This paper develops a novel interval type-2 fuzzy Proportional-Derivative (PD) control scheme for electrically driven flexible-joint robots using the direct method of Lyapunov. The controller has a simple design in a decentralized structure. Compared to the previous controllers reported for the flexible-joint robots which use two control loops, it has a simpler structure using only one control loop. It guarantees stability and provides a good tracking performance. The controller considers the whole robotic system including the manipulator and motors by applying the voltage control strategy. Stability analysis is presented and the effectiveness of the proposed control approach is demonstrated by simulations using a three link flexible-joint robot driven by permanent magnet DC motors. Simulation results show that the interval type-2 fuzzy PD controller can handle external disturbance better than the type-1 fuzzy PD controller. In addition, it spends less control effort than the type-1 in order to deal with disturbance.
KeywordsType-2 Fuzzy ControlFlexible-Joint RobotsVoltage Control StrategyUncertainty Estimation
Hagras, H.A. (2004) A Hierarchical Type-2 Fuzzy Logic Control Architecture for Autonomous Mobile Robots. IEEE Transactions on Fuzzy Systems, 12, 524-539. https://doi.org/10.1109/TFUZZ.2004.832538
Hsiao, M.-Y., et al. (2008) Design of Interval Type-2 Fuzzy Sliding-Mode Controller. Information Sciences, 178, 1696-1716. https://doi.org/10.1016/j.ins.2007.10.019
Mendel, J.M. (2001) Uncertain Rule-Based Fuzzy Logic System: Introduction and New Directions. Spinge, Berlin.
Mendel, J.M. and John, R.B. (2002) Type-2 Fuzzy Sets Made Simple. Fuzzy Systems, IEEE Transactions on, 10, 117-127. https://doi.org/10.1109/91.995115
Wu Woei Wan Tan, D. (2006) A Simplified Type-2 Fuzzy Logic Controller for Real-Time Control. ISA Transactions, 45, 503-516. https://doi.org/10.1016/S0019-0578(07)60228-6
Yager, R.R. (1980) Fuzzy Subsets of Type II in Decisions. Cybernetics and System, 10, 137-159. https://doi.org/10.1080/01969728008927629
Lin, T.-C. and Roopaei, M. (2010) Based on Interval Type-2 Adaptive Fuzzy H∞ Tracking Controller for SISO Time-Delay Nonlinear Systems. Communications in Nonlinear Science and Numerical Simulation, 15, 4065-4075. https://doi.org/10.1016/j.cnsns.2010.01.029
Khooban, M.H., Alfi, A. and Abadi, D.N.M. (2013) Control of a Class of Non-Linear Uncertain Chaotic Systems via an Optimal Type-2 Fuzzy Proportional Integral Derivative Controller. IET Science, Measurement & Technology, 7, 50-58. https://doi.org/10.1049/iet-smt.2012.0092
Dwivedy, S.K. and Eberhard, P. (2006) Dynamic Analysis of Flexible Manipulators, a Literature Review. Mechanism and Machine Theory, 41, 749-777. https://doi.org/10.1016/j.mechmachtheory.2006.01.014
Tokhi, M.O. and Azad A.K. (2008) Flexible Robot Manipulators: Modelling, Simulation and Control. IET, Stevenage, 68. https://doi.org/10.1049/PBCE068E
Book, W.J. (1979) Analysis of Massless Elastic Chains with Servo Controlled Joints. Journal of Dynamic Systems, Measurement, and Control, 101, 187-192. https://doi.org/10.1115/1.3426423
Fateh, M.M. (2012) Nonlinear Control of Electrical Flexible-Joint Robots. Nonlinear Dynamics, 67, 2549-2559. https://doi.org/10.1007/s11071-011-0167-3
Sweet, L.M. and Good, M. (1985) Redefinition of the Robot Motion-Control Problem. Control Systems Magazine, 5, 18-25. https://doi.org/10.1109/MCS.1985.1104955
Kokotovic, P., Khali, H.K. and O’reilly, J. (1999) Singular Perturbation Methods in Control: Analysis and Design. SIAM, Vol. 25. https://doi.org/10.1137/1.9781611971118
De Luca, A., Isidori, A. and Nicolo, F. (1985) Control of Robot Arm with Elastic Joints via Nonlinear Dynamic Feedback. 24th IEEE Conference on Decision and Control.
Chien, M.-C. and Huang, A.-C. (2007) Adaptive Control for Flexible-Joint Electrically Driven Robot with Time-Varying Uncertainties. IEEE Transactions on Industrial Electronics, 54, 1032-1038.
Wilson, G. and Irwin, G. (1994) Robust Tracking of Elastic Joint Manipulators using Sliding Mode Control. Transactions of the Institute of Measurement and Control, 16, 99-107. https://doi.org/10.1177/014233129401600206
Lih-Chang, L. and Chiang-Chuan, C. (1995) Rigid Model-Based Fuzzy Control of Flexible-Joint Manipulators. Journal of Intelligent and Robotic Systems, 13, 107-126. https://doi.org/10.1007/BF01254847
Zeman, V., Patel, R. and Khorasani, K. (1997) Control of a Flexible-Joint Robot using Neural Networks. IEEE Transactions on Control Systems Technology, 5, 453-462. https://doi.org/10.1109/87.595927
Li, Y., Tong, S. and Li, T. (2013) Adaptive Fuzzy Output Feedback Control for a Single-Link Flexible Robot Manipulator Driven DC Motor via Backstepping. Nonlinear Analysis: Real World Applications, 14, 483-494.
Tarn, T., et al. (1991) Effect of Motor Dynamics on Nonlinear Feedback Robot Arm Control. IEEE Transactions on Robotics and Automation, 7, 114-122.
Fateh, M.M. (2012) Robust Control of Flexible-Joint Robots Using Voltage Control Strategy. Nonlinear Dynamics, 67, 1525-1537. https://doi.org/10.1007/s11071-011-0086-3
Spong, M.W. (1987) Modeling and Control of Elastic Joint Robots. Journal of Dynamic Systems, Measurement, and Control, 109, 310-318. https://doi.org/10.1115/1.3143860
Fateh, M.M. (2008) On the Voltage-Based Control of Robot Manipulators. International Journal of Control, Automation, and Systems, 6, 702-712.
Ailon, A., Lozano, R. and Gil, M. (2000) Iterative Regulation of an Electrically Driven Flexible-Joint Robot with Model Uncertainty. IEEE Transactions on Robotics and Automation, 16, 863-870. https://doi.org/10.1109/70.897798
Liang, Q. and Mendel, J.M. (2000) Interval Type-2 Fuzzy Logic Systems: Theory and Design. IEEE Transactions on Fuzzy Systems, 8, 535-550.
Wu, D. and Mendel, J.M. (2009) Enhanced Karnik-Mendel Algorithms. IEEE Transactions on Fuzzy Systems, 17, 923-934.
Karnik, N.N. and Mendel, J.M. (2001) Centroid of a Type-2 Fuzzy Set. Information Sciences, 132, 195-220.
Zirkohi, M.M., Fateh, M.M. and Shoorehdeli, M.A. (2013) Type-2 Fuzzy Control for a Flexible-Joint Robot using Voltage Control Strategy. International Journal of Automation and Computing, 10, 242-255. https://doi.org/10.1007/s11633-013-0717-x