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.

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Fig. 1

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

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Fig. 2

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

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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.

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Fig. 4

Dynamic model of nanopositioning stage

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Fig. 5

Picture of ADE 6810 capacitive gauge and SIM 965 programmable filters

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Fig. 6

Chain of used instrumentation

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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

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Fig. 8

Conditioning of signals before entering the EKF and MHEKF

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Fig. 9

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

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Fig. 10

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

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Fig. 11

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

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Fig. 12

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

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Fig. 13

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

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Fig. 14

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

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Fig. 15

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

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Fig. 16

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

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Fig. 17

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




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