Quasi-repetitive control for fast and accurate atomic force microscopy
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Repetitive controllers use delayed feedback for periodic operations to provide a feedforward-like control action capable of high bandwidth operation. However, the signal to be tracked/rejected must be perfectly periodic, with known time-period, to obtain asymptotic convergence. Any deviation from periodicity can severely degrade the tracking performance of the controller. This paper explores the idea of employing a variation of repetitive controller to expand the domain of signals that can be tracked with the repetitive framework. The signals intended to be tracked belong to a class of quasiperiodic signals that can be represented as an algebraic sum of periodic and polynomial signals. Many of the commonly occurring physiologic signals, speech, and vibration signals belong to this signal class. Moreover, periodic signals that drift can also be modeled as this type of quasiperiodic signals. The derived quasi-repetitive controller guarantees asymptotic convergence with a plug-in architecture that can be added to an existing feedback design. One practical application of this controller occurs in atomic force microscopy (AFM), where imaging a sloped or non-flat sample surface induces quasiperiodic disturbances in the control loop. Experimental results demonstrate accurate and high speed imaging can be performed using the prescribed controller.Keywords:
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Level statistics is a crucial tool in the exploration of localization physics. The level spacing distribution of the disordered localized phase follows Poisson statistics, and many studies naturally apply it to the quasiperiodic localized phase. Here we analytically obtain the level spacing distribution of the quasiperiodic localized phase, and find that it deviates from Poisson statistics. Moreover, based on this level statistics, we derive the ratio of adjacent gaps and find that for a single sample, it is a $δ$ function, which is in excellent agreement with numerical studies. Additionally, unlike disordered systems, in quasiperiodic systems, there are variations in the level spacing distribution across different regions of the spectrum, and increasing the size and increasing the sample are non-equivalent. Our findings carry significant implications for the reevaluation of level statistics in quasiperiodic systems and a profound understanding of the distinct effects of quasiperiodic potentials and disorder induced localization.
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In this chapter adaptive feedforward and fixed feedback controllers are reviewed and their robust stability conditions contrasted for active control applications. Inspec keywords: feedback; robust control; adaptive control; nonlinear control systems; feedforward Other keywords: adaptive methods; fixed feedback controllers; robust stability conditions; adaptive feedforward controllers Subjects: Self-adjusting control systems
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Quasiperiodic lattices have been widely studied in cold atoms, which make one study extended-Anderson localization transition in one-dimensional (1D) or two-dimensional (2D) systems. In 2008, Inguscio's group prepared one-dimensional quasiperiodic lattice in cold atomic system and observed Anderson localization, which promoted the theoretical and experimental studies of quasiperiodic systems. Later, Bloch's group observed the many body localization in their prepared 1D and 2D quasiperiodic lattices. Recently, they also successfully observed the mobility edge and many body localization in a system with mobility edge in quasiperiodic lattices. These cold atom experiments have promoted the researches of many body localization and mobility edge. Quasiperiodic lattices have become a platform and its effects on many physical phenomena are being extensively studied, which can be expectantly observed in cold atomic experiments. This paper is based on the authors' some related work and briefly review some recent studies on the 1D quasiperiodic lattices, including some important cold atom experiments, some important properties of the quasiperiodic lattices and their effects on some physical phenomena, such as topological states.
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This paper examines a coordinated feedback and feedforward control design strategy for precision motion control (PMC) systems. It is assumed that the primary exogenous signals are repeated; including disturbances and references. Therefore, an iterative learning control (ILC) feedforward strategy can be used. The introduction of additional non-repeating exogenous signals, including disturbances, noise, and reset errors, necessitates the proper coordination between feedback and feedforward controllers to achieve high performance. A novel ratio of repeated versus non-repeated signal power in the frequency domain is introduced and defined as the repetitive-to-non-repetitive (RNR) ratio. This frequency specific ratio allows for a new approach to delegating feedback and feedforward control efforts based on RNR value. A systematic procedure for control design is given whereby the feedback addresses the non-repeating exogenous signal content (RNR ≪ 0 dB) and the feedforward ILC addresses the repeating signal content (RNR ≫ 0 dB). To illustrate the design approach, two case studies using different nano-positioning devices are given.
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A kind of photovoltaic grid-connected generation system based on repetitive control and feedforward control of utility grid voltage is produced. Repetitive control may restrain the periodic disturbance of the load and improve the wave of grid-connected current under steady state; simultaneously, the system uses the feedforward control of utility grid voltage to counteract the influence of utility grid, and make the system to be a simple passive tracking system. The control strategy has been proved to be simple and effective by experiment results, and the grid-connected current wave of the system is better.
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This paper considers repetitive control of a class of nonlinear uncertain systems. We present a simple repetitive control scheme for nonlinear systems without the assumption of linearisability, and an adaptive repetitive control scheme when the upper bound of the uncertainties is uncertain. Asymptotic stability is proved for the repetitive control system and uniform boundedness is proved for the adaptive repetitive control system.
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A combination of adaptive and repetitive control for dynamic control of robot manipulators is introduced. The repetitive controller is a plug-in controller for connection to an existing model-reference adaptive controller. The input to the repetitive controller is the same as the adaptation error signal for the adaptive controller. In this scheme, desired trajectories and external disturbance are assumed to be periodic. Global stability for this control system is achieved and disturbance is rejected successfully. Based on the characteristics of the reference model, two types of control algorithm are presented: a unity-gain and a pure-integrator reference model. Discretized versions suitable for digital implementations, and sufficient conditions for their stability in the discrete time domain are presented. The performance of the adaptive and repetitive controller is demonstrated by simulation.< >
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A feedforward modification for both positive- and negative-feedback schemes of repetitive control is described. It was shown that repetitive controllers can be a useful tool for tracking of periodic reference signals and compensation of periodic disturbances, in other words, for harmonic compensation. It was shown that the feedforward modification considerably improves the frequency response and performance, providing higher gains with enhanced selectivity. Simple analog circuits are presented to implement both positive- and negative-feedback repetitive schemes. A description of the circuits and their corresponding experimental frequency responses are also given
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Low dimensional quasiperiodic systems exhibit localization transitions by turning all quantum states localized after a critical quasidisorder. While certain systems with modified or constrained quasiperiodic potential undergo multiple localization transitions in one dimension, we predict an emergence of multiple localization transitions without directly imposing any constraints on the quasiperiodic potential. By considering a one-dimensional system described by the Aubry-And\'{r}e (AA) model, we show that an additional staggered onsite potential can drive the system through a series of localization transitions as a function of the staggered potential. Interestingly, we find that the number of localization transitions strongly depends on the strength of the quasiperiodic potential. Moreover, we obtain the signatures of these localization transitions in the expansion dynamics and propose an experimental scheme for their detection in the quantum gas experiment.
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Weak localization
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A feed drive control method to improve the accuracy of periodic trajectory is described and evaluated. The method is based on the combination of feedforward control (zero phase error tracking control) and repetitive control. Adding the repetitive control compensates for the model mismatching which generally degrades feedforward control performance. Investigations on robust stability and disturbance effects reveal some tips on controller design. A repetitive controller is proposed to assure robust stability for unmodelled dynamics and dead-time while maintaining tracking performance in low frequencies. The regulation error, however, is increased in certain frequencies by adding the repetitive controller under the existence of load disturbances and measurement noise. Simulation results indicate that the proposed approach greatly decreases the tracking error.
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