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... Micro-manipulator for medical application [67]; mechanical ventilation [68,69]; patient-robottherapist [70]; robot in telesurgery [71]; fluid resuscitation [72]; actuator for nanobiomedicine [73] In [69], a repetitive control design for Lurie-type SISO systems without delay (as Eq (3.1)) is applied to mechanical ventilation in intensive care unit, ensuring stable target pressure profile tracking. ...
... While these works use the term "absolute stability", further investigation is needed to determine their connection to the Lurie problem. In [73], the absolute stability conditions for control systems with electro magneto elastic actuators in nano-biomedicine are analyzed using frequency methods and Lyapunov's criterion. The Yankelovich criterion, extending Popov's criterion, is applied to account for the hysteresis nonlinearity of the actuators, simplifying the system's stability analysis. ...
This paper provided a review of the Lurie problem and its applications to control as well as modeling problems in the medical and biological fields, highlighting its connection with robust control theory, more specifically the works of Doyle, Skogestad, and Zhou. The Lurie problem involved the study of control systems with nonlinearities incorporated into the feedback loop. Providing a simpler and broader approach, this review returned to the Lurie problem, covering basic stability concepts and Aizerman's conjecture, establishing it as a special instance of the Lurie problem. The paper also explained the connection between the Lurie problem and robust control theory, which resulted in the establishment of new conditions for the Lurie problem. The principal contribution of this paper was a comprehensive review, utilizing the preferred reporting items for systematic reviews and meta-analyses (PRISMA) methodology of the applications of the Lurie problem in the medical and biological fields, demonstrating its significance in various domains such as medical device controllers, mechanical ventilation systems, patient-robot-therapist collaboration, tele-surgery, fluid resuscitation control, nanobiomedicine actuators, anesthesia systems, cardiac mechanics models, oncology cell dynamics, epidemiological models, diabetes modeling, population dynamics and neuroscience, including artificial neural networks (ANN). This article seeked to present the latest advancements in the Lurie problem, offering an update for researchers in the area and a valuable starting point for new researchers with several suggestions for future work, showcasing the importance of Lurie-type systems theory in advancing medical research and applications.
In this work, the parametric structural schematic diagrams of a multilayer electromagnetoelastic actuator and a multilayer piezoactuator for nanomechanics were determined in contrast to the electrical equivalent circuits of a piezotransmitter and piezoreceiver, the vibration piezomotor. The decision matrix equation of the equivalent quadripole of the multilayer electromagnetoelastic actuator was used. The structural-parametric model, the parametric structural schematic diagram, and the matrix transfer function of the multilayer electromagnetoelastic actuator for nanomechanics were obtained.
The generalized parametric structural schematic diagram, the generalized structural-parametric model, and the generalized matrix transfer function of an electromagnetoelastic actuator with output parameters displacements are determined by solving the wave equation with the Laplace transform, using the equation of the electromagnetolasticity in the general form, the boundary conditions on the loaded working surfaces of the actuator, and the strains along the coordinate axes. The parametric structural schematic diagram and the transfer functions of the electromagnetoelastic actuator are obtained for the calculation of the control systems for the nanomechanics. The structural-parametric model of the piezoactuator for the transverse, longitudinal, and shift piezoelectric effects are constructed. The dynamic and static characteristics of the piezoactuator with output parameter displacement are obtained.
Design and analysis of piezoelectric actuators having over 20% effective strain using an exponential strain amplification mechanism are presented in this paper. Piezoelectric ceramic material, such as lead zirconate titanate (PZT), has large stress and bandwidth, but its extremely small strain, i.e., only 0.1%, has been a major bottleneck for broad applications. This paper presents a new strain amplification design, called a “nested rhombus” multilayer mechanism, that increases strain exponentially through its hierarchical cellular structure. This allows for over 20% effective strain. In order to design the whole actuator structure, not only the compliance of piezoelectric material but also the compliance of the amplification structures needs to be taken into account. This paper addresses how the output force and displacement are attenuated by the compliance involved in the strain amplification mechanism through kinematic and static analysis. An insightful lumped parameter model is proposed to quantify the performance degradation and facilitate design tradeoffs. A prototype-nested PZT cellular actuator that weighs only 15 g has produced 21% effective strain (2.5 mm displacement from 12-mm actuator length and 30 mm width) and 1.7 N blocking force. ©2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. DOI: 10.1109/TMECH.2009.2034973
Structural-parametric models, parametric structural schematic diagrams and transfer functions of electromagnetoelastic actuators are determined. A generalized parametric structural schematic diagram of the electromagnetoelastic actuator is constructed. Effects of geometric and physical parameters of actuators and external load on its dynamic characteristics are determined. For calculations the mechatronic systems with piezoactuators for nano- and microdisplacement the parametric structural schematic diagrams and the transfer functions of piezoactuators are obtained.
This chapter introduces control methods for the single cellular actuator and cellular actuator arrays. Segmented binary control (SBC) is introduced to control an actuator array where one must compensate for the hysteresis in each actuator unit. This method enables the use of bistable, or ON–OFF, control for individual actuator units, resulting in a simpler controller. Because the rhomboidal strain amplification mechanisms consist of thin metallic members, bistable control can introduce mechanical vibration. This is a problem because there is little structural damping in the material, the frequencies are low enough (because of the low stiffness of the structure) to be within an order of magnitude of the frequencies of operation, and the amplitudes of oscillation in response to the impulsive activation of the piezoelectric stacks are significant. For smooth operation and reasonable cycle times of operation of robotic devices using this technology, a reliable compensation method is necessary. Discrete switching vibration suppression (DSVS) is a technique that strategically phases the activation of the driving piezoelectric stacks to limit or even eliminate vibration from point-to-point moves. Large arrays of cellular actuators can pose a different problem altogether; signal routing from the main controller becomes unwieldy and fault-prone. When an actuator array consists of a large number of cellular units, stochastic broadcast control is more effective than using deterministic control. In this architecture, each unit is an independent agent with access to a common control signal that is broadcast wirelessly to all agents, eliminating the need for each unit to have an address or wire associated with. Units are constantly entering and leaving the active state stochastically such that in the aggregate the actuator array produces the contraction desired. In order to facilitate faster response in binary controlled actuator units, a technique named Hysteresis Loop Control (HLC) is introduced. The stochastic broadcast technique can be combined with HLC to compensate for pronounced hysteresis.
We developed a structural-parametric models, obtained solution for the wave equation of electroelastic actuators and constructed their transfer functions. Effects of geometric and physical parameters of electroelastic actuators and external loading on their dynamic characteristics determined. For calculation of automatic control systems for nanometric movements with electroelastic actuators, we obtained the parametric structural schematic diagrams and the transfer functions of piezoactuators. Static and dynamic characteristics of piezoactuators determined.
The objective of this paper is to describe the mathematical modelling and numerical testing of the static
behaviour and natural frequency of a flexure hinge transducer. The actuator is constructed of two parallel
beams mounted by stiff links with an offset to a piezoceramic rod. A monolithic hinge lever mechanism is
applied by cutting constricted hinges at the links to generate and magnify the in-plane displacement created
by the application of a voltage to the piezorod. This mechanism enables the piezoelectric transducers
to amplify displacement efficiently. A non-linear analytical model of the actuator is developed on the
basis of Hamilton’s principle and solved with use of the perturbation method. During the numerical analysis,
the static deflection and internal axial force generated by the electric field application are determined
by changing actuator properties such as the distance between the beams and the rod as well as
the stiffness of the constricted hinges. It is shown that for the flextensional actuator with a very high
flexibility of constricted hinges, the generated transverse displacement is limited by the maximum
electric field as the characteristic property for each piezoceramic material. In the dynamic analysis, the
fundamental vibration frequency and the adequate modes are studied in relation to the piezoelectric
force. The natural vibration frequency, affected by the piezoelectric force, also depends on the stiffness
of the beam supports, the matched beam and rod materials, the ratio of the cross section of the rod to
the beam and the direction of the electric field.
To simplify the design of the linear ultrasonic motor (LUSM) and improve its output performance, a method of modal decoupling for LUSMs is proposed in this paper. The specific embodiment of this method is decoupling of the traditional LUSM stator¿s complex vibration into two simple vibrations, with each vibration implemented by one vibrator. Because the two vibrators are designed independently, their frequencies can be tuned independently and frequency consistency is easy to achieve. Thus, the method can simplify the design of the LUSM. Based on this method, a prototype modal- independent LUSM is designed and fabricated. The motor reaches its maximum thrust force of 47 N, maximum unloaded speed of 0.43 m/s, and maximum power of 7.85 W at applied voltage of 200 Vpp. The motor¿s structure is then optimized by controlling the difference between the two vibrators¿ resonance frequencies to reach larger output speed, thrust, and power. The optimized results show that when the frequency difference is 73 Hz, the output force, speed, and power reach their maximum values. At the input voltage of 200 Vpp, the motor reaches its maximum thrust force of 64.2 N, maximum unloaded speed of 0.76 m/s, maximum power of 17.4 W, maximum thrust¿weight ratio of 23.7, and maximum efficiency of 39.6%.
The use of nano- and micro-scale piezomotors in precision electromechanical systems is considered. The deformation of the piezoconverter corresponding to its stress state is investigated.
Block diagrams of a multilayer piezoelectric motor based on the longitudinal piezoelectric effect with account for the electromotive counterforce are designed. Transfer functions of the piezoelectric motor with regard to its geometric and physical parameters, electromotive counterforce, and external load are obtained.
A simple proof of the quadratic criterion for absolute stability is given for the nondegenerate case. A similar result was proved earlier (for both degenerate and nondegenerate cases) by the author (1967) by using completely different methods. The proof given has some similarities with the ideas used by Popov (1959-1961) in the proof of his now widely known frequency-domain criterion of absolute stability. The new frequency-domain criterion of absolute stability is given for the system with the periodic coefficient. One illustrative example is considered.
Piezoelectric actuators have been used successfully to enable locomotion in aerial and ambulatory microrobotic platforms. However, the use of piezoelectric actuators presents two major challenges for power electronic design: generating high-voltage drive signals in systems typically powered by low-voltage energy sources, and recovering unused energy from the actuators. Due to these challenges, conventional drive circuits become too bulky or inefficient in low mass applications. This work describes electrical characteristics and drive requirements of low mass piezoelectric actuators, the design and optimization of suitable drive circuit topologies, aspects of the physical instantiation of these topologies, including the fabrication of extremely lightweight magnetic components, and a custom, ultra low power integrated circuit that implements control functionality for the drive circuits. The principles and building blocks presented here enable efficient high-voltage drive circuits that can satisfy the stringent weight and power requirements of microrobotic applications.
This chapter highlights some recent advances in high resolution printing methods, in which a “stamp” forms a pattern of “ink” on the surface it contacts. It focuses on two approaches whose capabilities, level of development, and demonstrated applications indicate a strong potential for widespread use, especially in areas where conventional methods are unsuitable. The first of these, known as microcontact printing, uses a high resolution rubber stamp to print patterns of chemical inks, mainly those that lead to the formation of organic self-assembled monolayers (SAMs). These printed SAMs can be used either as resists in selective wet etching, or as templates in selective deposition to form structures of a variety of materials. The other approach, referred to as nanotransfer printing, uses similar high resolution stamps, but ones inked with solid thin film materials. In this case, SAMs, or other types of surface chemistries, bond these films to a substrate that the stamp contacts. The material transfer that results upon removal of the stamp forms a pattern in the geometry of the relief features, in a purely additive fashion. In addition to providing detailed descriptions of these micro/nanoprinting techniques, this chapter illustrates their use in some areas where these methods may provide attractive alternatives to more established lithographic methods. The demonstrator applications span fields as diverse as biotechnology (intravascular stents), fiber optics (tunable fiber devices), nanoanalytical chemistry (high resolution nuclear magnetic resonance), plastic electronics (paper-like displays), and integrated optics (distributed feedback lasers). The growing interest in nanoscience and nanotechnology motivates research and the development of new methods that can be used for nanofabricating the relevant test structures or devices. The attractive capabilities of the techniques described here, together with the interesting and subtle materials science, chemistry, and physics associated with them, make this a promising area for basic and applied study.
We study the compression diagrams and elastic compliances of composite piezoelectric transducers. We find the typical points
on the compression diagram which correspond to the mechanical stress of clearance cutting and smoothing the microroughnesses
and to the ultimate compression strength with crack formation on the edges of piezoelectric crystal plates. We construct mechanical
and adjusting characteristics of piezoelectric transducers and determine their static and dynamic characteristics.
The use of the solution to the wave equation to construct a generalized structural parametric model of an electromagnetoelastic transducer to determine the effect of its geometry and physical parameters is discussed. High-precision electromechanical drives are operated under working loads ensuring elastic strains of the executive device. Piezoelectric transducers are characterized by high piezoelectric moduli and they are frequently used to produce nanoscale displacements. The solution of the wave equation supplemented with the corresponding electromagnetoelasticity equation and boundary conditions on the transducer's two working surfaces allows to construct a structural parametric model of an electromagnetoelastic transducer. The transfer functions of a piezoelectric transducer are derived from its generalized structural parametric model and are obtained as the ratio of the Laplace transform of the transducer face displacement to the Laplace transform of the input electric parameter.
A study was conducted to prepare a structural parametric model of a pie piezoelectric nanodisplacement transducer. The structural parametric model was prepared to investigate the potential application of the piezoelectric transducer in the equipment of nanotechnology, microbiology, microelectronics, astronomy, for high-precision superposition, compensation, and wavefront correction. It was found that the piezoelectric transducer operates on the basis of the inverse piezoelectric effect, in which a displacement is due to the deformation of the piezoelectric element, caused by the application of an external electric voltage. The wave equations also needed to solved, to construct a structural parametric model of the voltage-controlled piezoelectric transducer.
Structural-parametric model of piezo actuator nano and micro displacement for nanoscience
- S M Afonin
Afonin SM (2017) Structural-parametric model of piezo actuator nano
and micro displacement for nanoscience. AASCIT Journal of Nanoscience
3(3): 12-18.
Solution wave equation and parametric structural schematic diagrams of electro magnetoelastic actuators nano-and micro displacement
- S M Afonin
Afonin SM (2016) Solution wave equation and parametric structural
schematic diagrams of electro magnetoelastic actuators nano-and
micro displacement. International Journal of Mathematical Analysis and
Applications 3(4): 31-38.
Parametric block diagrams of a multi-layer piezoelectric transducer of nano-and micro displacements under transverse piezoelectric effect
- S M Afonin
Afonin SM (2017) Parametric block diagrams of a multi-layer
piezoelectric transducer of nano-and micro displacements under
transverse piezoelectric effect. Mechanics of Solids 52(1): 81-94.
Electro magnetoelastic actuator for Nano mechanics
- S M Afonin
Afonin SM (2018) Electro magnetoelastic actuator for Nano mechanics.
Global Journal of Research in Engineering : A Mechanical and Mechanics
Engineering 18(2): 19-23.