The Mathematical Algorithm for Analysis of Piezoelectric Stacks with Structural Damping

2015 ◽  
Vol 220-221 ◽  
pp. 385-390
Author(s):  
Andrzej Buchacz ◽  
Marek Płaczek ◽  
Andrzej Wróbel
Keyword(s):  
Piezoelectric Materials ◽  
Piezoelectric Transducers ◽  
Structural Damping ◽  
Electrical Parameters ◽  
Mathematical Algorithm ◽  
System A ◽  
Effective Operation ◽  
The Matrix ◽  
Piezoelectric Stacks ◽  
Voigt Model

The work presents a proposal of mathematical algorithm developed for analysis of piezoelectric stacks that consist of classical PZT piezoelectric transducers. The considered systems vibrate longitudinally. Piezoelectric plates are combined in order to obtain multiplied displacement of the system and ensure more effective operation. Using constitutive equations of piezoelectric materials and an equation of the single plate’s motion, a matrix of characteristics of the system was obtained. The matrix of characteristics consists of relations between mechanical and electrical parameters (forces, displacements, electric current and voltage) that describe behaviour of the system. A structural damping of the plate’s material was being taken into consideration using Kelvin-Voigt model of material and its influence on the plate’s dynamic flexibility was analyzed [1, 2]. A dynamic flexibility – relation between the plate’s deformation and a force applied to the system is considered. Using the obtained dependences and non-classical methods, characteristics of piezoelectric stacks were designated and presented on charts. The obtained results were juxtaposed with characteristics of the system without structural damping.

Dynamic Characteristics of a Piezoelectric Transducer with Structural Damping

2013 ◽  
Vol 198 ◽  
pp. 633-638 ◽  
Author(s):  
Marek Płaczek
Keyword(s):  
Piezoelectric Transducer ◽  
Piezoelectric Materials ◽  
Research Centre ◽  
Structural Damping ◽  
Mechatronic Systems ◽  
Mathematical Algorithm ◽  
Analysis And Synthesis ◽  
The Matrix ◽  
Piezoelectric Stacks ◽  
Future Work

Work presents a proposal of an analysis method of the piezoelectric transducer. The considered system is a longitudinally vibrating single PZT plate. The main aim of this work is to designate characteristics of the considered PZT plate. Using constitutive equations of piezoelectric materials and an equation of the plates motion a matrix of characteristics of the system was obtained. Relations between mechanical and electrical parameters (forces, displacements, electric current and voltage) that describe behaviour of the system are included in the matrix of characteristics. A dynamic flexibility relation between the plates deformation and a force applied to the system is considered. A structural damping of the plates material was being taken into consideration and its influence on the plates dynamic flexibility is analysed. This work is an introduction to a task of analysis of complex systems. In future work the developed model and proposed mathematical algorithm will be used to analyse piezoelectric stacks. Non-classical methods will be used. It is a part of research works of Gliwice research centre related with an analysis and synthesis of mechanical and mechatronic systems [4-7,9,10,16-18]. Passive and active mechanical and mechatronic systems with piezoelectric transducers were analysed [1-3]. Works were also supported by computer-aided methods [8]. Both classical and non-classical methods were being considered. The discussed subject is important due to increasing number of applications of both simple and reverse piezoelectric phenomena in various modern technical devices.

A survey of control strategies for simultaneous vibration suppression and energy harvesting via piezoceramics

2012 ◽  
Vol 23 (18) ◽  
pp. 2021-2037 ◽  
Author(s):  
Ya Wang ◽  
Daniel J Inman
Keyword(s):  
Energy Dissipation ◽  
Energy Harvesting ◽  
Vibration Control ◽  
Active Control ◽  
Vibration Suppression ◽  
Piezoelectric Materials ◽  
Control Strategies ◽  
Piezoelectric Transducers ◽  
Control Methods ◽  
Structural Damping

This article presents a summary of passive, semipassive, semiactive, and active control methods for schemes using harvested energy as the main source of energy to suppress vibrations via piezoelectric materials. This concept grew out of the fact that energy dissipation effects resulting from energy harvesting can cause structural damping. First, the existing equivalent electromechanical modeling methods are reviewed for vibration-based energy harvesters using piezoelectric transducers. Modeling of base excitation cantilever beam ranges from lumped to distributed parameter formulations. The commonly used electrical power conditioning circuits and their optimization are also summarized and discussed. The energy dissipation from harvesting induces structural damping, and this leads to the concept of purely passive shunt damping. This article reviews the literature on vibration control laws along the lines of purely passive, semipassive, semiactive, and active control. The classification of pervious results is built on whether external power is supplied to the piezoelectric transducers. The focus is placed on recent articles investigating semipassive and semiactive control strategies derived from synchronized switching damping. However, whether or not the harvested energy is large enough to satisfy a vibration suppression requirement has become an important topic of research but has not yet specifically been addressed in previous studies. Hence, this survey also reviews the possible control methods aiming for less control energy consumption and addresses the potential application for simultaneous vibration control and energy harvesting.

scholarly journals The Meaning of the Matrix: Towards a Cybernetic Critical Theory of Capitalism

2018 ◽  
Vol 6 (1) ◽  
pp. 1
Author(s):  
Shay Hershkovitz
Keyword(s):  
Social Systems ◽  
Theoretical Concept ◽  
Social Actors ◽  
System A ◽  
The Social ◽  
Social Entity ◽  
Key Concepts ◽  
The Matrix ◽  
Critical Approaches ◽  
Operational Logic

Marxist criticism is most discernible; despite the oft-repeated claim that it is now irrelevant, belonging to an age now past. This essay assumes that criticism originating in the Marxist school of thought continue to be relevant also in this present time; though it may need to be further developed and improved by integrating newer critical approaches into the classic Marxist discourse. This essay therefore integrates basic Marxist ideas with key concepts from ‘social systems theory’; especially the theory of the German sociologist Niklas Luhmann's. In this light, capitalism is conceptualized here as a ‘super (social) system’: a meaning-creating social entity, in which social actors, behaviors and structures are realized. This theoretical concept and terminology emphasizes the social construction of control and stability, when discussing the operational logic of capitalism.

Nonlinear Vibrations of Viscoelastic Plane Truss Under Harmonic Excitation

2014 ◽  
Vol 14 (04) ◽  
pp. 1450009 ◽  
Author(s):  
Andrew Yee Tak Leung ◽  
Hong Xiang Yang ◽  
Ping Zhu
Keyword(s):  
Steady State ◽  
Fractional Derivatives ◽  
Harmonic Excitation ◽  
Homotopy Continuation ◽  
Response Curves ◽  
System A ◽  
Structural Responses ◽  
Voigt Model ◽  
Two Degree Of Freedom ◽  
Steady State Solutions

This paper is concerned with the steady state bifurcations of a harmonically excited two-member plane truss system. A two-degree-of-freedom Duffing system having nonlinear fractional derivatives is derived to govern the dynamic behaviors of the truss system. Viscoelastic properties are described by the fractional Kelvin–Voigt model based on the Caputo definition. The combined method of harmonic balance and polynomial homotopy continuation is adopted to obtain steady state solutions analytically. A parametric study is conducted with the help of amplitude-response curves. Despite its seeming simplicity, the mechanical system exhibits a wide variety of structural responses. The primary and sub-harmonic resonances and chaos are found in specific regions of system parameters. The dynamic snap-through phenomena are observed when the forcing amplitude exceeds some critical values. Moreover, it has been shown that, suppression of undesirable responses can be achieved via changing of viscosity of the system.

scholarly journals CONSTRUCTION OF MINIMAX CONTROL FOR ALMOST CONSERVATIVE CONTROLLED DYNAMIC SYSTEMS WITH THE LIMITED PERTURBATIONS

2017 ◽  
Vol 2 ◽  
pp. 9-15
Author(s):  
Iryna Svyatovets
Keyword(s):  
Riccati Equation ◽  
Infinite System ◽  
Conservative System ◽  
Coefficient Matrix ◽  
Necessary Condition ◽  
Existence Of A Solution ◽  
Minimax Control ◽  
System Of Matrix Equations ◽  
System A ◽  
The Matrix

The problem is considered for constructing a minimax control for a linear stationary controlled dynamical almost conservative system (a conservative system with a weakly perturbed coefficient matrix) on which an unknown perturbation with bounded energy acts. To find the solution of the Riccati equation, an approach is proposed according to which the matrix-solution is represented as a series expansion in a small parameter and the unknown components of this matrix are determined from an infinite system of matrix equations. A necessary condition for the existence of a solution of the Riccati equation is formulated, as well as theorems on additive operations on definite parametric matrices. A condition is derived for estimating the parameter appearing in the Riccati equation. An example of a solution of the minimax control problem for a gyroscopic system is given. The system of differential equations, which describes the motion of a rotor rotating at a constant angular velocity, is chosen as the basis.

Leontev Input-Output Balance Model as a Dynamic System Control Problem

2021 ◽  
pp. 66-82
Author(s):  
S.N. Masaev
Keyword(s):  
Dynamic System ◽  
Matrix Representation ◽  
External Environment ◽  
Balance Model ◽  
System Control ◽  
Operational Mode ◽  
Input Output ◽  
System A ◽  
The Matrix ◽  
Research Show

The purpose of the study was to determine the problem of control of a dynamic system of higher dimension. Relying on Leontev input-output balance, we formalized the dynamic system and synthesized its control. Within the research, we developed a mathematical model that combines different working objects that consume and release various resources. The value of the penalty for all nodes and objects is introduced into the matrix representation of the problem, taking into account various options for their interaction, i.e., the observation problem. A matrix representation of the planning task at each working object is formed. For the formed system, a control loop is created; the influencing parameters of the external environment are indicated. We calculated the system operational mode, taking into account the interaction of the nodes of objects with each other when the parameters of the external environment influence them. Findings of research show that in achieving a complex result, the system is inefficient without optimal planning and accounting for the matrix of penalties for the interaction of nodes and objects of the dynamic system with each other. In a specific example, for a dynamic system with a dimension of 4.8 million parameters, we estimated the control taking into account the penalty matrix, which made it possible to increase the inflow of additional resources from the outside by 2.4 times from 130 billion conv. units up to 310 conv. units in 5 years. Taking into account the maximum optimization of control in the nodes, an increase of 3.66 times in the inflow of additional resources was ensured --- from 200.46 to 726.62 billion rubles

Sliding mode observer based hysteresis compensation control for piezoelectric stacks

2020 ◽  
Vol 42 (14) ◽  
pp. 2760-2770
Author(s):  
Jiaming Hu ◽  
Xiaojin Zhu ◽  
Yubin Fang ◽  
Zhiyuan Gao ◽  
Yijia Zhou
Keyword(s):  
Sliding Mode ◽  
Piezoelectric Materials ◽  
External Disturbance ◽  
Linear Matrix ◽  
Observation Error ◽  
Hysteresis Compensation ◽  
Compensation Control ◽  
Hysteretic Effect ◽  
Practical Engineering ◽  
Piezoelectric Stacks

Piezoelectric stacks (PS) are wildly used as actuator mechanism for precise instrument in practical engineering. Nevertheless, hysteretic effect that is carried by the piezoelectric materials can degrade the control performance dramatically. For the purpose of improving the control precision, the problem of hysteresis compensation control for PS system is investigated in this paper. First, in order to compensate the hysteretic effect, two kinds of observers are proposed. The design of the observers has considered external disturbance and the creep effect in PS system. By utilizing Lyapunov function and linear matrix inequalities (LMI) technique, the observers can asymptotically estimate the hysteretic output with [Formula: see text] performance. Second, a hysteresis-compensation based back-stepping controller is established. The design of the controller has considered the observation error, and it has a certain robustness. At last, numerical and experimental simulations are carried out to verify the effectiveness of the proposed methods.

The use of a silica-based heat sink to “uncouple” the matrix-assisted laser desorption/ionization (MALDI) mechanism

2011 ◽  
Vol 89 (4) ◽  
pp. 446-460 ◽  
Author(s):  
E. Lourantos ◽  
O. M. Ramirez ◽  
A. E. Giannakopulos ◽  
K. A. Beran ◽  
Peter J. Derrick ◽  
...  
Keyword(s):  
Gas Phase ◽  
Heat Sink ◽  
Model System ◽  
Model Systems ◽  
Laser Desorption Ionization ◽  
System A ◽  
The Matrix ◽  
Pass Through ◽  
Maldi Mechanism ◽  
Silicon Based

The relationships between ion yield(s) as a function of desorption alone and (or) ionization was investigated using two model systems. In the first model system, a carbohydrate (2,3,6-tri-O-methyl-β-cyclodextrin, TMBCD), which could be directly laser desorbed, was analyzed with and without a silicon-based heat sink compound (HSC). The HSC allowed heat to pass through but obstructed the flow of charge. In the second model system, a peptide (substance P), which ccould not be laser desorbed, was analyzed under similar conditions. The ion yield of TMBCD under either system of heat conductivity was similar, whereas the ion yield of the peptide with the heat sink was negligible. Compounds that are predominately cationized either in the gas phase or preformed in solution give an ion yield that is not dependent upon the surface conditions, whereas compounds that are not ordinarily cationized are affected by the emission of electrons from the metal surface.

A Comparative Study of Actively Controlled and Shunted Piezoelectric Materials for Structural Damping

2007 ◽  
Author(s):  
Mehdi Ahmadian
Keyword(s):  
Active Control ◽  
Piezoelectric Materials ◽  
Structural Vibration ◽  
Structural Damping ◽  
Test Plate ◽  
Plate Vibrations ◽  
Positive Position Feedback ◽  
Position Feedback ◽  
Control Authority ◽  
Circuit Technique

A comparison between actively-controlled piezoelectric (PZT) material with positive position feedback (PPF) and a parallel resistor-inductor shunt circuit technique is provided. This study focuses on the performance of each technique at reducing structural vibration on a test plate for both narrowband and broadband frequency reductions. The comparison between the shunted and active PZT damping techniques used in this study shows that active control with positive position feedback was more effective at controlling vibrations of a test plate. The active PZT method was able to add damping to each of the modes targeted in the frequency range of interest. In addition, active control with positive position feedback was able to achieve this level of control authority with a single PZT patch located in the center of the test plate. Conversely, shunted PZTs used three PZT actuators to reduce the test plate vibrations. The results show that actively-controlled PZTs can provide much more damping per square area of PZT than shunted PZTs, by as much as four times more.

Characterization of Piezoelectric Materials for Thermoacoustic Power Transduction

2008 ◽  
Author(s):  
A. Wekin ◽  
C. Richards ◽  
K. Matveev ◽  
M. Anderson
Keyword(s):  
Experimental Study ◽  
Piezoelectric Materials ◽  
Electrical Power ◽  
Power Production ◽  
Piezoelectric Transducers ◽  
Maximum Power ◽  
Small Scale ◽  
Thermoacoustic Engine ◽  
Thermoacoustic Engines

In this work an experimental study of the performance of piezoelectric transducers for power production from a small-scale thermoacoustic engine is presented. Four piezoelectric samples are identified and characterized. These samples are tested on a variable acoustic driver and electrical power produced is measured. Finally, the samples are tested on four experimental thermoacoustic engines to verify the results from the acoustic setup. The maximum power produced is 177 μW from a closed thermoacoustic engine coupled to a 15mm PZT disk.

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