Stiffness Sensor for Cubic Nonlinear Elasticity Using Nonlinear Self-Excited Oscillation

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Yosuke Kokubun ◽  
Hiroshi Yabuno
Keyword(s):  
Nonlinear Elasticity ◽  
Response Amplitude ◽  
Feedback Gain ◽  
Nonlinear Stiffness ◽  
Nonlinear Feedback ◽  
Backbone Curve ◽  
Van Der Pol ◽  
Stiffness Sensor ◽  
Excited Oscillation ◽  
Measurement Object

The present paper develops a nonlinear stiffness sensor for measuring cubic nonlinear elasticity. The measurement system consists of a vibrator with a control circuit. We apply linear-plus-nonlinear feedback to actuate the vibrator attached to a measurement object for inducing van der Pol type self-excited oscillation so that the response amplitude of the oscillation can be set arbitrarily by changing the nonlinear feedback gain. We focus on the fact that the nonlinear elasticity of the measurement object causes a natural frequency shift related to the magnitude of vibration amplitude of the vibrator. We can set the response amplitude to various values by changing the nonlinear feedback gain and measuring the shift of the response frequency depending on the magnitude of the response amplitude. As a result, based on the bend of the experimentally obtained backbone curve, the nonlinear elasticity of the measurement object is identified.

Hardness Detection Sensor for Cubic Nonlinear Elasticity Using Nonlinear Self-Excited Oscillation

2013 ◽  
Author(s):  
Yosuke Kokubun ◽  
Hiroshi Yabuno ◽  
Masaharu Kuroda ◽  
Yasuyuki Yamamoto
Keyword(s):  
Nonlinear Elasticity ◽  
Vibration Amplitude ◽  
Measurement Method ◽  
Response Amplitude ◽  
Feedback Gain ◽  
Nonlinear Feedback ◽  
Backbone Curve ◽  
Van Der Pol ◽  
Response Frequency ◽  
Excited Oscillation

This paper proposes a measurement method of cubic non-linear elasticity. The measurement system consists of a vibrator and a control circuit. We apply a nonlinear feedback to actuate the vibrator for inducing van der Pol type self-excited oscillation, so that the response amplitude of the oscillation can be arbitrarily set by changing the nonlinear feedback gain. We focus on the fact that the nonlinear elasticity causes a natural frequency shift related to the vibration amplitude of the object. We can set the response amplitude various values by changing the nonlinear feedback gain and measure the shift of the response frequency depending on the magnitude of the response amplitude. As a result, the bend of the backbone curve reflecting the nonlinear elasticity of the object is obtained.

Nonlinear Analysis of a Self-Excited Cantilever Beam

2005 ◽  
Author(s):  
Hiroyuki Kaneko ◽  
Hiroshi Yabuno ◽  
Masaharu Kuroda
Keyword(s):  
Cantilever Beam ◽  
Positive Feedback ◽  
Response Amplitude ◽  
The Self ◽  
Steady State Response ◽  
Nonlinear Feedback ◽  
Van Der Pol ◽  
Restoring Force ◽  
State Response ◽  
Excited Oscillation

In this study, we investigate the dynamics of a self-excited cantilever beam by a positive feedback proportional to the velocity. In particular, we focus on the response amplitude in the self-excited oscillation and analyze the effect of the nonlinear component of the restoring force in the cantilever. It is theoretically and experimentally clarified that the response amplitude grows with time under the positive feedback proportional to the velocity (positive feedback). Furthermore, van der Pol type self-excited cantilever beam is designed by applying the nonlinear feedback proportional to the squared deflection and the velocity, and the steady state response is realized in the cantilever beam. The theoretically predicted effects of the nonlinear feedback are qualitatively confirmed by performing some experiments.

Experimental amplitude and frequency control of a self-excited microcantilever by linear and nonlinear feedback

2021 ◽  
Author(s):  
Eisuke Higuchi ◽  
Hiroshi Yabuno ◽  
Yasuyuki Yamamoto ◽  
Sohei Matsumoto
Keyword(s):  
Steady State ◽  
Frequency Control ◽  
High Sensitivity ◽  
High Viscosity ◽  
Measurement Methods ◽  
Nonlinear Feedback ◽  
Force Microscopy ◽  
Atomic Force ◽  
Excited Oscillation ◽  
Experimental Approaches

Abstract In recent years, measurement methods that use resonators as microcantilevers have attracted attention because of their high sensitivity, high accuracy, and rapid response time. They have been widely utilized in mass sensing, stiffness sensing, and atomic force microscopy (AFM), among other applications. In all these methods, it is essential to accurately detect shifts in the natural frequency of the resonator caused by an external force from a measured object or sample. Experimental approaches based on self-excited oscillation enable the detection of these shifts even when the resonator is immersed in a high-viscosity environment. In the present study, we experimentally and theoretically investigate the nonlinear characteristics of a microcantilever resonator and their control by nonlinear feedback. We show that the steady-state response amplitude and the corresponding response frequency can be controlled by cubic nonlinear velocity feedback and cubic nonlinear displacement feedback, respectively. Furthermore, the amplitude and frequency of the steady-state self-excited oscillation can be controlled separately. These results will expand application of measurement methods that use self-excited resonators.

Digital Model of Bench-Marking for Development of Competitive Advantage

2018 ◽  
pp. 288-303 ◽  
Author(s):  
Vardan Mkrttchian ◽  
Alexander Bershadsky ◽  
Alexey Finogeev ◽  
Artiom Berezin ◽  
Irina Potapova
Keyword(s):  
Differential Equations ◽  
Competitive Advantage ◽  
Time Lag ◽  
Digital Model ◽  
Nonlinear Feedback ◽  
Van Der Pol ◽  
Market Interaction ◽  
Digital Modeling ◽  
Working Out ◽  
Aggregate System

The chapter deals with the problems of digital modeling and the study of the interaction of the companies competing within the framework of the bench-marking process for definition, understanding and working out the strategy of effective functioning and increasing competitiveness. The companies are considered in the organizational field, representing iterative aggregate system of a big order with a nonlinear feedback where the order is defined by the number of differential equations. The system is described by coupled Van Der Pol differential equations with random right parts and a time lag. The model is built on the example of the market interaction of the two largest retailer networks. The developed model shows the mechanism of competition of the companies' pairs which are suggested to be investigated within the framework of the bench-marking concept.

SDRE-based high performance feedback control for nonlinear mechatronic systems

2019 ◽  
Vol 38 (4) ◽  
pp. 1164-1176
Author(s):  
Slawomir Jan Stepien ◽  
Paulina Superczynska ◽  
Damian Dobrowolski ◽  
Jerzy Dobrowolski
Keyword(s):  
Control Problem ◽  
High Performance ◽  
Computational Effort ◽  
Control Technique ◽  
Feedback Gain ◽  
Nonlinear Feedback ◽  
Mechatronic System ◽  
Mechatronic Systems ◽  
Content Type ◽  
State Dependent

Purpose The purpose of the paper is to present modeling and control of a nonlinear mechatronic system. To solve the control problem, the modified state-dependent Riccati equation (SDRE) method is applied. The control problem is designed and analyzed using the nonlinear feedback gain strategy for the infinite time horizon problem. Design/methodology/approach As a new contribution, this paper deals with state-dependent parametrization as an effective modeling of the mechatronic system and shows how to modify the classical form of the SDRE method to reduce computational effort during feedback gain computation. The numerical example compares described methods and confirms usefulness of the proposed technique. Findings The proposed control technique can ensure optimal dynamic response, reducing computational effort during control law computation. The effectiveness of the proposed control strategy is verified via numerical simulation. Originality/value The authors introduced an innovative approach to the well-known SDRE control methodology and settled their research in the newest literature coverage for this issue.

scholarly journals Transient amplitude behavior analysis of nonlinear power ultrasonic transducers with application to ultrasonic squeeze film levitation

2012 ◽  
Vol 24 (6) ◽  
pp. 745-752 ◽  
Author(s):  
Sebastian Mojrzisch ◽  
Jörg Wallaschek
Keyword(s):  
Behavior Analysis ◽  
Vibration Amplitude ◽  
Nonlinear Effects ◽  
Analytical Form ◽  
Ultrasonic Transducers ◽  
Squeeze Film ◽  
Nonlinear Stiffness ◽  
Van Der Pol ◽  
Jump Phenomena ◽  
Averaged Models

In this article, force and self-excitation driving methods for ultrasonic transducers are compared with each other in sense of their transient amplitude behavior in the presence of nonlinearities. An equivalent circuit transducer model is simplified to a series oscillator. The simplified model is averaged by the Van der Pol method in order to reduce the system at hand to its amplitude dynamics. The transient amplitude behavior of both driving methods is presented in an analytical form. At high vibration amplitudes, the system’s natural frequency varies due to the nonlinear stiffness of the piezoelectric material and the vibration amplitude is likely to break down due to the jump phenomena. Therefore, the averaged models are extended by the nonlinear effects. From the amplitude behavior analysis of both systems, it follows that self-excitation is the preferable driving method in sense of obtaining a high operation bandwidth and a stable oscillation.

CONTROLLING UNCERTAIN VAN DER POL OSCILLATOR VIA ROBUST NONLINEAR FEEDBACK CONTROL

2004 ◽  
Vol 14 (05) ◽  
pp. 1671-1681 ◽  
Author(s):  
MAO-YIN CHEN ◽  
ZHENG-ZHI HAN ◽  
YUN SHANG ◽  
GUANG-DENG ZONG
Keyword(s):  
Feedback Control ◽  
Control Method ◽  
Reference Signal ◽  
Variable Structure ◽  
Van Der Pol Oscillator ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Van Der Pol ◽  
Feedback Control Method ◽  
System Uncertainties

Combining the backstepping design and the variable structure control, we propose a robust nonlinear feedback control method to control an uncertain van der Pol oscillator even if there exist system uncertainties and external disturbances in this oscillator. If system uncertainties are estimated and some parameters are chosen suitably, the output of van der Pol osicllator can track arbitrary smooth reference signal. Theoretical analysis and numerical simulations verify the effectiveness of this method.

On the Delayed van der Pol Oscillator with Time-Varying Feedback Gain

2014 ◽  
Vol 706 ◽  
pp. 149-158 ◽  
Author(s):  
Mustapha Hamdi ◽  
Mohamed Belhaq
Keyword(s):  
Numerical Simulation ◽  
Type System ◽  
Stationary Solutions ◽  
Van Der Pol Oscillator ◽  
Feedback Gain ◽  
Time Varying ◽  
Van Der Pol ◽  
Existence Region ◽  
The Stability ◽  
Time Delayed Feedback

This work studies the effect of time delayed feedback on stationary solutions in a van derPol type system. We consider the case where the feedback gain is harmonically modulated with a resonantfrequency. Perturbation analysis is conducted to obtain the modulation equations near primaryresonance, the stability analysis for stationary solutions is performed and bifurcation diagram is determined.It is shown that the modulated feedback gain position can influence significantly the steadystates behavior of the delayed van der Pol oscillator. In particular, for appropriate values of the modulateddelay parameters, the existence region of the limit cycle (LC) can be increased or quenched.Moreover, new regions of quasiperiodic vibration may emerge for certain values of the modulatedgain. Numerical simulation was conducted to validate the analytical predictions.

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