Performance-Based Adaptive Gradient Descent Optimal Coefficient Fuzzy Sliding Mode Methodology

Full Text (PDF, 1286KB), PP.40-52

Views: 0 Downloads: 0

Author(s)

Farzin Piltan 1,* Bamdad Boroomand 1 Arman Jahed 1 Hossein Rezaie 1

1. Industrial Electrical and Electronic Engineering SanatkadeheSabze Pasargad. CO (S.S.P. Co), NO:16 , PO.Code 71347- 66773, Fourth floor , Dena Apr , Seven Tir Ave , Shiraz , Iran

* Corresponding author.

DOI: https://doi.org/10.5815/ijisa.2012.11.05

Received: 12 Feb. 2012 / Revised: 1 Jun. 2012 / Accepted: 20 Aug. 2012 / Published: 8 Oct. 2012

Index Terms

Gradient Descent Optimal Algorithm, Sliding Mode Controller, Gradient Descent Optimal Fuzzy Sliding Mode Controller, Fuzzy Based Tuning Methodology, Lyapunov Based Stability

Abstract

Design a nonlinear controller for second order nonlinear uncertain dynamical systems is the main challenge in this paper. This paper focuses on the design and analysis of a chattering free Mamdani’s fuzzy-based tuning gradient descent optimal error-based fuzzy sliding mode controller for highly nonlinear dynamic six degrees of freedom robot manipulator, in presence of uncertainties. Conversely, pure sliding mode controller is used in many applications; it has two important drawbacks namely; chattering phenomenon and nonlinear equivalent dynamic formulation in uncertain dynamic parameter. In order to solve the uncertain nonlinear dynamic parameters, implement easily and avoid mathematical model base controller, Mamdani’s performance/error-based fuzzy logic methodology with two inputs and one output and 49 rules is applied to pure sliding mode controller. Pure sliding mode controller and error-based fuzzy sliding mode controller have difficulty in handling unstructured model uncertainties. To solve this problem applied fuzzy-based tuning method to error-based fuzzy sliding mode controller for adjusting the sliding surface gain. Since the sliding surface gain is adjusted by gradient descent optimization method. Fuzzy-based tuning gradient descent optimal error-based fuzzy sliding mode controller is stable model-free controller which eliminates the chattering phenomenon without to use the boundary layer saturation function. Lyapunov stability is proved in fuzzy-based tuning gradient descent optimal fuzzy sliding mode controller based on switching (sign) function. This controller has acceptable performance in presence of uncertainty (e.g., overshoot=0%, rise time=0.8 second, steady state error = 1e-9 and RMS error=1.8e-12).

Cite This Paper

Farzin Piltan, Bamdad Boroomand, Arman Jahed, Hossein Rezaie, "Performance-Based Adaptive Gradient Descent Optimal Coefficient Fuzzy Sliding Mode Methodology", International Journal of Intelligent Systems and Applications(IJISA), vol.4, no.11, pp.40-52, 2012. DOI:10.5815/ijisa.2012.11.05

Reference

[1]T. R. Kurfess, Robotics and automation handbook: CRC, 2005.

[2]J. J. E. Slotine and W. Li, Applied nonlinear control vol. 461: Prentice hall Englewood Cliffs, NJ, 1991.

[3]K. Ogata, Modern control engineering: Prentice Hall, 2009.

[4]B. Siciliano and O. Khatib, Springer handbook of robotics: Springer-Verlag New York Inc, 2008.

[5]I. Boiko, L. Fridman, A. Pisano and E. Usai, "Analysis of chattering in systems with second-order sliding modes," IEEE Transactions on Automatic Control, No. 11, vol. 52,pp. 2085-2102, 2007. 

[6]J. Wang, A. Rad and P. Chan, "Indirect adaptive fuzzy sliding mode control: Part I: fuzzy switching," Fuzzy Sets and Systems, No. 1, vol. 122,pp. 21-30, 2001.

[7]V. Utkin, "Variable structure systems with sliding modes," Automatic Control, IEEE Transactions on, No. 2, vol. 22, pp. 212-222, 2002.

[8]J. J. Slotine and S. Sastry, "Tracking control of non-linear systems using sliding surfaces, with application to robot manipulators†," International Journal of Control, No. 2, vol. 38, pp. 465-492, 1983.

[9]P. Kachroo and M. Tomizuka, "Chattering reduction and error convergence in the sliding-mode control of a class of nonlinear systems," Automatic Control, IEEE Transactions on, No. 7, vol. 41, pp. 1063-1068, 2002.

[10]H. Elmali and N. Olgac, "Implementation of sliding mode control with perturbation estimation (SMCPE)," Control Systems Technology, IEEE Transactions on, No. 1, vol. 4, pp. 79-85, 2002.

[11]Farzin Piltan , N. Sulaiman, Zahra Tajpaykar, Payman Ferdosali, Mehdi Rashidi, “Design Artificial Nonlinear Robust Controller Based on CTLC and FSMC with Tunable Gain,” International Journal of Robotic and Automation, 2 (3): 205-220, 2011.

[12]Farzin Piltan, A. R. Salehi and Nasri B Sulaiman.,” Design artificial robust control of second order system based on adaptive fuzzy gain scheduling,” world applied science journal (WASJ), 13 (5): 1085-1092, 2011.

[13]Farzin Piltan, N. Sulaiman, Atefeh Gavahian, Samira Soltani, Samaneh Roosta, “Design Mathematical Tunable Gain PID-Like Sliding Mode Fuzzy Controller with Minimum Rule Base,” International Journal of Robotic and Automation, 2 (3): 146-156, 2011.

[14]Farzin Piltan , A. Zare, Nasri B. Sulaiman, M. H. Marhaban and R. Ramli, , “A Model Free Robust Sliding Surface Slope Adjustment in Sliding Mode Control for Robot Manipulator,” World Applied Science Journal, 12 (12): 2330-2336, 2011.

[15]Farzin Piltan , A. H. Aryanfar, Nasri B. Sulaiman, M. H. Marhaban and R. Ramli “Design Adaptive Fuzzy Robust Controllers for Robot Manipulator,” World Applied Science Journal, 12 (12): 2317-2329, 2011.

[16]Farzin Piltan, N. Sulaiman , Arash Zargari, Mohammad Keshavarz, Ali Badri , “Design PID-Like Fuzzy Controller With Minimum Rule Base and Mathematical Proposed On-line Tunable Gain: Applied to Robot Manipulator,” International Journal of Artificial intelligence and expert system, 2 (4):184-195, 2011.

[17] Farzin Piltan, Nasri Sulaiman, M. H. Marhaban and R. Ramli, “Design On-Line Tunable Gain Artificial Nonlinear Controller,” Journal of Advances In Computer Research, 2 (4): 75-83, 2011.

[18]Farzin Piltan, N. Sulaiman, Payman Ferdosali, Iraj Assadi Talooki, “ Design Model Free Fuzzy Sliding Mode Control: Applied to Internal Combustion Engine,” International Journal of Engineering, 5 (4):302-312, 2011.

[19]Farzin Piltan, N. Sulaiman, Samaneh Roosta, M.H. Marhaban, R. Ramli, “Design a New Sliding Mode Adaptive Hybrid Fuzzy Controller,” Journal of Advanced Science & Engineering Research , 1 (1): 115-123, 2011. 

[20]Farzin Piltan, Atefe Gavahian, N. Sulaiman, M.H. Marhaban, R. Ramli, “Novel Sliding Mode Controller for robot manipulator using FPGA,” Journal of Advanced Science & Engineering Research, 1 (1): 1-22, 2011.

[21]Farzin Piltan, N. Sulaiman, A. Jalali & F. Danesh Narouei, “Design of Model Free Adaptive Fuzzy Computed Torque Controller: Applied to Nonlinear Second Order System,” International Journal of Robotics and Automation, 2 (4):232-244, 2011.

[22]Farzin Piltan, N. Sulaiman, Iraj Asadi Talooki, Payman Ferdosali, “Control of IC Engine: Design a Novel MIMO Fuzzy Backstepping Adaptive Based Fuzzy Estimator Variable Structure Control ,” International Journal of Robotics and Automation, 2 (5):360-380, 2011.

[23]Farzin Piltan, N. Sulaiman, Payman Ferdosali, Mehdi Rashidi, Zahra Tajpeikar, “Adaptive MIMO Fuzzy Compensate Fuzzy Sliding Mode Algorithm: Applied to Second Order Nonlinear System,” International Journal of Engineering, 5 (5): 380-398, 2011. 

[24]Farzin Piltan, N. Sulaiman, Hajar Nasiri, Sadeq Allahdadi, Mohammad A. Bairami, “Novel Robot Manipulator Adaptive Artificial Control: Design a Novel SISO Adaptive Fuzzy Sliding Algorithm Inverse Dynamic Like Method,” International Journal of Engineering, 5 (5): 399-418, 2011.

[25]Farzin Piltan, N. Sulaiman, Sadeq Allahdadi, Mohammadali Dialame, Abbas Zare, “Position Control of Robot Manipulator: Design a Novel SISO Adaptive Sliding Mode Fuzzy PD Fuzzy Sliding Mode Control,” International Journal of Artificial intelligence and Expert System, 2 (5):208-228, 2011.

[26]Farzin Piltan, SH. Tayebi HAGHIGHI, N. Sulaiman, Iman Nazari, Sobhan Siamak, “Artificial Control of PUMA Robot Manipulator: A-Review of Fuzzy Inference Engine And Application to Classical Controller ,” International 

Journal of Robotics and Automation, 2 (5):401-425, 2011.

[27]Farzin Piltan, N. Sulaiman, Abbas Zare, Sadeq Allahdadi, Mohammadali Dialame, “Design Adaptive Fuzzy Inference Sliding Mode Algorithm: Applied to Robot Arm,” International Journal of Robotics and Automation , 2 (5): 283-297, 2011. 

[28]Farzin Piltan, Amin Jalali, N. Sulaiman, Atefeh Gavahian, Sobhan Siamak, “Novel Artificial Control of Nonlinear Uncertain System: Design a Novel Modified PSO SISO Lyapunov Based Fuzzy Sliding Mode Algorithm ,” International Journal of Robotics and Automation, 2 (5): 298-316, 2011.

[29]Farzin Piltan, N. Sulaiman, Amin Jalali, Koorosh Aslansefat, “Evolutionary Design of Mathematical tunable FPGA Based MIMO Fuzzy Estimator Sliding Mode Based Lyapunov Algorithm: Applied to Robot Manipulator,” International Journal of Robotics and Automation, 2 (5):317-343, 2011.

[30]Farzin Piltan, N. Sulaiman, Samaneh Roosta, Atefeh Gavahian, Samira Soltani, “Evolutionary Design of Backstepping Artificial Sliding Mode Based Position Algorithm: Applied to Robot Manipulator,” International Journal of Engineering, 5 (5):419-434, 2011.

[31]Farzin Piltan, N. Sulaiman, S.Soltani, M. H. Marhaban & R. Ramli, “An Adaptive sliding surface slope adjustment in PD Sliding Mode Fuzzy Control for Robot Manipulator,” International Journal of Control and Automation , 4 (3): 65-76, 2011. 

[32]Farzin Piltan, N. Sulaiman, Mehdi Rashidi, Zahra Tajpaikar, Payman Ferdosali, “Design and Implementation of Sliding Mode Algorithm: Applied to Robot Manipulator-A Review ,” International Journal of Robotics and Automation, 2 (5):265-282, 2011.

[33]Farzin Piltan, N. Sulaiman, Amin Jalali, Sobhan Siamak, and Iman Nazari, “Control of Robot Manipulator: Design a Novel Tuning MIMO Fuzzy Backstepping Adaptive Based Fuzzy Estimator Variable Structure Control ,” International Journal of Control and Automation, 4 (4):91-110, 2011.

[34]Farzin Piltan, N. Sulaiman, Atefeh Gavahian, Samaneh Roosta, Samira Soltani, “On line Tuning Premise and Consequence FIS: Design Fuzzy Adaptive Fuzzy Sliding Mode Controller Based on Lyaponuv Theory,” International Journal of Robotics and Automation, 2 (5):381-400, 2011.

[35]Farzin Piltan, N. Sulaiman, Samaneh Roosta, Atefeh Gavahian, Samira Soltani, “Artificial Chattering Free on-line Fuzzy Sliding Mode Algorithm for Uncertain System: Applied in Robot Manipulator,” International Journal of Engineering, 5 (5):360-379, 2011.

[36]Farzin Piltan, N. Sulaiman and I.AsadiTalooki, “Evolutionary Design on-line Sliding Fuzzy Gain Scheduling Sliding Mode Algorithm: Applied to Internal Combustion Engine,” International Journal of Engineering Science and Technology, 3 (10):7301-7308, 2011.

[37]Farzin Piltan, Nasri B Sulaiman, Iraj Asadi Talooki and Payman Ferdosali.,” Designing On-Line Tunable Gain Fuzzy Sliding Mode Controller Using Sliding Mode Fuzzy Algorithm: Applied to Internal Combustion Engine,” world applied science journal (WASJ), 15 (3): 422-428, 2011.

[38]B. K. Yoo and W. C. Ham, "Adaptive control of robot manipulator using fuzzy compensator," Fuzzy Systems, IEEE Transactions on, No. 2, vol. 8, pp. 186-199, 2002.

[39]Xiaosong. Lu, "An investigation of adaptive fuzzy sliding mode control for robot manipulator," Carleton university Ottawa,2007.

[40]S. Lentijo, S. Pytel, A. Monti, J. Hudgins, E. Santi and G. Simin, "FPGA based sliding mode control for high frequency power converters," IEEE Conference, 2004, pp. 3588-3592.

[41]B. S. R. Armstrong, "Dynamics for robot control: friction modeling and ensuring excitation during parameter identification," 1988.

[42]C. L. Clover, "Control system design for robots used in simulating dynamic force and moment interaction in virtual reality applications," 1996.

[43]K. R. Horspool, Cartesian-space Adaptive Control for Dual-arm Force Control Using Industrial Robots: University of New Mexico, 2003.

[44]B. Armstrong, O. Khatib and J. Burdick, "The explicit dynamic model and inertial parameters of the PUMA 560 arm," IEEE Conference, 2002, pp. 510-518.

[45]P. I. Corke and B. Armstrong-Helouvry, "A search for consensus among model parameters reported for the PUMA 560 robot," IEEE Conference, 2002, pp. 1608-1613.

[46]Farzin Piltan, N. Sulaiman, M. H. Marhaban, Adel Nowzary, Mostafa Tohidian,” “Design of FPGA based sliding mode controller for robot manipulator,” International Journal of Robotic and Automation, 2 (3): 183-204, 2011.

[47]I. Eksin, M. Guzelkaya and S. Tokat, "Sliding surface slope adjustment in fuzzy sliding mode controller," Mediterranean Conference, 2002, pp. 160-168.

[48]Samira Soltani & Farzin Piltan, “Design Artificial Nonlinear Controller Based on Computed Torque 

like Controller with Tunable Gain”. World Applied Science Journal,14 (9): 1306-1312, 2011.

[49]Farzin Piltan, H. Rezaie, B. Boroomand, Arman Jahed,” Design robust back stepping online tuning feedback linearization control applied to IC engine,” International Journal of Advance Science and Technology, 42: 183-204, 2012.

[50]Farzin Piltan, I. Nazari, S. Siamak, P. Ferdosali ,”Methodology of FPGA-based mathematical error-based tuning sliding mode controller” International Journal of Control and Automation, 5(1): 89-110, 2012.

[51]Farzin Piltan, M. A. Dialame, A. Zare, A. Badri ,”Design Novel Lookup table changed Auto Tuning FSMC: Applied to Robot Manipulator” International Journal of Engineering, 6(1): 25-40, 2012.

[52]Farzin Piltan, B. Boroomand, A. Jahed, H. Rezaie ,”Methodology of Mathematical Error-Based Tuning Sliding Mode Controller” International Journal of Engineering, 6(2): 96-112, 2012.

[53]Farzin Piltan, F. Aghayari, M. R. Rashidian, M. Shamsodini, ”A New Estimate Sliding Mode Fuzzy Controller for Robotic Manipulator” International Journal of Robotics and Automation, 3(1): 45-58, 2012.

[54]Farzin Piltan, M. Keshavarz, A. Badri, A. Zargari , ”Design novel nonlinear controller applied to robot manipulator: design new feedback linearization fuzzy controller with minimum rule base tuning method” International Journal of Robotics and Automation, 3(1): 1-18, 2012.

[55]Piltan, F., et al. "Design sliding mode controller for robot manipulator with artificial tunable gain". Canaidian Journal of pure and applied science, 5 (2), 1573-1579, 2011.

[56]Farzin Piltan, A. Hosainpour, E. Mazlomian, M.Shamsodini, M.H Yarmahmoudi. ”Online Tuning Chattering Free Sliding Mode Fuzzy Control Design: Lyapunov Approach” International Journal of Robotics and Automation, 3(3): 2012.

[57]Farzin Piltan , M.H. Yarmahmoudi, M. Shamsodini, E.Mazlomian, A.Hosainpour. ” PUMA-560 Robot Manipulator Position Computed Torque Control Methods Using MATLAB/SIMULINK and Their Integration into Graduate Nonlinear Control and MATLAB Courses” International Journal of Robotics and Automation, 3(3): 2012.

[58]Farzin Piltan, R. Bayat, F. Aghayari, B. Boroomand. “Design Error-Based Linear Model-Free Evaluation Performance Computed Torque Controller” International Journal of Robotics and Automation, 3(3): 2012.

[59]Farzin Piltan, S. Emamzadeh, Z. Hivand, F. Shahriyari & Mina Mirazaei . ” PUMA-560 Robot Manipulator Position Sliding Mode Control Methods Using MATLAB/SIMULINK and Their Integration into Graduate/Undergraduate Nonlinear Control, Robotics and MATLAB Courses” International Journal of Robotics and Automation, 3(3): 2012.

[60]Farzin Piltan, J. Meigolinedjad, S. Mehrara, S. Rahmdel. ” Evaluation Performance of 2nd Order Nonlinear System: Baseline Control Tunable Gain Sliding Mode Methodology” International Journal of Robotics and Automation, 3(3): 2012.

[61]Farzin Piltan, M. Mirzaie, F. Shahriyari, Iman Nazari & S. Emamzadeh.” Design Baseline Computed Torque Controller” International Journal of Engineering, 3(3): 2012.