scholarly journals Ambiguities in input-output behavior of driven nonlinear systems close to bifurcation

2016 ◽  
Vol 65 (2) ◽  
pp. 337-347 ◽  
Author(s):  
Marco Reit ◽  
Michael Berens ◽  
Wolfgang Mathis
Keyword(s):  
Mathematical Formulation ◽  
Nonlinear Behavior ◽  
Output Characteristic ◽  
Input Output ◽  
Solution Sets ◽  
Dsp Implementation ◽  
Sinusoidal Input ◽  
Hearing Organ ◽  
Nonlinear Amplifiers ◽  
Output Behavior

Abstract Since the so-called Hopf-type amplifier has become an established element in the modeling of the mammalian hearing organ, it also gets attention in the design of nonlinear amplifiers for technical applications. Due to its pure sinusoidal response to a sinusoidal input signal, the amplifier based on the normal form of the Andronov-Hopf bifurcation is a peculiar exception of nonlinear amplifiers. This feature allows an exact mathematical formulation of the input-output characteristic and thus deeper insights of the nonlinear behavior. Aside from the Hopf-type amplifier we investigate an extension of the Hopf system with focus on ambiguities, especially the separation of solution sets, and double hysteresis behavior in the input-output characteristic. Our results are validated by a DSP implementation.

scholarly journals Implementation of a digital evaluation platform to analyze bifurcation based nonlinear amplifiers

2016 ◽  
Vol 14 ◽  
pp. 47-50 ◽  
Author(s):  
Sven Feldkord ◽  
Marco Reit ◽  
Wolfgang Mathis
Keyword(s):  
Focus Of Attention ◽  
Input Output ◽  
Control Interface ◽  
Digital Evaluation ◽  
Cpu Usage ◽  
Hearing Organ ◽  
Flexible Framework ◽  
Nonlinear Amplifiers ◽  
Output Behavior ◽  
Evaluation Platform

Abstract. Recently, nonlinear amplifiers based on the supercritical Andronov–Hopf bifurcation have become a focus of attention, especially in the modeling of the mammalian hearing organ. In general, to gain deeper insights in the input-output behavior, the analysis of bifurcation based amplifiers requires a flexible framework to exchange equations and adjust certain parameters. A DSP implementation is presented which is capable to analyze various amplifier systems. Amplifiers based on the Andronov–Hopf and Neimark–Sacker bifurcations are implemented and compared exemplarily. It is shown that the Neimark–Sacker system remarkably outperforms the Andronov–Hopf amplifier regarding the CPU usage. Nevertheless, both show a similar input-output behavior over a wide parameter range. Combined with an USB-based control interface connected to a PC, the digital framework provides a powerful instrument to analyze bifurcation based amplifiers.

scholarly journals Comparing global input-output behavior of frozen-equivalent LPV state-space models

2017 ◽  
Vol 50 (1) ◽  
pp. 9766-9771 ◽  
Author(s):  
Ziad Alkhoury ◽  
Mihály Petreczky ◽  
Guillaume Mercère
Keyword(s):  
State Space ◽  
State Space Models ◽  
Input Output ◽  
Output Behavior

A Lumped Parameter Electromechanical Model for Describing the Nonlinear Behavior of Piezoelectric Actuators

1997 ◽  
Vol 119 (3) ◽  
pp. 478-485 ◽  
Author(s):  
M. Goldfarb ◽  
N. Celanovic
Keyword(s):  
System Analysis ◽  
Nonlinear Behavior ◽  
Piezoelectric Actuators ◽  
Bond Graph ◽  
Lumped Parameter Model ◽  
Input Output ◽  
Mechanical Stiffness ◽  
Analysis And Design ◽  
Lumped Parameter ◽  
Proposed Model

A lumped-parameter model of a piezoelectric stack actuator has been developed to describe actuator behavior for purposes of control system analysis and design, and in particular for control applications requiring accurate position tracking performance. In addition to describing the input-output dynamic behavior, the proposed model explains aspects of nonintuitive behavioral phenomena evinced by piezoelectric actuators, such as the input-output rate-independent hysteresis and the change in mechanical stiffness that results from altering electrical load. Bond graph terminology is incorporated to facilitate the energy-based formulation of the actuator model. The authors propose a new bond graph element, the generalized Maxwell resistive capacitor, as a lumped-parameter causal representation of rate-independent hysteresis. Model formulation is validated by comparing results of numerical simulations to experimental data.

Design of Planar Large-Deflection Compliant Mechanisms With Decoupled Multi-Input-Output Using Topology Optimization

2019 ◽  
Vol 11 (3) ◽  
Author(s):  
Benliang Zhu ◽  
Qi Chen ◽  
Hai Li ◽  
Hongchuan Zhang ◽  
Xianmin Zhang
Keyword(s):  
Topology Optimization ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Geometrical Nonlinearity ◽  
Method Comparison ◽  
Output Coupling ◽  
Large Displacements ◽  
Interpolation Scheme ◽  
Input Output ◽  
Output Behavior

This paper presents a method for topology optimization of large-deflection compliant mechanisms with multiple inputs and outputs by considering the coupling issue. First, the objectives of the design problem are posed by modeling the output loads using several springs to enable control of the input–output behavior. Second, a scheme is proposed to obtain a completely decoupled mechanism. Both input coupling and output coupling are considered. Third, with the implementation of an energy interpolation scheme to stabilize the numerical simulations, the geometrical nonlinearity is considered to appropriately capture the large displacements of compliant mechanisms. Finally, several numerical examples are presented to demonstrate the validity of the proposed method. Comparison studies with the obtained results without considering the coupling issues are also presented.

A Design Method for Two-Degree-of-Freedom Simple Multi-Period Repetitive Control Systems

2010 ◽  
Vol 36 ◽  
pp. 243-252 ◽  
Author(s):  
Yoshinori Ando ◽  
Tatsuya Sakanushi ◽  
Kou Yamada ◽  
Iwanori Murakami ◽  
Takaaki Hagiwara ◽  
...  
Keyword(s):  
Control System ◽  
Control Systems ◽  
Transfer Functions ◽  
Design Method ◽  
Output Characteristic ◽  
Degree Of Freedom ◽  
Disturbance Attenuation ◽  
Input Output ◽  
Attenuation Characteristic ◽  
Two Degree Of Freedom

The multi-period repetitive (MPR) control system is a type of servomechanism for periodic reference inputs. Using MPR controllers, transfer functions from the reference input to the output and from the disturbance to the output of the MPR control system have infinite numbers of poles. To specify the input-output characteristic and the disturbance attenuation characteristic easily, Yamada and Takenaga proposed MPR control systems, named simple multi-period repetitive (simple MPR) control systems, where these transfer functions have finite numbers of poles. In addition, Yamada and Takenaga clarified the parameterization of all stabilizing simple MPR controllers. However, using the simple MPR repetitive controller by Yamada and Takenaga, we cannot specify the input-output characteristic and the disturbance attenuation characteristic separately. From the practical point of view, it is desirable to specify the input-output characteristic and the disturbance attenuation characteristic separately. The purpose of this paper is to propose the parameterization of all stabilizing two-degree-of-freedom (TDOF) simple MPR controllers that can specify the input-output characteristic and the disturbance attenuation characteristic separately.

Dynamic Modeling and Output Characteristic Analysis of a Micro Bistable Piezoelectric Generator

2015 ◽  
Vol 645-646 ◽  
pp. 995-1003
Author(s):  
Xin Hua Mao ◽  
Qing He ◽  
Ting Ting Huang
Keyword(s):  
Electromechanical Coupling ◽  
Low Frequency ◽  
Nonlinear Behavior ◽  
Output Characteristic ◽  
Electromechanical Coupling Coefficient ◽  
Transfer Model ◽  
Characteristic Analysis ◽  
System A ◽  
Low Frequency Vibration ◽  
Piezoelectric Generator

For effectively harvesting the broadband and low-frequency vibration energies in real environment, a micro bistable piezoelectric generator, without containing magnet, is designed. On the basis of analysis the nonlinear behavior of the stiffness, damping and the electromechanical coupling coefficient about the bistable vibration system, a precise mechanical-electric transfer model is built. The output characteristic of the piezoelectric generator is simulated and tested. The results showed that the piezoelectric generator can effectively harvest the broadband and low frequency vibration energies. And the output voltage can meet the electricity demand of a wireless sensor network node. The structure of the piezoelectric generator does not contain magnets, and it is easy to realize miniaturization and integration.

scholarly journals Nonlinear Input-Output Functions of Motoneurons

Physiology ◽  
2020 ◽  
Vol 35 (1) ◽  
pp. 31-39 ◽  
Author(s):  
Marc D. Binder ◽  
Randall K. Powers ◽  
C. J. Heckman
Keyword(s):  
Motor Control ◽  
Nonlinear Behavior ◽  
Comprehensive Model ◽  
Input Output ◽  
Persistent Inward Currents ◽  
Voltage Gated ◽  
Motor Commands ◽  
Nonlinear Input ◽  
Inward Currents

All movements are generated by the activation of motoneurons, and hence their input-output properties define the final step in processing of all motor commands. A major challenge to understanding this transformation has been the striking nonlinear behavior of motoneurons conferred by the activation of persistent inward currents (PICs) mediated by their voltage-gated Na+ and Ca2+ channels. In this review, we focus on the contribution that these PICs make to motoneuronal discharge and how the nonlinearities they engender impede the construction of a comprehensive model of motor control.

Data driven controller based on fuzzy rule adaptive network: with experimental validation

2019 ◽  
Vol 38 (6) ◽  
pp. 1782-1799
Author(s):  
Chidentree Treesatayapun
Keyword(s):  
Characteristic Curve ◽  
Tracking Error ◽  
Design Procedure ◽  
Output Characteristic ◽  
Data Driven ◽  
Superior Performance ◽  
Input Output ◽  
Output Data ◽  
Content Type ◽  
Experimental Systems

Purpose The purpose of this paper is to design an online-data driven adaptive control scheme based on fuzzy rules emulated network (FREN) for a class of unknown nonlinear discrete-time systems. Design/methodology/approach By using the input-output characteristic curve of controlled plant and the set of IF-THEN rules based on human knowledge inspiration, the adaptive controller is established by an adaptive FREN. The learning algorithm is established with convergence proof of the closed-loop system and controller’s parameters are directly designed by experimental data. Findings The convergence of tracking error is verified by the theoretical results and the experimental systems. The experimental systems and comparison results show that the proposed controller and its design procedure based on input-output data can achieve superior performance. Practical implications The theoretical aspect and experimental systems with the light-emitting diode (LED) current control and the robotic system prove that the proposed controller can be designed by using only input-output data of the controlled plants when the tracking error can be affirmed the convergence. Originality/value The proposed controller has been theoretically developed and used through experimental systems by using only input-output data of the controlled plant. The novel design procedure has been proposed by using the input-output characteristic curve for both positive and negative control directions.

The Design of a New Biaxial Decoupled Resonant Micro-Accelerometer

2013 ◽  
Vol 744 ◽  
pp. 466-469 ◽  
Author(s):  
Bo Yang ◽  
Hui Zhao ◽  
Bo Dai
Keyword(s):  
Basic Principle ◽  
Proof Mass ◽  
Mutual Interference ◽  
Scale Factor ◽  
Output Characteristic ◽  
Input Output ◽  
Simulation Results ◽  
Resonator Modes ◽  
Micro Accelerometer

A new biaxial decoupled resonant micro-accelerometer is researched. The new biaxial resonant micro-accelerometer consists of four same tuning forking resonators, four pair of decoupled beams, four lever mechanisms and a proof mass. The decoupling between two orthogonal axes is realized by the decoupling beams, which will benefit to isolate two axes acceleration detection. The simulation is implemented to verify the basic principle by the Ansys. The simulation results prove that the effective frequencies of two acceleration sensitive modes are 3.699 kHz and 3.718 kHz separately. Two pair of resonator modes which are 23.893 kHz, 23.946 kHz, 26.974 kHz and 26.999 kHz separately have about 3kHz difference in frequency in order to prevent the mutual interference. And the interference modes are isolated with effective mode apparently. The input-output characteristic simulation results indicate the y-axis scale factor is 57.1Hz/g and the coupling output in the x-axis is 0.0148Hz/g, while the x-axis scale factor is 56.1Hz/g and the coupling output in the y-axis is 0.0073Hz/g, which proves that the new biaxial resonant micro-accelerometer is practicable and has an excellent decoupled performance.

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