“…To design the controller for each axis, we use affine parametrization method [51]. Using the transfer functions obtained in Section VI-B for the piezoelectric outputs as the plant and considering all poles of the plant undesirable, affine parametrization method leads to the following poles assignment equation: (12) where and are numerator and denominator polynomials of the plant transfer function, respectively, is the desired characteristic polynomial after closing the damping loop, and and are the numerator and denominator polynomials of the damping compensator, respectively. Since and are of order three, selecting degree of two for the compensator polynomials and and degree of five for the desired polynomial lead to a unique solution for compensator.…”
Section: Damping Loopmentioning
confidence: 99%
“…The invention of scanning probe microscopy (SPM) is one of the revolutionary events in nanoscience and nanotechnology [3]- [5]. SPMs promise breakthroughs in areas such as nanometrology [6]- [9], nanolithography [10], [11], material science [12], [13], high-density data storage systems [14]- [16], and nano-fabrication [17]. SPMs are capable of generating 3-D maps of material surfaces on an atomic scale.…”
Abstract-In this paper, we design feedback controllers for lateral and transversal axes of an atomic force microscope (AFM) piezoelectric tube scanner. The controllers are constrained to keep the standard deviation of the measurement noise fed back to the displacement output around 0.13 nm. It is shown that the incorporation of appropriate inner loops provides disturbance rejection capabilities and robustness against dc gain uncertainties, two requirements for satisfactory operation of signal transformation method. Simulations and experiments show significant improvement of steady-state tracking error with signal transformation, while limiting the projected measurement noise.
“…To design the controller for each axis, we use affine parametrization method [51]. Using the transfer functions obtained in Section VI-B for the piezoelectric outputs as the plant and considering all poles of the plant undesirable, affine parametrization method leads to the following poles assignment equation: (12) where and are numerator and denominator polynomials of the plant transfer function, respectively, is the desired characteristic polynomial after closing the damping loop, and and are the numerator and denominator polynomials of the damping compensator, respectively. Since and are of order three, selecting degree of two for the compensator polynomials and and degree of five for the desired polynomial lead to a unique solution for compensator.…”
Section: Damping Loopmentioning
confidence: 99%
“…The invention of scanning probe microscopy (SPM) is one of the revolutionary events in nanoscience and nanotechnology [3]- [5]. SPMs promise breakthroughs in areas such as nanometrology [6]- [9], nanolithography [10], [11], material science [12], [13], high-density data storage systems [14]- [16], and nano-fabrication [17]. SPMs are capable of generating 3-D maps of material surfaces on an atomic scale.…”
Abstract-In this paper, we design feedback controllers for lateral and transversal axes of an atomic force microscope (AFM) piezoelectric tube scanner. The controllers are constrained to keep the standard deviation of the measurement noise fed back to the displacement output around 0.13 nm. It is shown that the incorporation of appropriate inner loops provides disturbance rejection capabilities and robustness against dc gain uncertainties, two requirements for satisfactory operation of signal transformation method. Simulations and experiments show significant improvement of steady-state tracking error with signal transformation, while limiting the projected measurement noise.
“…Such applications include scanning probe microscopy [3]- [5], nanometrology [6]- [9], nanolithography [10], [11], material science [12], [13], high-density data storage systems [14]- [16], and nano-fabrication [17]. Capacitive and inductive sensors are commonly used in nanopositioning systems due to their capability of providing simple solution for non-contact, high-resolution measurement.…”
Abstract-In this paper, we introduce a signal transformation (ST) methodology for tracking control of a large class of arbitrary references. The method can improve tracking performance of ordinary one-degree-of-freedom (1-DoF) feedback control structure, while keeping robustness against unmodeled dynamics and limiting the projected measurement noise by ensuring a low closed-loop bandwidth. Using singular perturbation theory, sufficient conditions for stability and convergence of the tracking error are derived. Effectiveness of the proposed method is demonstrated by simulations. It is shown how ST method can provide a better control performance compared to ordinary 2-DoF feedback control systems having similar projected noise power, and maintain robustness against uncertainties, disturbances, and unmodeled dynamics.
“…The atomic force microscope (AFM) cantilever was developed for producing high-resolution images of surface structures of both conductive and insulating samples in both air and liquid environments (Takaharu et al, 2003 ;Kageshima et al, 2002 ;Kobayashi et al, 2002 ;Yaxin & Bharat, 2007). In addition, the AFM cantilever can be applied to nanolithography in micro/nano electromechanical systems (MEMS/NEMS) (Fang & Chang, 2003) and as a nanoindentation tester for evaluating mechanical properties (Miyahara, et al, 1999). Therefore, it is essential to preciously calculate the vibration response of AFM cantilever during the sampling process.…”
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.