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DOĞRUSAL OLMAYAN DİZGELER İÇİN MODEL TEMELLİ ARIZA BULMA-YALITIMI VE ROBOT MANİPÜLATÖRLERE UYGULANMASI

Yıl 2009, Cilt: 24 Sayı: 1, 0 - , 14.02.2013

Tolga Yüksel Abdullah Sezgin

Öz

Gelişen teknoloji ile birlikte arıza bulma ve yalıtımı otomatik kontrol ve sinyal işlemenin ilginç ve önemli araştırma alanlarından biri haline gelmiştir. İlk yapılan çalışmalar doğrusal dizgeler üzerine yoğunlaşsa da gerçek hayattaki uygulamalardaki doğrusal olmayan karakteristikler bu çalışmaların doğrusal olmayan dizgelere uyarlanması veya yeni teknikler önerilmesi ihtiyacını ortaya çıkarmıştır. Bu çalışmada model temelli arıza bulma ve yalıtımı konusuna kısa bir giriş yapılmış, doğrusal olmayan dizgeler için uygulanan teknikler ve çalışmalar için geniş bir literatür özeti verilmiş, daha sonra doğrusal olmayan dizgelerde özel bir yeri olan robot manipülatörler için önerilen bir arıza bulma-yalıtım dizgesi sunulmuş ve gerçeklenen benzetimler üzerinde dizgenin çeşitli özellikleri tartışılmıştır.

Anahtar Kelimeler

Arıza bulma ve yalıtımı doğrusal olmayan dizgeler robot manipülatörler.

Kaynakça

  • Isermann, R., Ballé, P., “Trends In The Application Of Model-based Fault Detection And Diagnosis of Technical Processes”, Control Eng. Practice Cilt 5, No 5, 709-719, 1997.
  • Chen J., Patton, R. J., Robust Model-Based Fault Diagnosis For Dynamic Systems, Kluwer Academic Publishers, 1999.
  • Venkatasubramanian, V., Rengaswamy, R., Kavuri, S. N., Yin., K., “A Review Of Process Fault Detection and Diagnosis Part III: Process History Based Methods”, Computers and
  • Chemical Engineering, Cilt 27, 327-346, 2003.
  • Patton, R. J., Frank, P.M., Clark R.N., Issues Of Fault Diagnosis For Dynamic Systems, Springer-Verlag, 2000.
  • Frank, P. M., Ding, X., “Survey Of Robust Residual Generation And Evaluation Methods In Observer-Based Fault Detection Systems”, J. Proc. Cont. Cilt 7, No 6, 403-424, 1997.
  • Garcia, E. A., Frank, P. M., “Analysis Of A Class Of Dedicated Observer Schemes To Sensor Fault Isolation”, UKACC International Conference on CONTROL ’96, 60-65, 2-5 Eylül 1996.
  • Magni, J.F, Mouyon, P..“On Residual Generation by Observer and Parity Space Approaches”, IEEE Transactions On Automatic Control, Cilt 39, No 2., 441-447, 1994.
  • Patton R.J., Chen, J., “Observer-Based Fault Detection And Isolation: Robustness And Applications”, Control Eng. Practice, Cilt 5, No 5, 671-682, 1997.
  • Chow, E. Y., Willsky, A.S., “Analytical Redundancy and the Design of Robust Failure Detection Systems”, IEEE Transactions On Automatic Control, Cilt 29, No 7, 603-614, 1984.
  • Simani, S., Fantuzzi, C., Patton, R. J., Model- Based Fault Diagnosis In Dynamic Systems Using Identification Techniques,Springer-Verlag, 2002.
  • Liu,X.Q, Zhang, H.Y., Liu, J., Yang,J. “Fault Detection and Diagnosis of Permanent-Magnet DC Motor Based on Parameter Estimation and Neural Network”, IEEE Transactions On Industrıal Electronics, Cilt 47, No 5, 2000.
  • Adjallah, K., Maquin, D., Ragot, J., ”Non-linear Observer-Based Fault Detection”, Third IEEE Conf. on Control Applications, 1115-1120, 1994.
  • Garcia, E.A., Frank, P.M., “Deterministic Nonlinear Observer-Based Approaches To Fault Diagnosis: A survey”, Control Eng. Practice, Cilt 5, No 5, 663-670,1997.
  • Seliger, R., Frank, P.M., “Fault Diagnosis By Disturbance Decoupled Nonlinear Observers”, 30th Conf. on Decision and Control, 2248-2253, 1991.
  • Yang, H., Saif, M., “State Observation, Failure Detection And Isolation (FDI) In Bilinear Systems”, 34th Conference on Decision & Control, 2391-2396, 1995.
  • Kinnaert, M.,”Robust fault detection based on observers for bilinear systems”, Automatica, Cilt 35, 1829-1842, 1999.
  • Haykin, S., Neural Networks: A Compherensive Foundation, Prentice-Hall, 2. baskı, 1999.
  • Patton, R. J., Uppal, F. J., Lopez-Toribio, C. J., “Soft Computing Approaches To Fault Diagnosis For Dynamic Systems: A Survey “IFAC Symposium SAFEPROCESS, 298-311, 2000.
  • Lehtoranta, J., Koivo, H. N., “Fault Diagnosis of Induction Motors with Dynamical Neural Networks”, IEEE International Conference On Systems, Man and Cybernetics, Cilt 3,2979-2984, 2005.
  • Marcu, T., Mirea, L., Frank, P. M, “Neural Observer Schemes For Robust Detection And Isolation Of Process Faults”, UKACC International Conference on CONTROL '98, 958-963, 1998.
  • Pei, X., Chowdhury, F. N., “Unsupervised Neural Network for Fault Detection and Classification in Dynamic Systems”, IEEE International Conference on Control Applications, 640-645, 1999.
  • Karpenko, M., Sepheri, M., “Neural Network Detection And Identification Of Actuator Faults In A Pneumatic Process Control Valve”, IEEE International Symposium on Computational Intelligence In Robotics and Automation, 166-
  • , 2001.
  • Dai, S.J., Shi, Z.Q., Wang, J.Z., Yue, H., “A Comparison Of Neural Networks And Model Based Methods Applied For Fault Diagnosis Of Electro Hydraulic Control Systems”, First International Conference On Machine Learning and Cybernetics, 188-193, 2002.
  • Ayoubi, M., “Nonlinear Dynamic Systems Identification With Dynamic Neural Networks For Fault Diagnosis In Technical Processes”, IEEE International Conference On Systems,Man and Cybernetics,Cilt 3, 2120-2125, 1994.
  • Altuğ, S., Chow, M., Trussell, H. J., “Fuzzy Inference Systems Implemented on Neural Architectures for Motor Fault Detection and Diagnosis”, IEEE Transactions On Industrial
  • Electronics, Cilt 46, No 6, 1069-1079, 1999.
  • Liu, X.Q., Zhang, H.Y., Liu, J., Yang, J. “Fault Detection and Diagnosis of Permanent-Magnet DC Motor Based on Parameter Estimation and Neural Network”, IEEE Transactions On Industrial Electronics, Cilt. 47, No 5, 1021-1030, 2000.
  • Zhang, X., Polycarpou, M. M., Parisini, T. “A Robust Detection and Isolation Scheme for Abrupt and Incipient Faults in Nonlinear Systems”, IEEE Transactions On Automatic
  • Control, Cilt 47, No 4, 576-592, 2002.
  • Polycarpou, M. M., Helmicki A. J., “Automated Fault Detection and Accommodation: A Learning Systems Approach”, IEEE Transactions On Systems, Man and Cybernetics,Cilt 25, No 11, 1447-1458, 1995.
  • Polycarpou, M. M., Trunov, A.B., “Learning Approach to Nonlinear Fault Diagnosis: Detectability Analysis”, IEEE Transactions On Automatic Control, Cilt 45, No 4, 806-812.
  • Dexter, A.L., “ Fuzzy Model-Based Fault Diagnosis”, IEE Proceedings On Cont. Theory and Applications, Cilt 142, No 6, 545-550, 1995
  • Patton, R.J., Chen, J., Lopez-Toribio, C.J. ”Fuzzy Observers for Nonlinear Dynamic Systems Fault Diagnosis”, 37th IEEE Conference on Decision & Control, 84-89, 1998.
  • Isermann, R., “On Fuzzy Logic Applications for Automatic Control, Supervision, and Fault Diagnosis”, IEEE Transactions On Systems, Man, and Cybernetics-Part A:Systems and
  • Humans, Cilt 28, No 2, 221-235, 1998.
  • Ballé, P., “Fuzzy Model-Based Symptom Generation and Fault Diagnosis for Nonlinear Processes”, IEEE International Conference On Fuzzy Systems, Cilt 2, 945-950, 1998.
  • Jang, J.R., Sun, C.T.,. Mizutani E., Neuro-Fuzzy and Soft Computing, Prentice-Hall Inc., 1997
  • Schneider, H., Frank, P. M., “Observed Based Supervision and Fault Detection in Robots Using Nonlinear and Fuzzy Logic Residual Evaluation”, IEEE Transactions On System Technology, Cilt 4, No 3, 274-282, 1996.
  • Xiong, Y., Saif, M., “Sliding Mode Observers For Nonlinear Uncertain Systems”, IEEE Transactions On Automatic Control, Cilt 46, No 2, 2012-2017, 2001.
  • Join, C., Ponsart, J.C., Sauter, D., Theilliol, D. “Nonlinear Filter Design For Fault Diagnosis:Application To The Three-Tank System”, IEE Proc. Control Theory Appl.., Cilt 152, No 1, 55- 642005.
  • Guo, L., Wang, H., “Fault Detection and Diagnosis for General Stochastic Systems Using B-Spline Expansions and Nonlinear Filters”, IEEE Transactions On Circuits And Systems-I: Regular Papers, Cilt 52, No 8, 1644-1652, 2005.
  • Visinsky, M. L., Fault Detection And Fault Tolerance Methods For Robotics, Master Tezi, Rice Universitesi, 1991
  • Cavallaro, J. R., Walker, I. D., “A Survey Of NASA And Military Standards On Fault Tolerance And Reliability Applied To Robotics”, American Institute of Aeronautics and Astronautics.
  • Goel, P., Dedeoglu, G., Roumeliotis, S. I., Sukhatme, G. S., “Fault Detection and Identification In A Mobile Robot Using Multiple Model Estimation and Neural Network” IEEE International Conference on Robotics& Automation, 2302-2309, 2000.
  • Tinós, R., Terra, M. H., “Free-Swinging and Locked Joint Fault Detection and Isolation In Cooperative Manipulators”, European Syposium on Artificial Neural Networks, 513-518, 2002.
  • Notash, L., Moore, T. N. “Fault Analysis in Mechatronic Systems”, The Mechatronics Handbook, Bölüm 39,CRC Press, 2002.
  • Fantuzzi, C., Secchi, C., Visioli, A., ”On The Fault Detection And Isolation Of Industrial Robot Manipulators”, 7th International IFAC Symposium on Robot Control, 2003.
  • Caccavale, F., Walker, I. D., “Observer-based Fault Detection For Robot Manipulators”, IEEE International Conference on Robotics and Automation, 2881-2887, 1997.
  • Leuschen, M.L., Walker, I.D., Cavallaro, J.R., “Fault Residual Generation Via Nonlinear Analytical Redundancy”, IEEE Transactions on Control System Technology, Cilt 13, No 3, 452-45, 2005.
  • De Luca, A., Mattone, R., “An Adapt-and-Detect Actuator FDI For Robot Manipulators”, IEEE International Conference on Robotics & Automation, 879-884, 2004
  • Dixon, W. E., Walker, I. D., Dawson, D. M., “Fault Detection for Robot Manipulators with Parametric Uncertainty: A Prediction-Error-Based Approach ”,IEEE Transactions On Robotics And Automation, Cilt 16, No 6, 689-699, 2000.
  • Naughton, J. M., Chen, Y. C., Jiang, J., “A Neural Network Application to Fault Diagnosis”, IEEE International Conference on Control Applications, 988-993, 1996.
  • Vemuri, A.T., Polycarpou, M.M., ”Neural- Network-Based Robust Fault Diagnosis In Robotic Systems”, IEEE Transactions on Neural Networks, Cilt 8, No 6, 1410-1420, 1997
  • Terra, M. H., Tinós, R., ”Fault Detection And Isolation In Robotic Manipulators Via Neural Networks: A Comparison Among Three Architectures For Residual Analysis”, Journal of
  • Robotic Systems, Cilt 18, No 7, 357-374, 2001.
  • Riedmiller, M., Braun, H., “A Direct Adaptive Method For Faster Backpropagation Learning: The RPROP Algorithm”, IEEE International Conference on Neural Networks, Cilt 1, 586-
  • , 1993.
  • Lewis, F. L., Abdallah, C. T., Dawson, D. M, Control of Robot Manipulators, MacMillan Publishing, 1993.

Yıl 2009, Cilt: 24 Sayı: 1, 0 - , 14.02.2013

Tolga Yüksel Abdullah Sezgin

Öz

Kaynakça

  • Isermann, R., Ballé, P., “Trends In The Application Of Model-based Fault Detection And Diagnosis of Technical Processes”, Control Eng. Practice Cilt 5, No 5, 709-719, 1997.
  • Chen J., Patton, R. J., Robust Model-Based Fault Diagnosis For Dynamic Systems, Kluwer Academic Publishers, 1999.
  • Venkatasubramanian, V., Rengaswamy, R., Kavuri, S. N., Yin., K., “A Review Of Process Fault Detection and Diagnosis Part III: Process History Based Methods”, Computers and
  • Chemical Engineering, Cilt 27, 327-346, 2003.
  • Patton, R. J., Frank, P.M., Clark R.N., Issues Of Fault Diagnosis For Dynamic Systems, Springer-Verlag, 2000.
  • Frank, P. M., Ding, X., “Survey Of Robust Residual Generation And Evaluation Methods In Observer-Based Fault Detection Systems”, J. Proc. Cont. Cilt 7, No 6, 403-424, 1997.
  • Garcia, E. A., Frank, P. M., “Analysis Of A Class Of Dedicated Observer Schemes To Sensor Fault Isolation”, UKACC International Conference on CONTROL ’96, 60-65, 2-5 Eylül 1996.
  • Magni, J.F, Mouyon, P..“On Residual Generation by Observer and Parity Space Approaches”, IEEE Transactions On Automatic Control, Cilt 39, No 2., 441-447, 1994.
  • Patton R.J., Chen, J., “Observer-Based Fault Detection And Isolation: Robustness And Applications”, Control Eng. Practice, Cilt 5, No 5, 671-682, 1997.
  • Chow, E. Y., Willsky, A.S., “Analytical Redundancy and the Design of Robust Failure Detection Systems”, IEEE Transactions On Automatic Control, Cilt 29, No 7, 603-614, 1984.
  • Simani, S., Fantuzzi, C., Patton, R. J., Model- Based Fault Diagnosis In Dynamic Systems Using Identification Techniques,Springer-Verlag, 2002.
  • Liu,X.Q, Zhang, H.Y., Liu, J., Yang,J. “Fault Detection and Diagnosis of Permanent-Magnet DC Motor Based on Parameter Estimation and Neural Network”, IEEE Transactions On Industrıal Electronics, Cilt 47, No 5, 2000.
  • Adjallah, K., Maquin, D., Ragot, J., ”Non-linear Observer-Based Fault Detection”, Third IEEE Conf. on Control Applications, 1115-1120, 1994.
  • Garcia, E.A., Frank, P.M., “Deterministic Nonlinear Observer-Based Approaches To Fault Diagnosis: A survey”, Control Eng. Practice, Cilt 5, No 5, 663-670,1997.
  • Seliger, R., Frank, P.M., “Fault Diagnosis By Disturbance Decoupled Nonlinear Observers”, 30th Conf. on Decision and Control, 2248-2253, 1991.
  • Yang, H., Saif, M., “State Observation, Failure Detection And Isolation (FDI) In Bilinear Systems”, 34th Conference on Decision & Control, 2391-2396, 1995.
  • Kinnaert, M.,”Robust fault detection based on observers for bilinear systems”, Automatica, Cilt 35, 1829-1842, 1999.
  • Haykin, S., Neural Networks: A Compherensive Foundation, Prentice-Hall, 2. baskı, 1999.
  • Patton, R. J., Uppal, F. J., Lopez-Toribio, C. J., “Soft Computing Approaches To Fault Diagnosis For Dynamic Systems: A Survey “IFAC Symposium SAFEPROCESS, 298-311, 2000.
  • Lehtoranta, J., Koivo, H. N., “Fault Diagnosis of Induction Motors with Dynamical Neural Networks”, IEEE International Conference On Systems, Man and Cybernetics, Cilt 3,2979-2984, 2005.
  • Marcu, T., Mirea, L., Frank, P. M, “Neural Observer Schemes For Robust Detection And Isolation Of Process Faults”, UKACC International Conference on CONTROL '98, 958-963, 1998.
  • Pei, X., Chowdhury, F. N., “Unsupervised Neural Network for Fault Detection and Classification in Dynamic Systems”, IEEE International Conference on Control Applications, 640-645, 1999.
  • Karpenko, M., Sepheri, M., “Neural Network Detection And Identification Of Actuator Faults In A Pneumatic Process Control Valve”, IEEE International Symposium on Computational Intelligence In Robotics and Automation, 166-
  • , 2001.
  • Dai, S.J., Shi, Z.Q., Wang, J.Z., Yue, H., “A Comparison Of Neural Networks And Model Based Methods Applied For Fault Diagnosis Of Electro Hydraulic Control Systems”, First International Conference On Machine Learning and Cybernetics, 188-193, 2002.
  • Ayoubi, M., “Nonlinear Dynamic Systems Identification With Dynamic Neural Networks For Fault Diagnosis In Technical Processes”, IEEE International Conference On Systems,Man and Cybernetics,Cilt 3, 2120-2125, 1994.
  • Altuğ, S., Chow, M., Trussell, H. J., “Fuzzy Inference Systems Implemented on Neural Architectures for Motor Fault Detection and Diagnosis”, IEEE Transactions On Industrial
  • Electronics, Cilt 46, No 6, 1069-1079, 1999.
  • Liu, X.Q., Zhang, H.Y., Liu, J., Yang, J. “Fault Detection and Diagnosis of Permanent-Magnet DC Motor Based on Parameter Estimation and Neural Network”, IEEE Transactions On Industrial Electronics, Cilt. 47, No 5, 1021-1030, 2000.
  • Zhang, X., Polycarpou, M. M., Parisini, T. “A Robust Detection and Isolation Scheme for Abrupt and Incipient Faults in Nonlinear Systems”, IEEE Transactions On Automatic
  • Control, Cilt 47, No 4, 576-592, 2002.
  • Polycarpou, M. M., Helmicki A. J., “Automated Fault Detection and Accommodation: A Learning Systems Approach”, IEEE Transactions On Systems, Man and Cybernetics,Cilt 25, No 11, 1447-1458, 1995.
  • Polycarpou, M. M., Trunov, A.B., “Learning Approach to Nonlinear Fault Diagnosis: Detectability Analysis”, IEEE Transactions On Automatic Control, Cilt 45, No 4, 806-812.
  • Dexter, A.L., “ Fuzzy Model-Based Fault Diagnosis”, IEE Proceedings On Cont. Theory and Applications, Cilt 142, No 6, 545-550, 1995
  • Patton, R.J., Chen, J., Lopez-Toribio, C.J. ”Fuzzy Observers for Nonlinear Dynamic Systems Fault Diagnosis”, 37th IEEE Conference on Decision & Control, 84-89, 1998.
  • Isermann, R., “On Fuzzy Logic Applications for Automatic Control, Supervision, and Fault Diagnosis”, IEEE Transactions On Systems, Man, and Cybernetics-Part A:Systems and
  • Humans, Cilt 28, No 2, 221-235, 1998.
  • Ballé, P., “Fuzzy Model-Based Symptom Generation and Fault Diagnosis for Nonlinear Processes”, IEEE International Conference On Fuzzy Systems, Cilt 2, 945-950, 1998.
  • Jang, J.R., Sun, C.T.,. Mizutani E., Neuro-Fuzzy and Soft Computing, Prentice-Hall Inc., 1997
  • Schneider, H., Frank, P. M., “Observed Based Supervision and Fault Detection in Robots Using Nonlinear and Fuzzy Logic Residual Evaluation”, IEEE Transactions On System Technology, Cilt 4, No 3, 274-282, 1996.
  • Xiong, Y., Saif, M., “Sliding Mode Observers For Nonlinear Uncertain Systems”, IEEE Transactions On Automatic Control, Cilt 46, No 2, 2012-2017, 2001.
  • Join, C., Ponsart, J.C., Sauter, D., Theilliol, D. “Nonlinear Filter Design For Fault Diagnosis:Application To The Three-Tank System”, IEE Proc. Control Theory Appl.., Cilt 152, No 1, 55- 642005.
  • Guo, L., Wang, H., “Fault Detection and Diagnosis for General Stochastic Systems Using B-Spline Expansions and Nonlinear Filters”, IEEE Transactions On Circuits And Systems-I: Regular Papers, Cilt 52, No 8, 1644-1652, 2005.
  • Visinsky, M. L., Fault Detection And Fault Tolerance Methods For Robotics, Master Tezi, Rice Universitesi, 1991
  • Cavallaro, J. R., Walker, I. D., “A Survey Of NASA And Military Standards On Fault Tolerance And Reliability Applied To Robotics”, American Institute of Aeronautics and Astronautics.
  • Goel, P., Dedeoglu, G., Roumeliotis, S. I., Sukhatme, G. S., “Fault Detection and Identification In A Mobile Robot Using Multiple Model Estimation and Neural Network” IEEE International Conference on Robotics& Automation, 2302-2309, 2000.
  • Tinós, R., Terra, M. H., “Free-Swinging and Locked Joint Fault Detection and Isolation In Cooperative Manipulators”, European Syposium on Artificial Neural Networks, 513-518, 2002.
  • Notash, L., Moore, T. N. “Fault Analysis in Mechatronic Systems”, The Mechatronics Handbook, Bölüm 39,CRC Press, 2002.
  • Fantuzzi, C., Secchi, C., Visioli, A., ”On The Fault Detection And Isolation Of Industrial Robot Manipulators”, 7th International IFAC Symposium on Robot Control, 2003.
  • Caccavale, F., Walker, I. D., “Observer-based Fault Detection For Robot Manipulators”, IEEE International Conference on Robotics and Automation, 2881-2887, 1997.
  • Leuschen, M.L., Walker, I.D., Cavallaro, J.R., “Fault Residual Generation Via Nonlinear Analytical Redundancy”, IEEE Transactions on Control System Technology, Cilt 13, No 3, 452-45, 2005.
  • De Luca, A., Mattone, R., “An Adapt-and-Detect Actuator FDI For Robot Manipulators”, IEEE International Conference on Robotics & Automation, 879-884, 2004
  • Dixon, W. E., Walker, I. D., Dawson, D. M., “Fault Detection for Robot Manipulators with Parametric Uncertainty: A Prediction-Error-Based Approach ”,IEEE Transactions On Robotics And Automation, Cilt 16, No 6, 689-699, 2000.
  • Naughton, J. M., Chen, Y. C., Jiang, J., “A Neural Network Application to Fault Diagnosis”, IEEE International Conference on Control Applications, 988-993, 1996.
  • Vemuri, A.T., Polycarpou, M.M., ”Neural- Network-Based Robust Fault Diagnosis In Robotic Systems”, IEEE Transactions on Neural Networks, Cilt 8, No 6, 1410-1420, 1997
  • Terra, M. H., Tinós, R., ”Fault Detection And Isolation In Robotic Manipulators Via Neural Networks: A Comparison Among Three Architectures For Residual Analysis”, Journal of
  • Robotic Systems, Cilt 18, No 7, 357-374, 2001.
  • Riedmiller, M., Braun, H., “A Direct Adaptive Method For Faster Backpropagation Learning: The RPROP Algorithm”, IEEE International Conference on Neural Networks, Cilt 1, 586-
  • , 1993.
  • Lewis, F. L., Abdallah, C. T., Dawson, D. M, Control of Robot Manipulators, MacMillan Publishing, 1993.
Toplam 60 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Makaleler
Yazarlar

Tolga Yüksel Bu kişi benim

Abdullah Sezgin Bu kişi benim

Yayımlanma Tarihi 14 Şubat 2013
Gönderilme Tarihi 14 Şubat 2013
Yayımlandığı Sayı Yıl 2009 Cilt: 24 Sayı: 1

Kaynak Göster

APA Yüksel, T., & Sezgin, A. (2013). DOĞRUSAL OLMAYAN DİZGELER İÇİN MODEL TEMELLİ ARIZA BULMA-YALITIMI VE ROBOT MANİPÜLATÖRLERE UYGULANMASI. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 24(1).
AMA Yüksel T, Sezgin A. DOĞRUSAL OLMAYAN DİZGELER İÇİN MODEL TEMELLİ ARIZA BULMA-YALITIMI VE ROBOT MANİPÜLATÖRLERE UYGULANMASI. GUMMFD. Mart 2013;24(1).
Chicago Yüksel, Tolga, ve Abdullah Sezgin. “DOĞRUSAL OLMAYAN DİZGELER İÇİN MODEL TEMELLİ ARIZA BULMA-YALITIMI VE ROBOT MANİPÜLATÖRLERE UYGULANMASI”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 24, sy. 1 (Mart 2013).
EndNote Yüksel T, Sezgin A (01 Mart 2013) DOĞRUSAL OLMAYAN DİZGELER İÇİN MODEL TEMELLİ ARIZA BULMA-YALITIMI VE ROBOT MANİPÜLATÖRLERE UYGULANMASI. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 24 1
IEEE T. Yüksel ve A. Sezgin, “DOĞRUSAL OLMAYAN DİZGELER İÇİN MODEL TEMELLİ ARIZA BULMA-YALITIMI VE ROBOT MANİPÜLATÖRLERE UYGULANMASI”, GUMMFD, c. 24, sy. 1, 2013.
ISNAD Yüksel, Tolga - Sezgin, Abdullah. “DOĞRUSAL OLMAYAN DİZGELER İÇİN MODEL TEMELLİ ARIZA BULMA-YALITIMI VE ROBOT MANİPÜLATÖRLERE UYGULANMASI”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 24/1 (Mart 2013).
JAMA Yüksel T, Sezgin A. DOĞRUSAL OLMAYAN DİZGELER İÇİN MODEL TEMELLİ ARIZA BULMA-YALITIMI VE ROBOT MANİPÜLATÖRLERE UYGULANMASI. GUMMFD. 2013;24.
MLA Yüksel, Tolga ve Abdullah Sezgin. “DOĞRUSAL OLMAYAN DİZGELER İÇİN MODEL TEMELLİ ARIZA BULMA-YALITIMI VE ROBOT MANİPÜLATÖRLERE UYGULANMASI”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, c. 24, sy. 1, 2013.
Vancouver Yüksel T, Sezgin A. DOĞRUSAL OLMAYAN DİZGELER İÇİN MODEL TEMELLİ ARIZA BULMA-YALITIMI VE ROBOT MANİPÜLATÖRLERE UYGULANMASI. GUMMFD. 2013;24(1).