Abstract
This paper presents a novel control strategy for the efficient tracking of spiral patterns. Such patterns arise in different areas, as for example the Atomic Force Microscopy, where fast and smooth reference signals are required. In order to successfully track the above mentioned references, which are composed of amplitude and frequency-varying sinusoidal signals, the present work proposes a robust control strategy where a Resonant Controller is applied in a time-varying structure. The time varying nature of the controller is accommodated in a polytopic representation and the stabilizing state feedback gain is designed from an optimization problem subject to constraints in the form of Linear Matrix Inequalities. This synthesis is evaluated through a set of simulations using a numerical model of an Atomic Force Microscope nanopositioner and a new suitable scanning reference pattern. Numerical results demonstrate that the proposed controller achieves an improved performance when compared to traditional controllers available in the area.
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References
Jin, X.: Non-repetitive trajectory tracking for joint position constrained robot manipulators using iterative learning control. In: 2016 IEEE 55th Conference on Decision and Control (CDC), pp. 5490–5495, December 2016
Bazaei, A., Maroufi, M., Fowler, A.G., Moheimani, S.O.R.: Internal model control for spiral trajectory tracking with MEMS AFM scanners. IEEE Trans. Control Syst. Technol. 24(5), 1717–1728 (2016)
Ramos, G.A., Soto-Perez, R.A., Cifuentes, J.A.: A varying frequency LPV-based control strategy for three-phase inverters. IEEE Trans. Ind. Electron. 64(9), 7599–7608 (2017)
Mahmood, I.A., Moheimani, S.O.R., Bhikkaji, B.: A new scanning method for fast atomic force microscopy. IEEE Trans. Nanotechnol. 10(2), 203–216 (2011)
Meyer, E., Hug, H.J., Bennewitz, R.: Scanning Probe Microscopy: The Lab on a Tip. Advanced Texts in Physics. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-662-09801-1
Tuma, T., Sebastian, A., Lygeros, J., Pantazi, A.: The four pillars of nanopositioning for scanning probe microscopy: the position sensor, the scanning device, the feedback controller, and the reference trajectory. IEEE Control Syst. 33(6), 68–85 (2013)
Ziegler, D., Meyer, T.R., Amrein, A., Bertozzi, A.L., Ashby, P.D.: Ideal scan path for high-speed atomic force microscopy. IEEE/ASME Trans. Mechatron. 22(1), 381–391 (2017)
Bazaei, A., Maroufi, M., Moheimani, S.R.: Tracking of constant-linear-velocity spiral trajectories by approximate internal model control. In: 2017 IEEE Conference on Control Technology and Applications (CCTA), pp. 129–134. IEEE, August 2017
Habibullah, H., Pota, H., Petersen, I.: Phase-locked loop-based proportional integral control for spiral scanning in an atomic force microscope. IFAC Proc. Vol. 47(3), 6563–6568 (2014). 19th IFAC World Congress
Keiel, G., Flores, J.V., Pereira, L.F., Salton, A.T.: Discrete-time multiple resonant controller design for uninterruptible power supplies. IFAC-PapersOnLine 50(1), 6717–6722 (2017)
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de Oliveira, M.S., Salton, A.T., Flores, J.V., Pimentel, G.A. (2018). Resonant Gain Scheduling Controller for Spiral Scanning Patterns in Atomic Force Microscopy. In: Chen, Z., Mendes, A., Yan, Y., Chen, S. (eds) Intelligent Robotics and Applications. ICIRA 2018. Lecture Notes in Computer Science(), vol 10985. Springer, Cham. https://doi.org/10.1007/978-3-319-97589-4_22
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DOI: https://doi.org/10.1007/978-3-319-97589-4_22
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