Abstract
This paper proposes three fuzzy adaptive controller design methods based on the backstepping design technique. In the first method, the original parameters in a fuzzy logic system are updated real-time, on the other hand, in the second and third methods, the square of the norm of the original parameters is used as an unknown parameter. The third method utilizes the fact that the norm of the fuzzy logic system is less than or equal to one and the resulting controller is independent of the fuzzy logic system. The three methods were tested on the two-degree-of-freedom robot which was custom-made. The test results show that all three methods work and the first method works better than the other two methods with and without loads because it involves no simplification during the design process even though it requires longer computation time.
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References
Ghorbel, F., Chetelat, O., Gunawardana, R., Longchamp, R.: Modeling and Set Point Control of Closed-Chain Mechanisms: Theory and Experiment. IEEE Trans. on Control Systems Technology, 801–815 (2000)
Paccot, F., Andreff, N., Martinet, P., Khalil, W.: Vision-Based Computed Torque Control for Parallel Robots. In: IEEE Annual Conference on Industrial Electronics, pp. 3851–3856 (2006)
Fasse, E.D., Gosselin, C.M.: Spatio-Geometric Impedance Control of Gough–Stewart Platforms. IEEE Trans. on Robotics and Automation 15, 281–288 (1999)
Lin, H.M., McInroy, J.E.: Adaptive Sinusoidal Disturbance Cancellation for Precise Pointing of Stewart Platforms. IEEE Trans. on Control System Technology 11, 267–272 (2003)
Wang, L., Liu, X.P., Liu, K.F.: Adaptive Tracking Control of Parallel Robot: Backstepping and PD Schemes. Int. J. of Control Theory and Applications 1 (2009)
Begon, P., Pierrot, F., Dauchez, P.: Fuzzy Sliding Mode Control of a Fast Parallel Robot. In: IEEE International Conference on Robotics and Automation, pp. 1178–1183 (1995)
Gao, G.Q., Yan, Q., Wu, Y.Z.: The Control Method of Adaptive Backstepping and Neural Network in the Application of a Parallel Robot. In: 6th International Conference on Natural Computation, pp. 1397–1400
Kanellakopoulos, I., Kokotovic, P., Morse, A.S.: Systematic Design of Adaptive Controllers for Feedback Linearizable Systems. IEEE Trans. on Automatic Control 36, 1241–1253 (1991)
Hsu, F.Y., Fu, L.C.: A Novel Adaptive Fuzzy Variable Structure Control for a Class of Nonlinear Uncertain Systems via Backstepping. In: 37th IEEE on Decision and Control, pp. 2228–2233 (1998)
Wang, W.Y., Chan, M.L., Lee, T.T., Liu, C.H.: Adaptive Fuzzy Control for Strict-Feedback Canonical Nonlinear Systems with H Tracking Performance. IEEE Trans. on Systems, Man, and Cybernetics - Par B: Cybernetics 30, 878–885 (2000)
Yang, Y.S., Feng, G., Ren, J.S.: A Combined Backstepping and Small-Gain Approach to Robust Adaptive Fuzzy Control for Strict-Feedback Nonlinear Systems. IEEE Trans. on Systems, Man, and Cybernetics - Part A: Systems and Humans 34 (2004)
Chen, B., Liu, X.P., Tong, S.C.: Adaptive Fuzzy Output Tracking Control of MIMO Nonlinear Uncertain Systems. IEEE Trans. on Fuzzy Systems 15, 287–300 (2007)
Chen, B., Liu, X.P., Liu, K.L., Lin, C.: Fuzzy-Approximation-Based Adaptive Control of Strict-Feedback Nonlinear Systems With Time Delays. IEEE Trans. on Fuzzy Systems 18, 883–892 (2010)
Liu, Y.J., Wang, W., Tong, S.C., Liu, Y.-S.: Robust Adaptive Tracking Control for Nonlinear Systems Based on Bounds of Fuzzy Approximation Parameters. IEEE Trans. on Systems, Man, and Cybernetics - Part A: Systems and Humans 40, 170–184 (2010)
Wang, L.X., Mendel, J.M.: Fuzzy Basis Functions, Universal Approximation and Orthogonal, Least Squares Learning. IEEE Trans. on Neural Networks 3, 807–814 (1992)
Wang, L.X.: Stable Adaptive Fuzzy Control of Nonlinear Systems. IEEE Trans. on Fuzzy Systems 1, 146–155 (1993)
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Liu, X., Liadis, A. (2012). Fuzzy Adaptive Backstepping Control of a Two Degree of Freedom Parallel Robot. In: Su, CY., Rakheja, S., Liu, H. (eds) Intelligent Robotics and Applications. ICIRA 2012. Lecture Notes in Computer Science(), vol 7506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33509-9_60
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DOI: https://doi.org/10.1007/978-3-642-33509-9_60
Publisher Name: Springer, Berlin, Heidelberg
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