On an Optimal Control Applied in Atomic Force Microscopy (AFM) Including Fractional-Order

2017 ◽  
Author(s):  
Angelo M. Tusset ◽  
Jose M. Balthazar ◽  
Jeferson Jose de Lima ◽  
Rodrigo T. Rocha ◽  
Frederic C. Janzen ◽  
...  
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Nonlinear Behavior ◽  
Control Technique ◽  
Linear Feedback ◽  
Squeeze Film ◽  
Good Tool ◽  
Chaotic Motions ◽  
Atomic Force ◽  
Squeeze Film Damping

In this work, the nonlinear dynamics of an Atomic Force Microscope (AFM) operating in tapping mode is investigated, considering the influence of squeeze film damping in fractional-order. Its influence plays an important role because the dynamics of the AFM can be led to different responses, e.g., periodic and chaotic motions, specially the influence of the derivative order when in fractional-order. In a way to characterize the type of behavior, the 0–1 test was used once this is a good tool to characterize fractional-order differential systems. In addition, the linear feedback control technique for fractional-order systems is applied to control the chaotic behaviors. Therefore, the results showed a nonlinear behavior presented by the AFM system. In addition, the feedback control technique was efficient to control the chaotic motion of the micro cantilever beam of the AFM, whose results included variation of parameters of the fractional derivative of the squeeze film damping.

scholarly journals Projective Synchronization ofN-Dimensional Chaotic Fractional-Order Systems via Linear State Error Feedback Control

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Baogui Xin ◽  
Tong Chen
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Projective Synchronization ◽  
Control Technique ◽  
Linear Feedback ◽  
Fractional Order Systems ◽  
Financial Systems ◽  
Linear State ◽  
Synchronization Scheme ◽  
State Error

Based on linear feedback control technique, a projective synchronization scheme ofN-dimensional chaotic fractional-order systems is proposed, which consists of master and slave fractional-order financial systems coupled by linear state error variables. It is shown that the slave system can be projectively synchronized with the master system constructed by state transformation. Based on the stability theory of linear fractional order systems, a suitable controller for achieving synchronization is designed. The given scheme is applied to achieve projective synchronization of chaotic fractional-order financial systems. Numerical simulations are given to verify the effectiveness of the proposed projective synchronization scheme.

scholarly journals Numerical Exploratory Analysis of Dynamics and Control of an Atomic Force Microscopy in Tapping Mode with Fractional Order

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Mauricio A. Ribeiro ◽  
Jose M. Balthazar ◽  
Wagner B. Lenz ◽  
Rodrigo T. Rocha ◽  
Angelo M. Tusset
Keyword(s):  
Mathematical Model ◽  
Atomic Force Microscopy ◽  
Feedback Control ◽  
Fractional Order ◽  
Delayed Feedback Control ◽  
Linear Feedback ◽  
Tapping Mode ◽  
Force Microscopy ◽  
Control Techniques ◽  
Atomic Force

In this paper, we investigate the mechanism of atomic force microscopy in tapping mode (AFM-TM) under the Casimir and van der Waals (VdW) forces. The dynamic behavior of the system is analyzed through a nonlinear dimensionless mathematical model. Numerical tools as Poincaré maps, Lyapunov exponents, and bifurcation diagrams are accounted for the analysis of the system. With that, the regions in which the system presents chaotic and periodic behaviors are obtained and investigated. Moreover, the fractional calculus is introduced into the mathematical model, employing the Riemann-Liouville kernel discretization in the viscoelastic term of the system. The 0-1 test is implemented to analyze the new dynamics of the system, allowing the identification of the chaotic and periodic regimes of the AFM system. The dynamic results of the conventional (integer derivative) and fractional models reveal the need for the application of control techniques such as Optimum Linear Feedback Control (OLFC), State-Dependent Riccati Equations (SDRE) by using feedback control, and the Time-Delayed Feedback Control. The results of the control techniques are efficient with and without the fractional-order derivative.

Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xindong Si ◽  
Hongli Yang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback Control ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Control Law ◽  
Optimization Approach ◽  
Fractional Order Systems ◽  
Linear Feedback Control ◽  
Computational Point

AbstractThis paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

Time Delayed Feedback Control Applied in an Atomic Force Microscopy (AFM) Model in Fractional-Order

2019 ◽  
Vol 8 (2) ◽  
pp. 327-335 ◽  
Author(s):  
Angelo M. Tusset ◽  
Mauricio A. Ribeiro ◽  
Wagner B. Lenz ◽  
Rodrigo T. Rocha ◽  
Jose M. Balthazar
Keyword(s):  
Atomic Force Microscopy ◽  
Feedback Control ◽  
Fractional Order ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Force Microscopy ◽  
Atomic Force ◽  
Time Delayed Feedback

scholarly journals Stability of fractional order fuzzy cellular neural networks with distributed delays via hybrid feedback controllers

2021 ◽  
Author(s):  
Ajendra Sing ◽  
Jitendra Nath Rai
Keyword(s):  
Neural Networks ◽  
Feedback Control ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Control Technique ◽  
Fuzzy Cellular Neural Networks ◽  
Feedback Controllers ◽  
Lyapunov Approach ◽  
Analysis Techniques

Abstract This article studies the Global Mittag-Leffler stability of fractional order fuzzy cellular neural networks via hybrid feedback controllers. Based on hybrid feedback control technique Lyapunov approach, and some novel analysis techniques of fractional calculation, some sufficient conditions are obtained to guarantee the Global Mittag-lefflers stability. Finally, two simulation example are given to illustrate the effectiveness of the proposed method.

scholarly journals Squeeze Film Damping Effect on Different Microcantilever Probes in Tapping Mode Atomic Force Microscope

Scanning ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Yan Sun ◽  
Jing Liu ◽  
Kejian Wang ◽  
Zheng Wei
Keyword(s):  
Atomic Force Microscope ◽  
Theoretical Models ◽  
Sample Surface ◽  
Squeeze Film ◽  
Simplified Models ◽  
Tapping Mode ◽  
Damping Effect ◽  
Atomic Force ◽  
Squeeze Film Damping

During the operation of tapping mode atomic force microscope (TM-AFM), the gap between the cantilever and sample surface is very small (several nanometers to micrometers). Owing to the small gap distance and high vibration frequency, squeeze film force should be considered in TM-AFM. To explore the mechanism of squeeze film damping in TM-AFM, three theoretical microcantilever simplified models are discussed innovatively herein: tip probe, ball probe, and tipless probe. Experiments and simulations are performed to validate the theoretical models. It is of great significance to improve the image quality of atomic force microscope.

CHAOS IN DIFFUSIONLESS LORENZ SYSTEM WITH A FRACTIONAL ORDER AND ITS CONTROL

2012 ◽  
Vol 22 (04) ◽  
pp. 1250088 ◽  
Author(s):  
YONG XU ◽  
RENCAI GU ◽  
HUIQING ZHANG ◽  
DONGXI LI
Keyword(s):  
Feedback Control ◽  
Control Problem ◽  
Fractional Order ◽  
Lorenz System ◽  
Equilibrium Points ◽  
Control Technique ◽  
Order System ◽  
System Parameters ◽  
Simulation Results ◽  
The Stability

This paper aims to investigate the phenomenon of Diffusionless Lorenz system with fractional-order. We discuss the stability of equilibrium points of the fractional-order system theoretically, and analyze the chaotic behaviors and typical bifurcations numerically. We find rich dynamics in fractional-order Diffusionless Lorenz system with appropriate fractional order and system parameters. Besides, the control problem of fractional-order Diffusionless Lorenz system is examined using feedback control technique, and simulation results show the effectiveness of the method.

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