ICA  Vol.3 No.3 , August 2012
Robust H∞ Controller for High Precision Positioning System, Design, Analysis, and Implementation
Abstract: In this paper, a systematic robust control design and analysis for a single axis precise positioner is presented. The effects of uncertainties on closed-loop stability and performance are considered in the H∞ robust controllers design. v-gap metric is utilized to validate the intelligently estimated uncertainty. The robust controllers are formulated within the frame- work of the standard H∞ mixed sensitivity optimization problem. Furthermore, a specially designed integral-H∞ and two-degree-of-freedom 2 DOF H∞ controllers are developed to provide improved robust performance and resolution properties. It is shown that the proposed design schemes are very effective for robust control and precise tracking performance of the servo positioning system.
Cite this paper: nullS. Raafat, R. Akmeliawati and I. Abdulljabaar, "Robust H Controller for High Precision Positioning System, Design, Analysis, and Implementation," Intelligent Control and Automation, Vol. 3 No. 3, 2012, pp. 262-273. doi: 10.4236/ica.2012.33030.

[1]   S. Endo, H. Kobayashi, C. J. Kempf, S. Kobayashi, M. Tomizuka and Y. Hori, “Robust Digital Tracking Controller Design for High-Speed Positioning System,” Control Engineering Practice, Vol. 4, No. 4, 1996, pp. 527-536. doi:10.1016/0967-0661(96)00036-6

[2]   H.-S. Park, P. H. Chang and D. Y. Lee, “Concurrent Design of Continuous Zero Phase Error Tracking Controller and Sinusoidal Trajectory for Improved Tracking Control,” American Society of Mechanical Engineers, Journal of Dynamic Systems, Measurement, and Control, Vol. 123, 2001, pp. 127-129. doi:10.1115/1.1343464

[3]   Z. Z. Liu, F. L. L. Luo and M. H. Rashid, “QFT-Based Robust and Precision Motion Control System for a High Speed Direct-Drive XY Table Positioning Mechanism,” Industry Application Conference, 2003, 38th IAS Annual Meeting, 12-16 October 2003, Vol. 1, pp. 293-300.

[4]   L. Xu and B. Yao, “Output Feedback Adaptive Robust Precision Motion Control of Linear Motors,” Automatica, Vol. 37, No. 7, 2001, pp. 1029-1039. doi:10.1016/S0005-1098(01)00052-8

[5]   Y. Honga and B. Yao, “A Globally Stable Saturated Desired Compensation Adaptive Robust Control for Linear Motor Systems with Comparative Experiments,” Automatica, Vol. 43, No. 10, 2007, pp. 1840-1848. doi:10.1016/j.automatica.2007.03.021

[6]   W. F. Xie, “Sliding-Mode-Observer-Based Adaptive Control for Servo Actuator with Friction,” IEEE Transactions on Industrial Electronics, Vol. 54, No. 3, 2007, pp. 1517-1527. doi:10.1109/TIE.2007.894718

[7]   J. Dong, S. M. Salapaka and P. M. Ferreira, “Robust MIMO Control of a Parallel Kinematics Nano-Positioner for High Resolution High Bandwidth Tracking and Repetitive Tasks,” 46th IEEE Conference on Decision and Control, New Orleans, 12-14 December 2007, pp. 4495-4500.

[8]   K. B. Choi, S. H. Kim and B. W. Choi, “Moving-Magnet Type Precision Miniature Platform for Fine Positioning and Compliant Motion,” Mechatronics, Vol. 11, No. 7, 2001, pp. 921-937. doi:10.1016/S0957-4158(00)00055-6

[9]   H. J. Shin and H. J. Pahk, “Development of the Precision Planer Motor Stage Using a New Magnet Array and Robust Control with Parametric Uncertainty Model,” The International Journal of Advanced Manufacturing Technology, Vol. 33, No. 7-8, 2007, pp. 643-651. doi:10.1007/s00170-006-0514-6

[10]   Z. Z. Liu, F. L. Luo and M. A. Rahman, “Robust and Precision Motion Control System of Linear-Motor Direct Drive for High-Speed X-Y Table Positioning Mechanism,” IEEE Transactions on Industrial Electronics, Vol. 52, No. 5, 2005, pp. 1357-1363. doi:10.1109/TIE.2005.855661

[11]   E. Rijanto, “Quasi Mixed Controller for High Precision Positioning Device,” IEEE Proceedings of the 6th International Workshop on Advanced Motion Control, Nagoya, 30 March-1 April, 2000, pp. 335-338.

[12]   A. Sebastian and S. M. Salapaka, “Design Methodologies for Robust Nano-Positioning,” IEEE Transactions on Control Systems Technology, Vol. 13, No. 6, 2005, pp. 868-876. doi:10.1109/TCST.2005.854336

[13]   C. Lee and S. M. Salapaka, “Fast Robust Nanopositioning—A Linear-Matrix Inequalities-Based Optimal Control Approach,” IEEE/ASME Transactions on Mechatronics, Vol. 14, No. 4, 2009, pp. 414-422.

[14]   H. Choi, G. D. Buckner and N. S. Gibson, “Neural Robust Control of High-Speed Flexible Rotor Supported on Active Magnetic Bearings,” American Control Conference, Minneapolis, 14-16 June 2006.

[15]   G. R. Yu and C. W. Tao, “Intelligent H∞ Control of Nano-Positioning Systems,” IEEE International Conference on Systems, Man, and Cybernetics, Taiwan, 8-11 October 2006, pp. 1729-1733.

[16]   S. M. Raafat, R. Akmeliawati and W. Martono, “Intelligent Robust Control Design of a Precise Positioning System,” International Journal of Control, Automation and Systems, Vol. 8, No. 5, 2010, pp. 1123-1132.

[17]   R. Akmeliawati, S. M. Raafat and W. Martono, “Improved Intelligent Identification of Uncertainty Bounds; Design, Model Validation and Stability Analysis,” International Journal of Modeling, Identification, and Control, Vol. 15, No. 3, 2012, pp. 173-184. doi:10.1504/IJMIC.2012.045690

[18]   H.-P. Lee and D. K. Shmidt, “Robust Two-Degree of Freedom H∞ Control of a Seeker Scan Loop System,” IEEE Proceedings Control Theory and Applications, Vol. 149, No. 2, 2002, p. 149. doi:10.1049/ip-cta:20020097

[19]   M. H. Smith, A. M. Annaswamy and H. Slocum, “Adaptive Control Strategies for a Precision Machine Tool Axis,” Precision Engineering, Vol. 17, No. 3, 1995, pp. 192-206. doi:10.1016/0141-6359(94)00019-V

[20]   S. Skogestad and I. Postlethwait, “Multivariable Feedback Control: Analysis and Design,” John Wiley and Sons, Hoboken, 1997.

[21]   K. Zhou and J. C. Doyle, “Essentials of Robust Control,” Prentice-Hall, Inc., Upper Saddle River, 1998.

[22]   W. Reinelt, A. Garulli and L. Ljung, “Comparing Different Approaches to Model Error Modelling in Robust Identification,” Automatica, Vol. 38, No. 5, 2002, pp. 787-803. doi:10.1016/S0005-1098(01)00269-2

[23]   J. S. R. Jang, “ANFIS: Adaptive-Network-Based Fuzzy Inference System,” IEEE Transactions on Systems, Man and Cybernetics, Vol. 23, No. 3, 1993, pp. 665-685. doi:10.1109/21.256541

[24]   G. Vinnicombe, “Uncertainty and Feedback: H∞ loopshaping and the v-gap metric,” University of Cambridge, England, 2000.

[25]   G. Balas, R. Chiang, A. Packard and Safonov, “Robust Control ToolboxTM 3 User’s Guide,” The MathWorks Inc., Natick, 2008.

[26]   S. M. Raafat and R. Akmeliawati, “Bounded Constrained Optimization of Performance Weighting Function for Precise Robust Positioning Control System,” International Conference on Mechatronics, Kuala Lump, 17-19 May 2011, pp. 1-7.

[27]   G. F. Franklin, J. D. Powelland and A. Emami-Naeini, “Feedback Control of Dynamic Systems,” Prentice Hall, Inc., Upper Saddle River, 2002.

[28]   D.-W. Gu, P. H. Petkov and M. M. Konstantinov, “Robust Control Design with MATLAB,” Springer-Verlage, London, 2005.

[29]   M. Arzifian, “Design an H∞ Controller for Force Control in Magnetic Levitation Systems,” Master’s Thesis, University of Technology, Baghdad, 2006.