The edge shape of a silicon wafer is crucial for optimal device manufacturing. In polishing processes, it is necessary to form wafers into either a flat or roll-up shape, depending on the specific ...requirements of the process. However, the conventional process typically results in a roll-off shape. This study identifies the factors that influence a change in the edge shape during polishing. Polishing experiments were conducted to examine the effects of the initial edge shape and contact state between the wafer and polishing pad on the removal distribution. An approach for adjusting the resulting edge shapes was proposed.
Focusing on a quadrotor unmanned aerial vehicle (UAV), the presence of unintended actuator faults and external disturbances increases the risk of a crash. Although plenty of efforts have been ...devoted, how to integrate capability analysis into safety control design is still an open issue. This article presents the design of a safety control system for quadrotor UAVs. Firstly, a system capability analysis method based on a differential flatness algorithm is developed, so that the derivatives (i.e., velocity, jerk, and snap) of flight trajectory can be formulated as flat variables. A tradeoff between system capability and permissible flight maneuverability is made to avoid actuator saturation. Secondly, dual-loop nonlinear disturbance observers are exploited to identify the actuator faults and disturbances, which can thereby be handled by a cascade control scheme. Moreover, the trajectory is regenerated online at the expense of degraded flight maneuverability or even emergency landing, in view of the remaining actuator control authority. When comparing to the existing methods, the gap among safety control, trajectory generation, and system capability analysis is bridged to ameliorate practical flight safety. Finally, flight tests are carried out to demonstrate the unique merits of the proposed system.
Abstract Measuring the flatness error of large precision workpieces quickly and accurately is a difficult problem. A new method for preprocessing flatness measurement data based on MSE (mean squared ...error) is proposed. A mathematical model of a new data preprocessing method was established, and the mathematical formula for model solving was derived in detail. The data were measured by digital level on the plane of the granite base with dimensions of 2340 m×1540 mm. The new method and SmartLevel (basic measurement system of the level computer) were used to calculate and process the data. The flatness errors after diagonal evaluation were 4.07 μm and 3.90 μm, respectively. The relative error of the two was 4.36%, which confirmed the reliability and accuracy of the new method. The data results show that this method can be effectively used for the engineering measurement of the flatness of large precision workpieces.
Autonomous unmanned aerial vehicles (UAVs) that can execute aggressive (i.e., high-speed and high-acceleration) maneuvers have attracted significant attention in the past few years. This article ...focuses on accurate tracking of aggressive quadcopter trajectories. We propose a novel control law for tracking of position and yaw angle and their derivatives of up to fourth order, specifically velocity, acceleration, jerk, and snap along with yaw rate and yaw acceleration. Jerk and snap are tracked using feedforward inputs for angular rate and angular acceleration based on the differential flatness of the quadcopter dynamics. Snap tracking requires direct control of body torque, which we achieve using closed-loop motor speed control based on measurements from optical encoders attached to the motors. The controller utilizes incremental nonlinear dynamic inversion (INDI) for robust tracking of linear and angular accelerations despite external disturbances, such as aerodynamic drag forces. Hence, prior modeling of aerodynamic effects is not required. We rigorously analyze the proposed control law through response analysis and demonstrate it in experiments. The controller enables a quadcopter UAV to track complex 3-D trajectories, reaching speeds up to 12.9 m/s and accelerations up to 2.1 g, while keeping the root-mean-square tracking error down to 6.6 cm, in a flight volume that is roughly 18 m <inline-formula> <tex-math notation="LaTeX">\times 7 </tex-math></inline-formula> m and 3-m tall. We also demonstrate the robustness of the controller by attaching a drag plate to the UAV in flight tests and by pulling on the UAV with a rope during hover.
This paper presents a tracking control method for the lateral motion of an autonomous land vehicle (ALV). This method is based on active disturbance rejection control (ADRC) scheme and differential ...flatness theory. The lateral motion is hard to control since it is underactuated, nonlinear, and with large uncertainties. By making a small-angle approximation, the dynamic model is linearized. The flatness of the linear model is proved and a flat output is found. An equivalent form of the model is obtained based on the flat output and its derivatives only. Moreover, an ADRC is adopted to guarantee both control accuracy and strong robustness. Simulation results are presented and the results show the effectiveness of the control strategies.
Are 2D Interfaces Really Flat? Cheng, Zhihui; Zhang, Huairuo; Le, Son T ...
ACS nano,
04/2022, Volume:
16, Issue:
4
Journal Article
Peer reviewed
Two-dimensional (2D) van der Waals materials are subject to mechanical deformation and thus forming bubbles and wrinkles during exfoliation and transfer. A lack of interfacial “flatness” has ...implications for interface properties, such as those formed by metal contacts or insulating layers. Therefore, an understanding of the detailed properties of 2D interfaces, especially their flatness under different conditions, is of high importance. Here we use cross-sectional scanning transmission electron microscopy (STEM) to investigate various 2D interfaces (2D-2D and 3D-2D) under the effects of stacking, atomic layer deposition (ALD), and metallization. We characterize and compare the flatness of the hBN-2D and metal-2D interfaces down to angstrom resolution. It is observed that the dry transfer of hexagonal boron nitride (hBN) can dramatically alter the interface structure. When characterizing 3D metal-2D interfaces, we find that Ni-MoS2 interfaces are more uneven and have larger nanocavities compared to other metal-2D interfaces. The electrical characteristics of a MoS2-based field-effect transistor are correlated to the interfacial transformation in the contact and channel regions. The device transconductance is improved by 40% after the hBN encapsulation, likely due to the interface interactions at both the channel and contacts. Overall, these observations reveal the intricacy of 2D interfaces and their dependence on the fabrication processes.
This paper proposes a neural networks-based approach of finding flat output of linearized underactuated mechanical systems (UMS). Given that differential flatness and controllability are equivalent ...for linear systems, the problem is equivalent to finding the Brunovsky canonical form of linearized UMSs. We use a two degree-of-freedom (2DOF) system to illustrate the theoretical development. The proposed method identifies the local flat output of nonlinear mechanical systems from the measurements only, without a detailed mathematical model. The identification allows us to combine the well-known active disturbance rejection control (ADRC) and differential flatness control. A time-domain direct identification (TDDI) algorithm and its variant based on the algebraic method are proposed for flat output identification (FOID). The neural networks for implementing the TDDI algorithm called FOID-NN are created to evaluate flat output candidates and to use the flat output to reconstruct the system states in terms of a linear mapping. The neural networks are trained with the loss functions defined by reconstruction errors. Two special layers, namely tracking differentiator (TD) and algebraic layer, are inserted in the FOID-NN to handle noisy signal differentiations. Simulations of a cart–pole system and a stable 2DOF nonlinear UMS are carried out to show the range of applications of the FOID-NN. The experimental data of an underactuated rotary crane are used to validate the identified flat output.
This study proposes a robust tracking controller for an underactuated quadrotor model based on the flatness theory and active disturbance rejection control (ADRC). Exploiting the differential ...flatness characteristic, it is demonstrated that a non-linear quadrotor system can be changed into a linear canonical form, where it is easier to create a state feedback controller that ensures accurate trajectory tracking. In order to improve the tracking performance of the quadrotor, other factors are considered in the conception of the state feedback controller consisting in the estimation of the un-measurable state variables in a canonical (Brunovsky) form and in the elimination of external perturbations and modelling uncertainties affecting the quadrotor system. To deal with this problem, first, an extended state observer (ESO) is designed to estimate a system state and an extended state known as lumped uncertainties. The latter represents the total effects of uncertain parameters, the neglected part of non-linearity and the external disturbances. Second, based on the ESO result, an additional term is integrated into the feedback controller to eliminate the lumped disturbance effects and to ensure the stability of the closed loop. Simulation results are introduced to prove the benefits of associating the ADRC approach with flatness control.
In this article, we show that the flatness of a nonlinear discrete-time system can be checked by computing a unique sequence of involutive distributions. The well-known test for static feedback ...linearizability is included as a special case. Since the computation of the sequence of distributions requires only the solution of algebraic equations, it allows an efficient implementation in a computer algebra program. In case of a positive result, a flat output can be obtained by straightening out the involutive distributions with the Frobenius theorem.
On subpullback flat S-posets Liang, Xingliang; Dang, Yun; Wei, Boyan
Communications in algebra,
06/2024, Volume:
52, Issue:
6
Journal Article
Peer reviewed
In 1971, inspired by the work of Lazard and Govorov for R-modules over a ring R, B. Stenström proved that an S-act over a monoid S is isomorphic to a directed colimit of finitely generated free ...S-acts if and only if it is both pullback flat and equalizer flat. Such acts are now usually called strongly flat. In 1991, S. Bulman-Fleming discovered that every pullback flat S-act is in fact strongly flat by developing a new "interpolation" Condition (PF) for pullback-preservation. In 2005, V. Laan and S. Bulman-Fleming obtained a version of the Lazard-Govorov Theorem for S-posets over a pomonoid S, in which subpullbacks and subequalizers now take on the role previously played by pullbacks and equalizers. However, unlike the situation for acts, S. Bulman-Fleming showed in 2009 that subpullback flat S-posets need not be strongly flat, and also T. Zhao found in 2022 that Condition (PF) does not imply strongly flatness for S-posets. The present paper is devoted to the study of subpullback flatness and Condition (PF) in the context of S-posets over a pomonoid S. First we unexpectedly show that subpullback flatness is equivalent to Condition (PF). Furthermore, we give some classifications of pomonoids by subpullback flatness of (cyclic, Rees factor) S-posets, and give some classes of pomonoids that all (cyclic) S-posets have a PF-cover. Finally, we investigate products of subpullback flat S-posets.
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