Tracking of High-speed, Non-smooth and Microscale-amplitude Wave Trajectories

Jiradech Kongthon

Abstract

In this article, an inversion-based control approach is proposed and presented for tracking desired trajectories with high-speed (100Hz), non-smooth (triangle and sawtooth waves), and microscale-amplitude (10 micron) wave forms. The interesting challenge is that the tracking involves the trajectories that possess a high frequency, a microscale amplitude, sharp turnarounds at the corners. Two different types of wave trajectories, which are triangle and sawtooth waves, are investigated. The model, or the transfer function of a piezoactuator is obtained experimentally from the frequency response by using a dynamic signal analyzer. Under the inversion-based control scheme and the model obtained, the tracking is simulated in MATLAB. The main contributions of this work are to show that (1) the model and the controller achieve a good tracking performance measured by the root mean square error (RMSE) and the maximum error (Emax), (2) the maximum error occurs at the sharp corner of the trajectories, (3) tracking the sawtooth wave yields larger RMSE and Emax values,compared to tracking the triangle wave, and (4) in terms of robustness to modeling error or unmodeled dynamics, Emax is still less than 10% of the peak to peak amplitude of 20 micron if the increases in the natural frequency and the damping ratio are less than 5% for the triangle trajectory and Emax is still less than 10% of the peak to peak amplitude of 20 micron if the increases in the natural frequency and the damping ratio are less than 3.2 % for the sawtooth trajectory.

References

  1. Beschi, M., Dormido, S., Sanchez, J., Visioli, A., and Yebra, L. J.,(2014) 'Event-Based PI plus Feedforward Control Strategies for a Distributed Solar Collector field', IEEE Transactions on Control Systems Technology, Vol. 23, No. 4, July 2014,pp. 1615-1622.
  2. Boekfah, A., and Devasia, S.,(2016) 'Output-Boundary Regulation Using Event-Based Feedforward for Nonminimum-Phase Systems', IEEE Transactions on Control Systems Technology, Vol.24,No.1, January 2016, pp265-275.
  3. Devasia, S., (2002). 'Should Model-Based Inverse Inputs Be Used as Feedforward Under Plant Uncertainty?78, IEEE Transactions on Automatic Control, Vol.47, No.11, November 2002,pp1865-1871.
  4. Dunne, F., Pao, L. Y., Wright, A. D., Jonkman, B., and Kelley, N.,(2011) 'Adding Feedforward Blade Pitch Control to Standard Feedback Controllers for Load Mitigation in Wind Turbines', Mechatronics, Vol. 21, No. 4, June 2011, pp. 682-690.
  5. Hirschorn, R. M., (1979). 'Invertibility of Multivariable Nonlinear Control Systems', IEEE Transactions on Automatic Control, Vol.AC-24, No.6, December 1979,pp855-865.
  6. Kongthon, J., Chung, J.-H., Riley, J., and Devasia, S.,(2011)'Dynamics of Cilia-Based Microfluidic Devices', ASME Journal of Dynamic Systems, Measurement and Control,Vol. 133, September 2011,pp.051012-1-051012-11.
  7. Kongthon, J., and Devasia, S., (2013) 'Iterative Control of Piezoactuator for Evaluating Biomimetic, Cilia Based Micromixing', IEEE/ASME Transactions on Mechatronics, Vol.18, No. 3, June 2013, pp 944-953.
  8. Kongthon, J., McKay, B.,Iamratanakul, D., Oh, K., Chung, J.-H., Riley, J., and Devasia, S.,(2010) 'Added-Mass Effect in Modeling of Cilia-Based Devices for Microfluidic Systems', ASME Journal of Vibration and Acoustics, Vol.132, No.2, April 2010, pp.024501-1-024501-7.
  9. Martin, P., Devasia, S., and Paden, B., (1996). 'A Different Look at Output Tracking: Control of a VTOL Aircraft', Automatica, Vol. 32, No. 1,pp. 01- 107.
  10. Meckl, P. H.,and Kinceler, R.,(1994) 'Robust Motion Control of Flexible Systems Using Feedforward Forcing Functions', IEEE Transactions on Control Systems Technology, Vol. 2, No. 3, September 1994,pp. 245-254.
  11. Moallem, M., Kermani, M. R., Patel, R. V., and Ostojic, M.,(2004) 'Flexure Control of a Positioning System Using Piezoelectric Transducers', IEEE Transactions on Control Systems Technology., Vol. 12, No. 5,September 2004,pp. 757-762.
  12. Peng, H., and Tomizuka, M., (1993) 'Preview Control for Vehicle Lateral Guidance in Highway Automation', ASME Journal of Dynamic Systems, Measurement and Control, Vol. 115, No. 4, December 1993, pp.679- 686.
  13. Piazzi, A., and Visioli, A.,(2001) 'Optimal InversionBased Control for the Setpoint Regulation of Nonminimum-Phase Uncertain Scalar Systems', IEEE Transactions on Automatic Control,Vol. 46, October 2001, No. 10, pp. 1654-1659.
  14. Silverman, L. M.,(1969) 'Inversion of Multivariable Linear Systems', IEEE Transactions on Automatic Control, Vol.AC-14,No.3,June 1969,pp270-276.
  15. Yang, X., Garratt, M., and Pota, H., (2011) 'Flight Validation of a Feedforward Gust-Attenuation Controller for an Autonomous Helicopter', Robotics and Autonomous Systems, Vol. 59, No. 12, December 2011, pp. 1070-1079.
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Paper Citation


in Harvard Style

Kongthon J. (2016). Tracking of High-speed, Non-smooth and Microscale-amplitude Wave Trajectories . In Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-758-198-4, pages 499-507. DOI: 10.5220/0005979704990507


in Bibtex Style

@conference{icinco16,
author={Jiradech Kongthon},
title={Tracking of High-speed, Non-smooth and Microscale-amplitude Wave Trajectories},
booktitle={Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2016},
pages={499-507},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005979704990507},
isbn={978-989-758-198-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - Tracking of High-speed, Non-smooth and Microscale-amplitude Wave Trajectories
SN - 978-989-758-198-4
AU - Kongthon J.
PY - 2016
SP - 499
EP - 507
DO - 10.5220/0005979704990507