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.

scholarly journals Bond Graph Model of Cerebral Circulation: Toward Clinically Feasible Systemic Blood Flow Simulations

2020 ◽  
Author(s):  
Shan Su ◽  
Pablo J. Blanco ◽  
Lucas O. Müller ◽  
Peter J. Hunter ◽  
Soroush Safaei
Keyword(s):  
Cerebral Circulation ◽  
Graph Model ◽  
Bond Graph ◽  
The Body ◽  
Lumped Parameter Model ◽  
Desktop Computer ◽  
Detailed Model ◽  
Simulation Speed ◽  
Lumped Parameter ◽  
Proposed Model

The primary paper Safaei et al. (2018) proposed an anatomically detailed model of the human cerebral circulation that runs faster than real-time on a desktop computer and is designed for use in clinical settings when the speed of response is important. Based on a one-dimensional formulation of the flow of an incompressible fluid in distensible vessels, a lumped parameter model was developed for 218 arterial segments. The proposed model improved simulation speed by approximately 200-fold while preserved accuracy. Bond graph formulation was used to ensure mass and energy conservation. The model predicted the pressure and flow signatures in the body.

scholarly journals Bond Graph Model of Cerebral Circulation: Toward Clinically Feasible Systemic Blood Flow Simulations

2020 ◽  
Author(s):  
Shan Su ◽  
Pablo J. Blanco ◽  
Lucas O. Müller ◽  
Peter J. Hunter ◽  
Soroush Safaei
Keyword(s):  
Cerebral Circulation ◽  
Graph Model ◽  
Bond Graph ◽  
The Body ◽  
Lumped Parameter Model ◽  
Desktop Computer ◽  
Detailed Model ◽  
Simulation Speed ◽  
Lumped Parameter ◽  
Proposed Model

The primary paper Safaei et al. (2018) proposed an anatomically detailed model of the human cerebral circulation that runs faster than real-time on a desktop computer and is designed for use in clinical settings when the speed of response is important. Based on a one-dimensional formulation of the flow of an incompressible fluid in distensible vessels, a lumped parameter model was developed for 218 arterial segments. The proposed model improved simulation speed by approximately 200-fold while preserved accuracy. Bond graph formulation was used to ensure mass and energy conservation. The model predicted the pressure and flow signatures in the body.

scholarly journals Quantitative measure of hysteresis for memristors through explicit dynamics

2012 ◽  
Vol 468 (2144) ◽  
pp. 2210-2229 ◽  
Author(s):  
P. S. Georgiou ◽  
S. N. Yaliraki ◽  
E. M. Drakakis ◽  
M. Barahona
Keyword(s):  
Differential Equation ◽  
Analytical Solutions ◽  
Quantitative Measure ◽  
Explicit Solutions ◽  
Mathematical Framework ◽  
Input Output ◽  
Explicit Formulas ◽  
Hewlett Packard ◽  
Lumped Parameter ◽  
Proposed Model

We introduce a mathematical framework for the analysis of the input–output dynamics of externally driven memristors. We show that, under general assumptions, their dynamics comply with a Bernoulli differential equation and hence can be nonlinearly transformed into a formally solvable linear equation. The Bernoulli formalism, which applies to both charge- and flux-controlled memristors when either current or voltage driven, can, in some cases, lead to expressions of the output of the device as an explicit function of the input. We apply our framework to obtain analytical solutions of the i – v characteristics of the recently proposed model of the Hewlett–Packard memristor under three different drives without the need for numerical simulations. Our explicit solutions allow us to identify a dimensionless lumped parameter that combines device-specific parameters with properties of the input drive. This parameter governs the memristive behaviour of the device and, consequently, the amount of hysteresis in the i – v . We proceed further by defining formally a quantitative measure for the hysteresis of the device, for which we obtain explicit formulas in terms of the aforementioned parameter, and we discuss the applicability of the analysis for the design and analysis of memristor devices.

On the Nonlinear Behavior of Piezoelectric Actuators

2004 ◽  
Vol 10 (3) ◽  
pp. 387-398 ◽  
Author(s):  
M. Arafa ◽  
A. Baz
Keyword(s):  
Harmonic Balance ◽  
Linear Models ◽  
Mechanical Response ◽  
Piezoelectric Materials ◽  
Constitutive Relations ◽  
Primary Resonance ◽  
Nonlinear Behavior ◽  
Piezoelectric Actuators ◽  
Electrical Excitation ◽  
Lumped Parameter

In this paper we present a theoretical and experimental study of the nonlinear behavior of piezoelectric actuators. The nonlinearities are introduced as quadratic terms in the piezoelectric constitutive relations. These relations are employed, together with supporting experimental results, to establish an engineering description of the nonlinearities present in piezoelectric materials. We present a lumped-parameter representation of a system consisting of a piezoactuator driving a mass. The representation is valid in the vicinity of the primary resonance. The resulting nonlinear differential equation of motion is analyzed by the method of harmonic balance to study the effects of nonlinearities on the dynamics of forced vibrations. Experimental measurements of the steady-state mechanical response to harmonic electrical excitation over a range of excitation frequencies and amplitudes quantify the nature and level of nonlinear behavior. The nonlinear behavior, which is mainly evident around the resonant frequency, is shown to be of the softening type and becomes more pronounced at higher drive voltage levels. Numerical simulations based on the developed nonlinear model have shown significant improvement over previous linear models in predicting the experimental behavior of piezoelectric materials at the vicinity of primary resonance.

Bond Graph Models for Fluid Dynamic Systems

1972 ◽  
Vol 94 (3) ◽  
pp. 222-229 ◽  
Author(s):  
D. Karnopp
Keyword(s):  
Fluid Dynamic ◽  
Nonlinear Behavior ◽  
Bond Graph ◽  
Distributed Parameter ◽  
Graph Models ◽  
Modeling Process ◽  
Fluid Systems ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Control Volumes

The modeling process whereby distributed parameter fluid systems are described approximately by lumped parameter models is discussed using bond graph techniques. It is shown that despite the analogies which exist between some fluid systems and other physical systems, the lumping process for fluid systems introduces forms of nonlinear behavior not often encountered in other types of systems. Many such effects may be traced to the desire to use control volumes and Eulerian rather than Lagrangian descriptions of the fluid systems.

Effects of Bearing Radial Internal Clearance on Dynamic Behavior and Bifurcations in Planetary Gears

2011 ◽  
Author(s):  
Yi Guo ◽  
Robert G. Parker
Keyword(s):  
Dynamic Response ◽  
Harmonic Balance Method ◽  
Nonlinear Behavior ◽  
Nonlinear Effects ◽  
Lumped Parameter Model ◽  
Solution Stability ◽  
Planetary Gears ◽  
Gear Mesh ◽  
Bearing Clearance ◽  
Lumped Parameter

This study investigates the dynamics of planetary gears where nonlinearity is induced by bearing clearance. Lumped-parameter and finite element models of planetary gears with bearing clearance, tooth separation, and gear mesh stiffness variation are developed. The harmonic balance method with arc-length continuation is used to obtain the dynamic response of the lumped-parameter model. Solution stability is analyzed using Floquet theory. Rich nonlinear behavior is exhibited in the dynamic response, consisting of nonlinear jumps and a hardening effect induced by the transition from no bearing contact to contact. The bearings of the central members (sun, ring, and carrier) impact against the bearing races near resonance, which leads to coexisting solutions in wide speed ranges, grazing bifurcation, and chaos. Secondary Hopf bifurcation is the route to chaos. Input torque can significantly suppress the nonlinear effects caused by bearing clearance.

Analysis and Design of Cam-Driven Mechanisms With Nonlinearities

1973 ◽  
Vol 95 (3) ◽  
pp. 685-694 ◽  
Author(s):  
F. Y. Chen
Keyword(s):  
Computer Aided Design ◽  
Degrees Of Freedom ◽  
Lumped Parameter Model ◽  
Analysis Tool ◽  
Analysis And Design ◽  
Lumped Parameter ◽  
Method Of Solution ◽  
Parametric Studies ◽  
Rational Procedure ◽  
Aided Design

The cam-and-follower mechanism is represented by a lumped parameter model of finite degrees of freedom, in which nonlinear system parameters may be taken into account. An approximate dynamic analysis of the system excited by either functional or numerical form of the base motion of a cam is obtained. The method of solution which uses an interpolating polynomial for approximating the excitation function and mechanical quadrature for evaluating the convolution integral is well suited for computer programming. A digital computer program for analysis based on this scheme is developed. In order to utilize the analysis tool for design purposes, parametric studies are conducted, design stratagems are presented and a rational procedure of closed loop computer-aided design is outlined and discussed.

"Bond graph approach for input-output decoupling of linear MIMO systems with Derivative State Feedback"

2018 ◽  
Author(s):  
Christophe Sueur
Keyword(s):  
State Feedback ◽  
System Analysis ◽  
Mimo Systems ◽  
Bond Graph ◽  
State Feedback Control ◽  
Pole Placement ◽  
Control Law ◽  
Input Output ◽  
Placement Problem

"This paper presents a new solution for the well-known input-output decoupling problem of linear multivariable systems with a derivative state feedback control law. A simple solution to the pole placement problem is highlighted in the monovariable and multivariable cases with application to a mechanical system. Analysis up to control design are achieved structurally in the bond graph domain for the case study."

Lumped Parameter Modeling of Counterbalance Valves Considering the Effect of Flow Forces

2019 ◽  
Author(s):  
Annalisa Sciancalepore ◽  
Andrea Vacca ◽  
Oscar Pena ◽  
Steven T. Weber
Keyword(s):  
Controller Design ◽  
Complex Geometry ◽  
Control Volume ◽  
Analytical Description ◽  
Lumped Parameter Model ◽  
Hydraulic Control ◽  
Lumped Parameter ◽  
Proposed Model ◽  
Lumped Parameter Models ◽  
High Level

Abstract The lumped parameter approach based on equations describing of the physical behavior of the system still represents one of the most convenient way to simulate hydraulic control systems. The key advantages of this approach are given by its intrinsic simulation swiftness as well as the ease of deriving state space formulations for controller design purposes. However, the common limitation of lumped parameter models is the high level of simplification of for certain physical aspects. For the case of hydraulic control valves with complex geometry, the flow forces are usually one of the most difficult aspects to describe accurately. The present paper presents a lumped parameter model for counterbalance valves, which includes an accurate analytical approach to model the effect of the flow forces based acting on the valve poppet and piston. The model is based on a classic control volume scheme for the description of the flow through the valve, and it is coupled with a dynamic model for the descriptions of the motion of the moving parts inside the valve. The novelty of the proposed approach consists on the analytical description of the flow forces, which is based on fluid momentum considerations. After describing the modeling approach, the paper details the authors’ efforts for experimentally validate the model on the basis of tests performed on actual components. The comparison between simulation results and experimental data confirms the validity of the proposed model and also highlights the importance of accounting for flow forces while describing the operation of counterbalance valves, particularly for cases of high flow rates.

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