Research Papers

Adaptive Model Estimation of Vibration Motion for a Nanopositioner With Moving Horizon Optimized Extended Kalman Filter

[+] Author and Article Information
Tomáš Polóni

Faculty of Mechanical Engineering,
Institute of Automation, Measurement and Applied Informatics,
Slovak University of Technology,
Bratislava 812 31, Slovakia
e-mail: tomas.poloni@stuba.sk

Arnfinn Aas Eielsen

Department of Engineering Cybernetics,
Norwegian University of Science and Technology,
Trondheim N-7491, Norway
e-mail: eielsen@itk.ntnu.no

Boris Rohal’-Ilkiv

Faculty of Mechanical Engineering,
Institute of Automation,
Measurement and Applied Informatics,
Slovak University of Technology,
Bratislava 812 31, Slovakia
e-mail: boris.rohal-ilkiv@stuba.sk

Tor Arne Johansen

Department of Engineering Cybernetics,
Norwegian University of Science and Technology,
Trondheim N-7491, Norway
e-mail: tor.arne.johansen@itk.ntnu.no

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received January 26, 2012; final manuscript received March 8, 2013; published online May 27, 2013. Assoc. Editor: Won-jong Kim.

J. Dyn. Sys., Meas., Control 135(4), 041019 (May 27, 2013) (14 pages) Paper No: DS-12-1036; doi: 10.1115/1.4024008 History: Received January 26, 2012; Revised March 08, 2013

Fast, reliable online estimation and model adaptation is the first step towards high-performance model-based nanopositioning control and monitoring systems. This paper considers the identification of parameters and the estimation of states of a nanopositioner with a variable payload based on the novel moving horizon optimized extended Kalman filter (MHEKF). The MHEKF is experimentally tested and verified with measured data from the capacitive displacement sensor. The payload, attached to the nanopositioner's sample platform, suddenly changes during the experiment triggering the transient motion of the vibration signal. The transient is observed through the load dependent parameters of a single-degree-of-freedom vibration model, such as spring, damping, and actuator gain constants. The platform, before and after the payload change, is driven by the excitation signal applied to the piezoelectric actuator. The information regarding displacement and velocity, together with the system parameters and a modeled force disturbance, is estimated through the algorithm involving the iterative sequential quadratic programming (SQP) optimization procedure defined on a moving horizon window. The MHEKF provided superior performance in comparison with the benchmark method, extended Kalman filter (EKF), in terms of faster convergence.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Croft, D., Shed, G., and Devasia, S., 2001, “Creep, Hysteresis, and Vibration Compensation for Piezoactuators: Atomic Force Microscopy Application,” ASME J. Dyn. Sys., Meas., Control, 123(1), pp. 35–43. [CrossRef]
Devasia, S., Eleftheriou, E., and Moheimani, S., 2007, “A Survey of Control Issues in Nanopositioning,” IEEE Trans. Control Syst. Technol., 15(5), pp. 802–823. [CrossRef]
Al Janaideh, M., Rakheja, S., and Su, C.-Y., 2011, “An Analytical Generalized Prandtl-Ishlinskii Model Inversion for Hysteresis Compensation in Micropositioning Control,” IEEE/ASME Trans. Mechatron., 16(4), pp. 734–744. [CrossRef]
Ronkanen, P., Kallio, P., Vilkko, M., and Koivo, H., 2011, “Displacement Control of Piezoelectric Actuators Using Current and Voltage,” IEEE/ASME Trans. Mechatron., 16(1), pp. 160–166. [CrossRef]
Peng, J., and Chen, X., 2011, “Modeling of Piezoelectric-Driven Stick-Slip Actuators,” IEEE/ASME Trans. Mechatron., 16(2), pp. 394–399. [CrossRef]
Gelb, A., Joseph, F., Kasper, J., Raymond, A., Nash, J., Price, C. F., Arthur, A., and Sutherland, J., 2001, Applied Optimal Estimation, MIT Press, Cambridge, MA.
Corigliano, A., and Mariani, S., 2004, “Parameter Identification in Explicit Structural Dynamics: Performance of the Extended Kalman Filter,” Comput. Methods Appl. Mech. Eng., 193, pp. 3807–3835. [CrossRef]
Ghosh, S. J., Roy, D., and Manohar, C., 2007, “New Forms of Extended Kalman Filter via Transversal Linearization and Applications to Structural System Identification,” Comput. Methods Appl. Mech. Eng., 196, pp. 5063–5083. [CrossRef]
Eielsen, A. A., Polóni, T., Johansen, T. A., and Gravdahl, J. T., 2011, “Experimental Comparison of Online Parameter Identification Schemes for a Nanopositioning Stage With Variable Mass,” Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics. [CrossRef]
Fleming, A., Wills, A., and Moheimani, S., 2008, “Sensor Fusion for Improved Control of Piezoelectric Tube Scanners,” IEEE Trans. Control Syst. Technol., 16(6), pp. 1265–1276. [CrossRef]
Gao, F., and Lu, Y., 2006, “A Kalman-Filter Based Time-Domain Analysis for Structural Damage Diagnosis With Noisy Signals,” J. Sound Vib., 297, pp. 916–930. [CrossRef]
Moraal, P. E., and Grizzle, J. W., 1995, “Observer Design for Nonlinear Systems With Discrete-Time Measurement,” IEEE Trans. Autom. Control, 40(3), pp. 395–404. [CrossRef]
Alessandri, A., Baglietto, M., and Battistelli, G., 2008, “Moving-Horizon State Estimation for Nonlinear Discrete-Time Systems: New Stability Results and Approximation Schemes,” Automatica, 44(7), pp. 1753–1765. [CrossRef]
Ching, J., Beck, J. L., and Porter, K. A., 2006, “Bayesian State and Parameter Estimation of Uncertain Dynamical Systems,” Probab. Eng. Mech., 21, pp. 81–96. [CrossRef]
Namdeo, V., and Manohar, C., 2007, “Nonlinear Structural Dynamical System Identification Using Adaptive Particle Filters,” J. Sound Vib., 306, pp. 524–563. [CrossRef]
Sajeeb, R., Manohar, C., and Roy, D., 2009, “A Conditionally Linearized Monte Carlo Filter in Non-Linear Structural Dynamics,” Int. J. Non-Linear Mech., 44, pp. 776–790. [CrossRef]
Haseltine, E. L., and Rawlings, J. B., 2005, “Critical Evaluation of Extended Kalman Filtering and Moving-Horizon Estimation,” Ind. Eng. Chem. Res., 44(8), pp. 2451–2460. [CrossRef]
Polóni, T., Rohal’-Ilkiv, B., and Johansen, T. A., 2010, “Damped One-Mode Vibration Model State and Parameter Estimation via Pre-Filtered Moving Horizon Observer,” Proceedings of the IFAC Symposium on Mechatronic Systems. [CrossRef]
Rao, C. V., Rawlings, J. B., and Mayne, D. Q., 2003, “Constrained State Estimation for Nonlinear Discrete-Time Systems: Stability and Moving Horizon Approximations,” IEEE Trans. Autom. Control, 48(2), pp. 246–258. [CrossRef]
López-Negrete, R., Patwardhan, S. C., and Biegler, L. T., 2009, “Approximation of Arrival Cost in Moving Horizon Estimation Using a Constrained Particle Filter,” Computer Aided Chemical Engineering, Proceedings of the 10th International Symposium on Process Systems Engineering: Part A, R. M. de Brito Alves, C. A. Oller do Nascimento, and E. C. Biscaia, eds., Elsevier, New York, Vol. 27, pp. 1299–1304. [CrossRef]
Qu, C. C., and Hahn, J., 2009, “Computation of Arrival Cost for Moving Horizon Estimation via Unscented Kalman Filtering,” J. Process Control, 19(2), pp. 358–363. [CrossRef]
Ungarala, S., 2009, “Computing Arrival Cost Parameters in Moving Horizon Estimation Using Sampling Based Filters,” J. Process Control, 19(9), pp. 1576–1588. [CrossRef]
Nocedal, J., and Wright, S. J., 2006, Numerical Optimization, 2nd ed., Springer, New York.
Ljungquist, D., and Balchen, J. G., 1994, “Recursive Prediction Error Methods for Online Estimation in Nonlinear State-Space Models,” Model. Identif. Control, 15(2), pp. 109–121. [CrossRef]
Kwon, B. K., Han, S., Lee, H., and Kwon, W. H., 2007, “A Receding Horizon Kalman Filter With the Estimated Initial State on the Horizon,” Proceedings of the International Conference on Control, Automation and Systems (ICCAS 2007), pp. 1686–1690. [CrossRef]
do Val, J., and Costa, E., 2000, “Stability of Receding Horizon Kalman Filter in State Estimation of Linear Time-Varying Systems,” Proceedings of the 39th IEEE Conference on Decision and Control, Vol. 4, pp. 3801–3806. [CrossRef]
Tikhonov, A. N., and Arsenin, V. Y., 1977, Solutions of Ill-Posed Problems, Wiley, New York.
Sui, D., and Johansen, T. A., 2011, “Moving Horizon Observer With Regularisation for Detectable Systems Without Persistence of Excitation,” Int. J. Control, 84(6), pp. 1041–1054. [CrossRef]
Ascher, U. M., and Petzold, L. R., 1998, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, SIAM, Philadelphia, PA.
Butcher, J., 2003, Numerical Methods for Ordinary Differential Equations, John Wiley & Sons, New York.
Leang, K. K., 2011, “EasyLab Multi-Axis High-Performance Nanopositioning Stages,” http://www.kam.k.leang.com/academics/
Ljung, L., 1999, System Identification: Theory for the User, 2nd ed., Prentice Hall, Englewood Cliffs, NJ.
Houska, B., Ferreau, H. J., and Diehl, M., 2011, “An Auto-Generated Real-Time Iteration Algorithm for Nonlinear MPC in the Microsecond Range,” Automatica, 47(10), pp. 2279–2285. [CrossRef]
Knagge, G., Wills, A., Mills, A., and Ninness, B., 2009, “ASIC and FPGA Implementation Strategies for Model Predictive Control,” Proceedings of the European Control Conference (ECC).
Mattingley, J., Wang, Y., and Boyd, S., 2011, “Receding Horizon Control—Automatic Generation of High Speed Solvers,” IEEE Control Syst., 31(3), pp. 52–65. [CrossRef]


Grahic Jump Location
Fig. 1

Time sequences of state, input, and output variables in a moving horizon window of size N + 1

Grahic Jump Location
Fig. 2

Algorithmic scheme of MHEKF where z-1 is a one sample delay operator

Grahic Jump Location
Fig. 3

Nanopositioning stage with highly resonant vibration dynamics. The right side of this figure captures the sudden manual removal of the payload applying the unknown force disturbance fu.

Grahic Jump Location
Fig. 4

Dynamic model of nanopositioning stage

Grahic Jump Location
Fig. 5

Picture of ADE 6810 capacitive gauge and SIM 965 programmable filters

Grahic Jump Location
Fig. 6

Chain of used instrumentation

Grahic Jump Location
Fig. 7

Measured frequency response for the y-axis of the nanopositioning stage and the corresponding response using the model Eq. (24) (with fu=0), with and without the payload attached to the sample platform

Grahic Jump Location
Fig. 8

Conditioning of signals before entering the EKF and MHEKF

Grahic Jump Location
Fig. 13

Zoom of displacement and velocity errors of the EKF and MHEKF(b)

Grahic Jump Location
Fig. 14

Estimated parameters and disturbance of the EKF and MHEKF(b)

Grahic Jump Location
Fig. 15

Displacement and velocity errors of the EKF and MHEKF(c)

Grahic Jump Location
Fig. 16

Zoom of displacement and velocity errors of the EKF and MHEKF(c)

Grahic Jump Location
Fig. 17

Estimated parameters and disturbance of the EKF and MHEKF(c)

Grahic Jump Location
Fig. 9

Displacement and velocity errors of the EKF and MHEKF(a)

Grahic Jump Location
Fig. 10

Zoom of displacement and velocity errors of the EKF and MHEKF(a)

Grahic Jump Location
Fig. 11

Estimated parameters and disturbance of the EKF and MHEKF(a)

Grahic Jump Location
Fig. 12

Displacement and velocity errors of the EKF and MHEKF(b)



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In