Advertisement

Journal of Mechanical Science and Technology

, Volume 27, Issue 3, pp 895–907 | Cite as

Feedforward coefficient identification and nonlinear composite feedback control with applications to 3-DOF planar motor

  • Xin LiEmail author
  • Kai-ming Yang
  • Yu Zhu
  • Dong-dong Yu
Article

Abstract

Due to modeling errors, accurate feedforward coefficient of the controller cannot be obtained with the standard method on the basis of the nominal model. Meanwhile, the system is uncertain in practice. Consequently, the MIMO (multi-input multi-output) system of the planar motor cannot be completely decoupled by feedback linearization, and the convergence of the tracking errors is no longer guaranteed. In order to improve the robustness and the tracking ability of the planar motor, a feedforward coefficient identification method and nonlinear composite feedback controller are proposed, thus guaranteeing stability by Lyapunov theory, wherein the feedforward coefficient can be obtained by the PD control experiment. The results of two different trajectory tracking experiments show that it is more accurate than the standard method. Moreover, this coefficient is suitable for different trajectories, so it avoids the drawback of ILC (iterative learning control) method, by which the feedforward term obtained cannot be reused if the length of the trajectory changes. The nonlinear composite feedback controller consists of u 1 and u 2 terms. u 1 is designed to compensate for modeling errors, therefore the robustness is improved and the coupling effects among multi-DOF (degrees of freedom) are reduced. In balancing the trade-off between disturbance rejection and noise sensitivity, an amplitude-based variable-gain function is applied in u 2. The trajectory tracking experimental results show that the overall controller is an attractive approach for the uncertain multi-DOF systems.

Keywords

Planar motor Modeling errors Feedforward coefficient identification Nonlinear composite feedback controller Trajectory tracking 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    W. J. Kim and D. L. Trumper, High-precision magnetic levitation stage for photolithography. Precis Eng, 22(2) (1998) 66–77.CrossRefGoogle Scholar
  2. [2]
    K. S. Jung and Y. S. Baek, Precision stage using a noncontact planar actuator based on magnetic suspension technology. Mechatronics, 13(8–9) (2003) 981–999.CrossRefGoogle Scholar
  3. [3]
    H. S. Cho, Analysis and design of synchronous permanentmagnet planar motors. IEEE Transactions on Energy Conversion, 17(4) (2002) 492–499.CrossRefGoogle Scholar
  4. [4]
    W. Gao, S. Dejima, H. Yanai, K. Katakura, S. Kiyono and Y. Tomita, A surface motor-driven planar motion stage integrated with an XYθz surface encode for precision positioning. Precis Eng, 28(3) (2003) 329–337.CrossRefGoogle Scholar
  5. [5]
    Hu Tiejun, Extended range six DOF high-precision positioner for wafer processing. IEEE Transactions on Mechatronics, 11(6) (2006) 682–689.CrossRefGoogle Scholar
  6. [6]
    J. Boeij, Modeling ironless permanent-magnet planar actuator structures, IEEE Transactions on Magnetics, 42(8) (2006) 2009–2016.CrossRefGoogle Scholar
  7. [7]
    J. W. Jansen, Magnetically levitated planar actuator with moving magnets, IEEE Transactions on Industry Applications, 44(4) (2008) 1108–1115.CrossRefGoogle Scholar
  8. [8]
    M. M. Cornelis, Magnetically levitated planar actuator with moving magnets: Dynamics, commutation and control design, Einhoven: Technische Universiteit Einhoven (2008).Google Scholar
  9. [9]
    J. W. Jansen, Magnetically levitated planar actuator with moving magnets: Electromechanical analysis and design, Einhoven: Technische Universiteit Einhoven (2007).Google Scholar
  10. [10]
    J. W. Jansen, Modeling of magnetically levitated planar actuators with moving magnets, IEEE Transactions on Magnets, 43(1) (2007) 15–18.CrossRefGoogle Scholar
  11. [11]
    A. Tayebi, Adaptive iterative learning control for robot manipulators. Automatica, 40 (2004) 1195–1203.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    H.-S. Ahn, Kevin L. Moore and Yang Quan Chen, Stability analysis of discrete-time iterative learning control systems with interval uncertainty. Automatica, 43(5) (2007) 892–902.MathSciNetzbMATHCrossRefGoogle Scholar
  13. [13]
    Jay H. Lee and Kwang S. Lee, Iterative learning control applied to batch processes: An overview, 15(10) (2007) 1306–1318.Google Scholar
  14. [14]
    H. Wang and Y. Xie, Adaptive inverse dynamics control of robots with uncertain kinematics and dynamics. Automatica, 45(9) (2009) 2114–2119.MathSciNetzbMATHCrossRefGoogle Scholar
  15. [15]
    M. Mistry, J. Buchli and S. Schaal, Inverse dynamics control of floating base systems using orthogonal decomposition. 2010 IEEE International Conference on Robotics and Automation (2010) 3406–3412.CrossRefGoogle Scholar
  16. [16]
    J. K. Tar, J. F. Bito and I. J. Ruda, An SVD based modification of the adaptive inverse dynamics controller. Applied Computational Intelligence and Informatics (2009) 193–198.Google Scholar
  17. [17]
    J. H. Park, D. H. Kim and Y. J. Kim, Anti-lock brake system control for buses based on fuzzy logic and a slidingmode observer, Journal of Mechanical Science and Technology, 15(10) (2001) 1398–1407.Google Scholar
  18. [18]
    J. Freudenberg, J. Middleton and Stefanopoulou, A survey of inherent design limitations, Proc. American Control Conference, Chicago (2000) 2987–3001.Google Scholar
  19. [19]
    J. Freudenberg, C. V. Hollot, R. H. Middleton and V. Toochinda, Fundamental design limitations of the general control configuration, IEEE Transactions on Automatic Control, 48(8) (2003) 1355–1370.MathSciNetCrossRefGoogle Scholar
  20. [20]
    M. Arcak, M. Larsen and P. Kokotovic, Boundedness without absolute stability in systems with stiffening nonlinearities, European Journal of Control, 8(3) (2003) 243–250.CrossRefGoogle Scholar
  21. [21]
    M. Iwasaki, K. Sakai and N. Matsui, High-speed and highprecision table position system by using mode switching control, Industrial Electronics Society, Proceedings of the 24th Annual Conference of the IEEE, 3 (1998) 1727–1732.Google Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.State Key Laboratory of Tribology, Department of Precision Instruments and MechanologyTsinghua UniversityBeijingChina

Personalised recommendations