1second is considered for process simulation.

y (k ) 

1  0 .5 q 1  0 .5 q 2 0 . 2642 q  2  0 . 1353 q  3 v(k )  u ( k ) 1  0 . 7358 q 1  0 . 1353 q  2 1  0 . 7358 q 1  0 . 1353 q  2

(15)

A control valve stiction model with weak (fS=0.08, fD=0.05) and strong stiction (fS=0.32, fD=0.18) cases are simulated in the control loop. A measurement white noise with standard deviation of 0.1 is added in the closed loop simulation. To identify the parameters of the Hammerstein system from PV-OP data, the PSO parameters given in Table 1 are used. The process model identified is given by

yˆ ( k ) 

1  0 . 4945 q  1  0 . 6105 q  2 0 . 2634 q  2  0 . 1433 q  3 v(k ) u (k )  1  0 . 7142 q 1  0 . 1235 q  2 1  0 . 7142 q 1  0 . 1235 q  2

(16) 155

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Closed loop simulations are carried out for unit step change. All the computations reported in this study are carried out using MATLAB and Simulink. Fig. 6 shows the predicted MV, predicted PV (both are oscillatory) signal for weak stiction case. The corresponding values for strong stiction case are shown in Fig. 7. Table 1. Parameters of PSO algorithm.

Population Size Number of Iterations w c1 = c2

20 30 0.1 0.1

1.2

1.1

Ampl i t ude

1

0.9

set point predicted MV predicted PV

0.8

0.7

0.6

0.5 50

100

150

200

250 300 Time(s)

350

400

450

500

Fig. 6. Time response of predicted PV and MV for weak stiction.

1.3 1.2 1.1

Ampl i t ude

1 0.9 0.8 0.7 0.6 0.5 set point predicted MV predicted PV

0.4 50

100

150

200

250 300 Time(s)

350

400

450

500

Fig. 7. Time response of predicted PV and MV for strong stiction.

Table 2 lists the test conditions and results for weak and strong stiction cases. The results of GA based optimization technique are also presented. It can be concluded that the present technique accurately 156

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quantify stiction. The estimates of the recovered stiction model are very close to the true values. The convergence of cost functions are shown in Fig. 8 and Fig. 9. Table 2. Variation in Adaptation gains for the different controllers. Test condition

Weak Stiction Strong Stiction

Actual Value

PSO based optimization

GA based optimization

fS

fD

fˆS

fˆD

fˆS

fˆD

0.08

0.05

0.09256

0.04125

0.07453

0.04989

0.32

0.18

0.32989

0.20370

0.32100

0.18439

Fig. 8. Convergence of Cost function for weak stiction.

Fig. 9. Convergence of Cost function for strong stiction.

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The trajectories of the estimated parameters (fS and fD) for weak and strong stiction are shown in Fig. 10 and Fig. 11 respectively.

Fig. 10. Trajectories of Estimated Parameters (Weak Stiction).

Fig. 11. Trajectories of Estimated Parameters (Strong Stiction).

7. Real Time Implementation The objective of this section is to demonstrate the proposed framework and techniques on a laboratory air flow control system. The piping and instrumentation diagram of the process and its associated control system are shown in Fig. 12. The process variable (air flow rate) is sensed by differential pressure flow transmitter. This flow transmitter produces current output in the range of 4 to 20 mA. A current to voltage (I/V) converter is used to convert 4 to 20 mA into 1 to 5 Volts. This measured voltage (Process Variable) is compared with the reference signal. The difference between the two is 158

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given as input to the controller. The controller used is a well tuned PID controller. The controller produces manipulating variable based on the difference between the set point and process variable. The manipulating variable in voltage form is converted into current by a Voltage/Current (V/I) converter. A Current/Pneumatic (I/P) converter is used to convert this current to pressure (3 to 15 psi) accepted by the control valve. The air failure to open (AFO) pneumatic control valve restricts the path of the air flow in the process pipe line, thus controlling the air flow rate.

V1 to V4 - Manifold valves; FT - Flow Transmitter; MV-1 to MV-3 - Manual control valves; PS - Power Supply; M1 and M2 - Manometer connections; mA - Milliammeter; DH - De humidifier; I/P - Current to Pressure converter; AFR - Air Filter Regulator; PCV - Pneumatic Control Valve; PRG - Pressure Gauge; G-2 - Galvanized pipe for cold air flow Fig. 12. Piping and Instrumentation Diagram of Air Flow Control System.

Controller output (OP) and process variable (PV) data are used for the identification procedure. The sampling time is taken as 0.1s. It is known a priori that the control valve in this control loop is having stiction. The results of this air flow control loop are plotted in Figs. 13, 14 and 15. The oscillationdetection algorithm applied to controlled signal shows significant oscillations. The identified stiction parameters indicate the presence of stiction, which is causing the sustained oscillations in the OP and PV signals. The identified process is given in equation (17)

0 . 5309 q  1  0 . 9433 q  2 yˆ ( k )  u (k ) 1  0 . 3142 q 1

(17)

with controller parameters of KC = 0.1713 and KI = 0.03. 159

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Flow rate in

lpm(PV)

580 560 540 520 500 480 460 Actual PV Estimated PV

440 420 400 2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

Time(s)

Fig. 13. Actual and Estimated Process Variable in lpm. 8

Controller

out put ( OP)

7.5

7

6.5

6 5.5

5 Estimated OP Actual OP

4.5

4 2000

2200

2400

2600

2800

3000 Time(s)

3200

3400

3600

3800

4000

Fig. 14. Actual and Estimated Controller output in mA.

Valve position ( MV)

3.45 3.4 3.35 3.3 3.25 3.2 3.15 3.1 2000

2200

2400

2600

2800

3000 Time(s)

3200

3400

3600

3800

4000

Fig. 15. Estimated Valve position in inches.

160

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Fig. 13, Fig. 14 and Fig. 15 shows how well the estimated model fits the measured data, thus enabling one to estimate time trends of MV. The stiction parameter estimates are found to be fS=0.081 and fD=0.029. The laboratory air flow control system with control valve is shown in Fig. 16. It is a cascade control loop with temperature as the primary variable and flow as the secondary variable. The inner flow control loop is considered in the present work.

Fig. 16. Laboratory Air Flow Control System.

8. Conclusion A novel closed-loop stiction quantification method using routine closed-loop operating data is presented based on a closed-loop model-identification approach. The approach uses PV and OP signals to estimate the parameters of a Hammerstein system consisting of a two parameter stiction model and a linear low order process model. The Hammerstein model identification problem has been formulated as an optimization problem and Particle Swarm Optimization is used to estimate the unknown parameters from input-output data. Simulation studies reveal that accurate and consistent results can be obtained even for low signal to noise ratios. It is also shown that the identification by this method is easy in computation and can give accurate estimated models even in the presence of the measurement noises and also prove the convergence properties of the identification scheme. Moreover the performance of the proposed PSO based algorithm is superior to those of the GA based method. The performance of the method is validated in real time by interfacing the laboratory Air Flow Control System through dSPACE interface card and MATLAB software. The stiction-quantification technique has been demonstrated successfully by obtaining process variable (PV) and controller output (OP) data sets from laboratory flow control loop. The relatively high CPU time required for the identification 161

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process is not critical, as the analysis is performed offline. A cost effective optimization technique is adopted to find the best valve-stiction models representing more realistic valve behaviour in the oscillating control loop.

References [1]. M. Jelali, An overview of control performance assessment technology and industrial applications, Control Engineering Practice, Vol. 14, 2006, pp. 441–466. [2]. M. A. A. S. Choudhury, N. F. Thornhill, S. L. Shah, Modelling Valve Stiction, Control Engineering Practice, Vol. 13, 2005, pp. 641–658. [3]. R. Srinivasan, R. Rengaswamy, Stiction compensation in control loops: a framework for integrating stiction measure and compensation, Industrial and Engineering Chemistry Research, Vol. 44, 2005, pp. 9164–9174. [4]. R. Srinivasan, R. Rengaswamy, R. Narasimhan, R. Miller, Control loop performance assessment: Hammerstein model approach for stiction diagnosis, Industrial and Engineering Chemistry Research, Vol. 44, 2005, pp. 6719–6728. [5]. A. R. Rodrigo, G. Claudio Garcia, Valve friction quantification and nonlinear process model identification, Proceedings of Symposium on Dynamics and Control of Process Systems, 2010, pp. 115-122. [6]. M. A. A. S. Choudhury, D. Shook, S. L. Shah, Linear or nonlinear ? A bicoherence based metric of nonlinearity measure, in Proceedings of the IFAC symposium( SAFEPROCESS), Beijing, China, 2006. [7]. M. A. A. S. Choudhury, M. Jain, S. L. Shah, Stiction definition, modelling, detection and quantification. Journal of Process Control, Vol. 18, 2008, pp. 232–243. [8]. I. W. Hunter and M. J. Korenberg, The Identification of Nonlinear Biological Systems: Wiener and Hammerstein Cascade Models, Biological Cybernetics, Vol. 55, 1986, pp. 135-144. [9]. C. Maurice and James Kennedy, The particle swarm–explosion, stability, and convergence in a multidimensional complex space, IEEE Transactions on Evolutionary Computation, Vol. 6, 2002, pp. 58–73. [10].Y. H. Shi, R. C. Eberhart, and Y. B. Chen, Design of Evolutionary Fuzzy Expert System, in Proceedings of Artificial Neural Networks in Engineering, 1997. [11].Q. P. He, J. Wang, M. Pottmann, S. J. Qin, A curve fitting method for detecting valve stiction in oscillating control loops, Industrial and Engineering Chemistry Research, Vol. 46, 2007, pp. 4549–4560. ___________________ 2011 Copyright ©, International Frequency Sensor Association (IFSA). All rights reserved. (http://www.sensorsportal.com)

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