AN AFM PROBE CONTROLLER DESIGN BASED ON μ‐SYNTHESIS

The atomic force microscope (AFM) is one of the most important tools for measuring atomic resolution. The AFM system maintains constant force between a tip and the sample in order to track the sample topography. The controller that maintains the constant interaction force plays a significant role in measurement accuracy. This paper presents a μ‐synthesis controller design to deal with model uncertainty and establish a measurement error bound. The system's nonlinearity and the set‐point drift are lumped into a multiplicative uncertainty. The performance bound allows specification of the error magnitude over the frequency range. Simulation results show that the proposed control can tolerate uncertainties. The error spectrum from the experiments shows consistency with the design specifications. Images were taken to compare μ‐synthesis control with a well‐tuned PID control at a 480μm/s scan rate. The results verify the outstanding performance of the μ‐controller.     

ROBUST TWO‐DEGREE‐OF‐FREEDOM CONTROL OF AN ATOMIC FORCE MICROSCOPE

The performance of an atomic force microscope (AFM) is improved substantially by utilizing modern model‐based control methods in comparison to a standard proportional‐integral (PI) controlled AFM system. We present the design and implementation of a two‐degree‐of‐freedom (2DOF)‐controller to accomplish topography measurements at high scan‐rates with reduced measurement error. An H_∞‐controller operates the AFM system in a closed loop while a model‐based feedforward controller tracks the scanner to the last recorded scan‐line. Experimental results compare the actual performance of the standard PI‐controlled AFM and the 2DOF controlled system. The new controller reduces the control error considerably and enables imaging at higher speeds and at weaker tip‐sample interaction forces.     

On the Robust Nonlinear Motion Position and Force Control of Flexible Joints Robot Manipulators

The design of a robust nonlinear position and force controller for a flexible joints robot manipulator interacting with a rigid environment is presented. The controller is designed using the concept of feedback linearization, sliding mode techniques, and LQE estimation methodologies. It is shown that the nonlinear robot manipulator model is feedback linearizable. A robust performance of the proposed control approach is achieved by accounting for the system parameters uncertainties in the derivation of the nonlinear control law. An upper bound of the error introduced by parametric uncertainties in the system is computed. Then, the feedback linearizing control law is modified by adding a switching action to compensate the errors and to guarantee the achievement of the desired tracking performance. The relationship between the minimum achievable boundary layer thickness and the parametric uncertainties is derived. The proposed controller is tested using an experimental flexible joints robot manipulator, and the results demonstrate its potential benefits in reducing the number of sensors required and the complexity of the design. This is achieved by eliminating the need for nonlinear observers. A robust performance is obtained with minimum control effort by taking into account the effect of system parameter uncertainties and measurement noise.     

Real-time Topography and Hamaker Constant Estimation in Atomic Force Microscopy Based on Adaptive Fading Extended Kalman Filter

In this study, a novel technique based on adaptive fading extended Kalman filter for atomic force microscopy is proposed to directly estimate the topography of a sample surface without needing any control system. While in conventional imaging techniques, the scanning speed or the bandwidth is limited due to a relatively large settling time, the method proposed in this research is able to address this issue and estimate the topography throughout transient oscillation of the microcantilever. With this aim, an estimation process using an adaptive fading extended Kalman filter (augmented with forgetting factor) as the system observer is designed and coupled with the system dynamics to obtain sample topography. Obtained results demonstrate that the sample height is estimated by this algorithm with high accuracy and a relatively high scanning speed. Moreover, the observer is able to identify the topography and Hamaker constant simultaneously. Therefore, the presented approach can compensate for the low scanning speed of the classical imaging method as well as eliminate the need for a closed-loop controller.

     

Nonlinear and hysteretic influence of piezoelectric actuators in AFMs on lateral dimension measurement

Piezoelectric actuators that are used in atomic force microscopes (AFM) have undesirable properties. The nonlinear and hysteretic characteristics of piezoelectric actuators introduce geometric deformations in the reconstructed AFM images. Due to these deformations, the quantitative interpretation of the absolute dimensions of surface features is difficult and often not accurate.A real-time measuring ‘Nano-metrological Atomic Force Microscope’ system equipped with an ultra-high resolution three-axis laser interferometer system is developed, in which the undesirable properties of piezoelectric actuators are compensated completely. Using this AFM and a one-dimensional (1D) grating reference standard with pitches of 240 nm, which is one of the widely used reference standards as nano-metrological lateral scales, the influences of nonlinear and hysteretic characteristics of piezoelectric actuators on image reconstruction and lateral dimension measurement are examined and compared quantitatively among three different measurement methods. The three measurement methods are: (1) the relative movement between probe tip and sample is controlled and measured directly by voltage signals applied on the XYZ scanner, the nonlinear and hysteretic characteristics of piezoelectric actuators are not compensated; (2) the relative movement between probe tip and sample is controlled by voltage signals applied on the XYZ scanner, but it is measured accurately by interferometers; (3) the relative movement between probe tip and sample in lateral directions are both controlled and measured accurately by interferometers. According to the comparison results, an accurate displacement control system is key to reduce the influences of undesirable properties of piezoelectric actuators and the developed AFM system with three-axis laser interferometer system is proved to eliminate the nonlinear and hysteretic characteristics of piezoelectric actuators completely.     

Adaptive trajectory control of microcantilever's tip utilised in atomic force microscopy-based manipulation

This article presents a hybrid distributed-parameters model and an adaptive control framework for microcantilevers utilised in atomic force microscope systems for controlled force manipulations. The model assumes a general nonlinear interaction force between the microcantilever's tip and the surface of the sample. This interaction force includes the sample's surface and probe's tip distance as well as the first and second derivatives of this force implicitly. Despite such detailed modelling of interaction force, there are a number of uncertainties including tip mass, damping coefficients and nature of the interaction force that would affect the response of the system and hence, an adaptive controller is needed to compensate for these unmodelled dynamics and uncertainties. Unlike the current practices that deal with the lumped-parameters model of the cantilever, a comprehensive distributed-parameters model based on the Euler–Bernoulli theory is considered here. An adaptive controller is then designed such that by giving a force input to the base of the microcantilever, the tip of the microcantilever can track a desired trajectory despite the flexibility of the microcantilever and aforementioned uncertainties. Extensive simulation results are provided to illustrate that the microcantilever's tip can asymptotically follow a harmonic trajectory even for a system with higher modes of vibration when it is designed based on single-mode model.     

Robust nonlinear control of atomic force microscope via immersion and invariance

This paper reports an immersion and invariance (I&I)–based robust nonlinear controller for atomic force microscope (AFM) applications. The AFM dynamics is prone to chaos, which, in practice, leads to performance degradation and inaccurate measurements. Therefore, we design a nonlinear tracking controller that stabilizes the AFM dynamics around a desired periodic orbit. To this end, in the tracking error state space, we define a target invariant manifold, on which the system dynamics fulfills the control objective. First, considering a nominal case with full state measurement and no modeling uncertainty, we design an I&I controller to render the target manifold exponentially attractive. Next, we consider an uncertain AFM dynamics, in which only the displacement of the probe cantilever is measured. In the framework of the I&I method, we recast the robust output feedback control problem as the immersion of the output feedback closed‐loop system into the nominal full state one. For this purpose, we define another target invariant manifold that recovers the performance of the nominal control system. Moreover, to handle large uncertainty/disturbances, we incorporate the method of active disturbance rejection into the I&I output feedback control. Through Lyapunov‐based analysis of the closed‐loop stability and robustness, we show the semiglobal practical stability and convergence of the tracking error dynamics. Finally, we present a set of detailed, comparative software simulations to assess the effectiveness of the control method.     

A robust two degree-of-freedom controller for systems with both model and measurement uncertainty

This paper presents a design method for robust two degree-of-freedom (DOF) controllers that optimize the control performance with respect to both model uncertainty and signal measurement uncertainty. In many situations, non-causal feedforward is a welcome control addition when closed loop feedback bandwidth limitations exist due to plant dynamics such as: delays, non-minimum phase zeros, poorly placed zeros and poles (Xie, Alleyne, Greer, and Deneault (2013); Xie (2013), etc. However, feedforward control is sensitive to both model uncertainty and signal measurement uncertainty. The latter is particularly true when the feedforward is responding to pre-measured disturbance signals. The combined sensitivity will deteriorate the feedforward controller performance if care is not taken in design. In this paper a two DOF design is introduced which optimizes the performance based on a given estimate of uncertainties. The controller design uses H_∞ tools to balance the controlled system bandwidth with increased sensitivity to signal measurement uncertainties. A successful case study on an experimental header height control system for a combine harvester is shown as an example of the approach.     

A comparison of nonlinear observers for output feedback model-based control of seeded batch crystallization processes

This paper presents a comparative analysis of various nonlinear estimation techniques when applied for output feedback model-based control of batch crystallization processes. Several nonlinear observers, namely an extended Luenberger observer, an extended Kalman filter, an unscented Kalman filter, an ensemble Kalman filer and a moving horizon estimator are used for closed-loop control of a semi-industrial fed-batch crystallizer. The performance of the nonlinear observers is evaluated in terms of their closed-loop behavior as well as their ability to cope with model imperfections and process uncertainties such as measurement errors and uncertain initial conditions. The simulation results suggest that the extended Kalman filter and the unscented Kalman filter provide accurate state estimates that ensure adequate fulfillment of the control objective. The results also confirm that adopting a time-varying process noise covariance matrix further enhances the estimation accuracy of the latter observers at the expense of a slight increase in their computational burden. This tuning method is particularly suited for batch processes as the state variables often vary significantly along the batch run. It is observed that model imperfections and process uncertainties are largely detrimental to the accuracy of state estimates. The degradation in the closed-loop control performance arisen from inadequate state estimation is effectively suppressed by the inclusion of a disturbance model into the observers.     

Parameter estimation in time-triggered and event-triggered model-based control of uncertain systems

In this article on-line parameter estimation of dynamical systems is addressed in the context of model-based networked control systems (MB-NCSs). Stability conditions that are robust to parameter uncertainties and lack of feedback for extended intervals of time are presented. The updated model is used to control the real system the next time feedback information is unavailable. Additionally, new estimation models are proposed that offer better convergence properties than typical state-space parameter estimation methods; common assumptions such as availability of persistently exciting inputs and estimation of only a canonical form of the system are relaxed. The implementation of upgraded models in MB-NCSs results in better usage of the network by allowing longer intervals without the need for measurement updates.     

MEMS力平衡加速度传感器以测量误差最小为目标的控制算法

力平衡传感器(FBA)测量加速度是由反馈控制力与外界惯性力平衡时的控制力计算得到的,力平衡控制算法是力平衡传感器的核心.传统控制算法多以敏感元件偏移平衡位置最小为目标,限制了力平衡加速度计的测量精度和适用带宽.本文以MEMS力平衡传感器为对象,提出了一种以测量误差最小为目标的力平衡加速度计最优控制算法.引入测量误差新变量,将难以处理的力平衡控制转化为以响应最小为目标的经典控制问题,在此基础上获得了最优控制力的解析表达式,实现了对未知加速度信号的实时高精度检测.分别针对三种不同类型的输入加速度信号（阶跃、周期和随机）进行检测仿真,发现提出的算法能够准确地检测各类输入加速度信号,测量信号频带达kHz量级,同时在该控制算法下敏感元件的振动响应也得到有效控制,保证了加速度传感器的大动态范围.研究成果可为高精度和宽频带力平衡加速度传感器的研究提供基础.     

适用于原子力显微镜先进扫描模式的学习控制系统

原子力显微镜(AFM)是进行纳米测量和操作的一种重要工具.针对原子力显微镜系统,论文提出了一种基于学习控制的先进扫描模式.具体而言,首先构造了一种适用于AFM的学习控制系统,它由对于扫描管动态特性的最优逆补偿环节和对于样品表面特性的学习算法两部分组成.然后,针对测量过程中扫描线之间的偏移,通过将常见的比例-积分控制算法与这种学习控制相结合,实现了一种基于学习算法的先进扫描模式.论文将这种模式应用于周期性样品来测试其性能,仿真和实验结果表明它可以显著提高测量的速度和精度,同时将样品与探针针尖的距离控制在一个合理的范围之内,以避免损坏样品或探针.这种先进扫描模式可以应用于对快速生物过程的实时监测,同时也可以用来完成重复刻写等纳米操作.     

Output feedback adaptive RISE control for uncertain nonlinear systems

In this article, committed to extending the robust integral of the sign of the error (RISE) feedback control to the working condition of output feedback, a novel output feedback controller with a continuously bounded control input which combines the adaptive control and integral robust feedback will be proposed for trajectory tracking of a family of nonlinear systems subject to modeling uncertainties. A novel adaptive state observer (ASO) with disturbance rejection performance is creatively constructed to derive real-time estimation of the unmeasured state signals. Moreover, a projection-type adaption law is integrated to handle parameter uncertainties and an integral robust term is employed to deal with external disturbances. It is shown that asymptotic estimation performance and meanwhile asymptotic tracking result can eventually be derived. Simulation validations are implemented to demonstrate the high tracking performance of the presented controller. Notably, the synthesized control algorithm can be readily extended to the Euler–Lagrange systems. Typically, it can be extended to practical electromechanical equipment such as three-dimensional vector forming robots to improve the real-time forming accuracy.     

Compensation of Scanner Creep and Hysteresis for AFM Nanomanipulation

Nanomanipulation with atomic force microscopes (AFMs) for nanoparticles with overall sizes on the order of 10 nm has been hampered in the past by the large spatial uncertainties encountered in tip positioning. This paper addresses the compensation of nonlinear effects of creep and hysteresis on the piezo scanners which drive most AFMs. Creep and hysteresis are modeled as the superposition of fundamental operators, and their inverse model is obtained by using the inversion properties of the Prandtl-Ishlinskii operator. Identification of the parameters in the forward model is achieved by a novel method that uses the topography of the sample and does not require position sensors. The identified parameters are used to compute the inverse model, which in turn serves to drive the AFM in an open-loop, feedforward scheme. Experimental results show that this approach effectively reduces the spatial uncertainties associated with creep and hysteresis, and supports automated, computer-controlled manipulation operations that otherwise would fail.     

Adaptive control based on fast online algebraic identification and GPI control for magnetic levitation systems with time-varying input gain

This paper considers the position tracking problem of a voltage-controlled magnetic levitation system (MLS) in the presence of modelling errors caused by uncertainties in the system’s physical parameters. An adaptive control based on fast online algebraic parameter estimation and generalised proportional integral (GPI) output feedback control is considered as a control scheme candidate. The GPI controller guarantees an asymptotically exponentially stable behaviour of the controlled ball position and the possibilities of carrying out rest-to-rest trajectory tracking tasks. The nature of the control input gain in an MLS is that of a state-dependent time-varying gain, reflecting the nonlinear character of the magnetic force with regard to the distance and the properties of the metallic ball. The system gain has therefore been locally approximated using a periodically updated time polynomial function (of second degree), where the coefficients of the polynomial are estimated during a very short period of time. This estimation is achieved using the recently introduced algebraic online parameter estimation approach. The stability of the closed-loop system is demonstrated under the assumption that no external factors cause changes in the parameter during the time interval in which the stability is analysed. Finally, experimental results are presented for the controlled MLS demonstrating the excellent stabilisation and position tracking performance of the control system designed in the presence of significant nonlinearities and uncertainties of the underlying system.     

基于等价输入干扰滑模观测器的磁悬浮球系统模型预测控制

本文针对系统不确定性和外部干扰引起的磁悬浮球系统控制性能下降的问题,提出了一种基于等价输入干扰滑模观测器的模型预测控制(MPC+EIDSMO)方法.首先将原系统转化为EID系统,采用等价输入干扰滑模观测器对EID系统状态变量及等价输入干扰进行估计;然后基于状态估计值设计模型预测控制器,并将等价输入干扰估计值以前馈的方式...     

A microwave probe nanostructure for atomic force microscopy

An atomic force microscope (AFM) probe on a GaAs wafer was studied as a new microwave probe structure. A waveguide was created by evaporating an Au film on the top and bottom surfaces of the GaAs AFM probe. The fabricated AMF probe’s tip is 8 μm long and has a radius of curvature of about 50 nm. The open structure of the waveguide at the tip of the probe was generated by using focused ion beam (FIB) fabrication. AFM topography of a grating sample was created by using the fabricated microwave AFM probe. The fabricated probe exhibits nanometer-scale resolution, and microwave emission was successfully detected at the tip of the probe by approaching Cr–V steel and Au wire samples.     

Intelligent desktop NC machine tool with compliant motion capability

In this paper, a new desktop NC machine tool with compliance control capability is presented for finishing metallic molds with small curved surface. The NC machine tool consists of three single-axis robots. Tools attached to the tip of the z-axis are ball-end abrasive tools. The control system of the NC machine tool is composed of a force feedback loop, position feedback loop and position feed-forward loop. The force feedback loop controls the polishing force consisting of tool contact force and kinetic friction force. The position feedback loop controls the position in pick feed direction. Further, the position feed-forward loop leads the tool tip along cutter location data. In order to first confirm the application limit of a conventional industrial robot to a finishing task, we evaluate the backlash that causes the position inaccuracy at the tip of an abrasive tool, through a simple position/force measurement. Through a similar measurement and a surface following control experiment along a lens mold, the basic position/force controllability with high resolutions is demonstrated. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Feedback Linearization Control for Systems with Mismatched Uncertainties via Disturbance Observers

This paper focuses on a novel feedback linearization control (FLC) law based on a self‐learning disturbance observer (SLDO) to counteract mismatched uncertainties. The FLC based on BNDO (FLC‐BNDO) demonstrates robust control performance only against mismatched time‐invariant uncertainties while the FLC based on SLDO (FLC‐SLDO) demonstrates robust control performance against mismatched time‐invariant and ‐varying uncertainties, and both of them maintain the nominal control performance in the absence of mismatched uncertainties. In the estimation scheme for the SLDO, the BNDO is used to provide a conventional estimation law, which is used as the learning error for the type‐2 neuro‐fuzzy system (T2NFS), and T2NFS learns mismatched uncertainties. Thus, the T2NFS takes the overall control of the estimation signal entirely in a very short time and gives unbiased estimation results for the disturbance. A novel learning algorithm established on sliding mode control theory is derived for an interval type‐2 fuzzy logic system. The stability of the overall system is proven for a second‐order nonlinear system with mismatched uncertainties. The simulation results show that the FLC‐SLDO demonstrates better control performance than the traditional FLC, FLC with an integral action (FLC‐I), and FLC‐BNDO.     

High-order sliding-mode observer based output feedback adaptive robust control of a launching platform with backstepping

A kind of launching platform driven by two permanent magnet synchronous motor (PMSM) motors which is used to launch kinetic load to hit the target, always faces strong parameter uncertainties and strong external disturbance such as the air current impulsion, which would degrade their tracking accuracy greatly. In this paper, an adaptive robust nonlinear controller is proposed for high-accuracy motion control of the launching platform, in which the adaption law is designed to estimate the unknown coupling coefficients of torque disturbance and feed-forward cancellation technique is used to compensate the coupling torque disturbance and some other constant disturbances. In addition, a nonlinear robust feedback term is designed to inhibit the influence of the parameter estimation error and the other model uncertainty to stabilise the closed-loop system. Considering that some system states are immeasurable due to cost-reduction, volume/weight limitations and structure restriction or heavy measurement noise is usually associated with the measurements, which may also deteriorate the achievable performance of full-state feedback controllers; a high-order sliding-mode observer is used to estimate the unmeasured system states, and it is synthesised with the adaptive robust controller via feed-forward cancellation method. The intermediary virtual control law and the final control law are derived by integrating the backstepping method. Furthermore, the controller theoretically guarantees a prescribed tracking transient performance and final tracking accuracy while achieving asymptotic tracking performance in the presence of parametric uncertainties only, which is very important for high-accuracy tracking control of launching platform. Extensive comparative experimental results are obtained to verify the high performance nature of the proposed control strategy.