Time-Domain Fixed-Structure Closed-Loop Model Identification of an Unstable Multivariable Maglev Nanopositioning System

다국어 초록 (Multilingual Abstract)

This paper presents improved empirical representations of a general class of open-loop unstable systems using closed-loop system identification. A multi-axis magnetic-levitation (maglev) nanopositioning system with an extended translational travel range is used as a test model to verify the closed-loop system-identification method presented in this paper. A closed-loop identification technique employing a known controller structure is used for model identification and validation. Direct and coupling transfer functions (TFs) are then derived from the experimental input-output time sequences and the knowledge of controller dynamics. A persistently excited signal with a bandwidth in the frequency range of interest is used as a reference input. An order-reduction algo-rithm is developed to obtain TFs with predefined orders, which gives the closest match in the fre-quency range of interest without missing any significant plant dynamics. The entire analysis is per-formed in the discrete-time domain in order to avoid any errors due to continuous-to-discrete-time conversion and vice versa. Continuous-time TFs are used only for order-reduction and performance analysis of the identified TFs. Experimental results are presented in the time as well as frequency domains to verify the accuracy of the identified plant TFs. These results also demonstrate the effectiveness of the developed closed-loop identification method in meeting all of the three core objectives—(i) reduction in cross-axial coupling from 9.213 μm to 0.911 μm in translation and from 22.03 μrad to 1.353 μrad in rotation, (ii) large range motion capability with a travel range of ±2.9 mm, and (iii) improved robust stability.

참고문헌 (Reference)

1 H. Shakir, "System identification and optimal control of a 6-DOF magnetic levitation stage with nanopositioning capabilities" 2004

2 R. Pintelon, "System Identification:A Frequency Domain Approach" IEEE Press 2001

3 L. Ljung, "System Identification: Theory for the User, 2nd ed" Prentice- Hall 1999

4 E. Villota, "Proc. American Control Conference" 1365-1370, 2005

5 X. Bombois, "Openloop versus closed-loop identification of Box-Jenkins models: a new variance analysis" 3117-3122, 2005

6 S. Earnshaw, "On the nature of the molecular forces which regulate the constitution of the luminiterous ether" 7 : 97-112, 1842

7 F. R. Hansen, "On a fractional representation approach to closed-loop experimental design" 1319-1320, 1988

8 S. Verma, "Novel electromagnetic actuation scheme for multiaxis nanopositioning" 42 (42): 2052-2062, 2006

9 K. Nakashima, "Multivariable control of a magnetic levitation system using closed loop identification and H∞ control theory" 3668-3673, 1996

10 S. K. Kuo, "Large travel ultra precision x-y-q motion control of a magneticsuspension stage" 8 (8): 334-341, 2003

11 P. M. J. Van den Hof, "Identification and control—Closed-loop issues" 31 (31): 1751-1770, 1995

12 C. E. Lin, "Force model identification for magnetic suspension systems via magnetic field measurement" 42 (42): 767-771, 1993

13 S. Dejima, "Dynamic modeling, controller design and experimental validation of a planar motion stage for precision positioning" 29 (29): 263-271, 2005

14 L. Sun, "Direct closedloop identification of magnetic suspension system" 1 : 749-754, 1999

15 U. Forssell, "Closed-loop identification revisited" 35 (35): 1215-1241, 1999

16 R. Pintelon, "Box-Jenkins identification revisited Part I: Theory" 42 (42): 63-75, 2006