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Signal Stabilization of Self-Oscillating Systems

The hunt (self-oscillations) of a physical system may often be removed by the introduction of an appropriate stabilizing signal which changed the open loop gain in a nonlinear manner. More generally, the performance of nonlinear systems in many cases may be improved by the introduction of extra signals. The theory of signal stabilization developed here extends the earlier work by Oldenburger and Liu involving an equivalent gain concept. It is shown that with the aid of the Fourier series the designer can determine the periodic signal to be inserted at one point in a loop to yield a desired stabilizing input to a nonlinear element in the loop. The use of sinusoidal and triangular inputs to a limiter are compared. An example where a limiter is the only nonlinearity is employed to illustrate the theory. The approach developed here explains experimental results previously reported by Oldenburger.

SELF-OSCILLATION↗

A synthesis theory for self-oscillating adaptive systems /SOAS/

A quantitative synthesis theory is presented for the Self-Oscillating Adaptive System (SOAS), whose nonlinear element has a static, odd character with hard saturation. The synthesis theory is based upon the quasilinear properties of the SOAS to forced inputs, which permits the extension of quantitative linear feedback theory to the SOAS. A reasonable definition of optimum design is shown to be the minimization of the limit cycle frequency. The great advantages of the SOAS is its zero sensitivity to pure gain changes. However, quasilinearity and control of the limit cycle amplitude at the system output, impose additional constraints which partially or completely cancel this advantage, depending on the numerical values of the design parameters. By means of narrow-band filtering, an additional factor is introduced which permits trade-off between filter complexity and limit cycle frequency minimization.

Horowitz, I.↗

Chemical pumps and flexible sheets spontaneously form self-regulating oscillators in solution

The synchronization of self-oscillating systems is vital to various biological functions, from the coordinated contraction of heart muscle to the self-organization of slime molds. Through modeling, we design bioinspired materials systems that spontaneously form shape-changing self-oscillators, which communicate to synchronize both their temporal and spatial behavior. Here, catalytic reactions at the bottom of a fluid-filled chamber and on mobile, flexible sheets generate the energy to “pump” the surrounding fluid, which also transports the immersed sheets. The sheets exert a force on the fluid that modifies the flow, which in turn affects the shape and movement of the flexible sheets. This feedback enables a single coated (active) and even an uncoated (passive) sheet to undergo self-oscillation, displaying different oscillatory modes with increases in the catalytic reaction rate. Two sheets (active or passive) introduce excluded volume, steric interactions. This distinctive combination of the hydrodynamic, fluid–structure, and steric interactions causes the sheets to form coupled oscillators, whose motion is synchronized in time and space. We develop a heuristic model that rationalizes this behavior. These coupled self-oscillators exhibit rich and tunable phase dynamics, which depends on the sheets’ initial placement, coverage by catalyst and relative size. Moreover, through variations in the reactant concentration, the system can switch between the different oscillatory modes. This breadth of dynamic behavior expands the functionality of the coupled oscillators, enabling soft robots to display a variety of self-sustained, self-regulating moves.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A synthesis theory for the externally excited adaptive system /EEAS/

The externally excited adaptive system (EEAS) is a two-degree-of-freedom feedback system with a nonlinearity which is saturated hard by an external periodic signal. Under certain conditions, the EEAS responds quasi-linearly to command and plant disturbance signals, permitting the development of a quantitative synthesis theory for satisfying system tolerances despite large plant uncertainty. The great advantage of the EEAS is its zero sensitivity to plant gain variations, a property it shares with the self-oscillating adaptive system (SOAS). The EEAS is, however, more flexible than the SOAS in satisfying the quasi-linearity constraints. The essential difference is that in the EEAS the loop transmission bandwidth is not rigorously tied to the 'carrier' signal, as it is in the SOAS. There is a class of problems for which the EEAS is superior to the purely linear system, which in turn is superior to the SOAS. The superiority of the EEAS over the SOAS is especially marked in the case of significant plant disturbances, which generally vitiate a SOAS design.

Horowitz, I. M.↗

Voltage regulator/amplifier is self-regulated

Signal modulated, self-regulating voltage regulator/amplifier controls the output b-plus voltage in modulated regulator systems. It uses self-oscillation with feedback to a control circuit with a discontinuous amplitude action feedback loop.

Day, W. E.↗

Self-Oscillating Inductive Boost Regulator

Improved voltage regulator designed for use in solar photovoltaic dc power system utilizing flywheel for energy storage. Includes self-oscillating inductive voltage-boosting circuit, which regulates withdrawal of energy from flywheel and motor/generator when output of solar cells insufficient to maintain load voltage at specified level of 150 Vdc. Features include optical coupling and rapid response.

Paulkovich, John↗

Part 2: Oscillations of elastic systems

Problems of oscillations of linear systems are discussed, including systems with a fractional number of degrees of freedom as well as free oscillations of a cantilever in the field of centrifugal forces. Four methods of solving the problem of the action of periodic instantaneous impulses are presented. The Tacoma catastrophe is analyzed and used as an example of aeroelastic oscillations. Problems of nonlinear system oscillations include the vibration maintenance of rotation, the Sommerfeld effect, and self-oscillations of a quasi-system with dry friction.

Source record↗

Self-oscillating synchronematic colloids

Self-oscillators that sustain periodic dynamics under constant input are ubiquitous in natural and engineered systems, where their interactions enable spatiotemporal coordination among many individual units. New forms of organization can emerge when these self-oscillating units are free to move and rotate, coupling their spatial arrangement and alignment with their oscillation frequencies and phases. Here, we report experiments and simulations on populations of Quincke colloids that behave as self-oscillating units with position, orientation, frequency, and phase. Depending on the initial distribution, these active oscillators spontaneously organize into distinct collective states characterized by temporal synchronization and directional alignment, which we term synchronematic order. In fluid-like clusters, this order is short-ranged and decays over a length scale set by the competition between hydrodynamic interactions and athermal noise. In crystalline clusters, these interactions drive flobal synchronization and circular alignment-synchronematic crystals-whose collective frequency increases with cluster size due to non-reciprocal interactions. Our results establish self-oscillating colloids as a model system for active oscillatory matter and reveal fundamental principles by which synchronization, alignment, and structure co-emerge, offering new pathways for designing adaptive, frequency-tunable materials.

colloids↗

Modeling and analysis of several classes of self-oscillating inverters. I - State-plane representations. II - Model extension, classification, and duality relationships

The present investigation is concerned with an important class of power conditioning networks, taking into account self-oscillating dc-to-square-wave transistor inverters. The considered circuits are widely used both as the principal power converting and processing means in many systems and as low-power analog-to-discrete-time converters for controlling the switching of the output-stage semiconductors in a variety of power conditioning systems. Aspects of piecewise-linear modeling are discussed, taking into consideration component models, and an equivalent-circuit model. Questions of singular point analysis and state plane representation are also investigated, giving attention to limit cycles, starting circuits, the region of attraction, a hard oscillator, and a soft oscillator.

Lee, F. C. Y.↗

Design of a Torque Current Generator for Strapdown Gyroscopes

The design, analysis, and experimental evaluation of an optimum performance torque current generator for use with strapdown gyroscopes, is presented. Among the criteria used to evaluate the design were the following: (1) steady-state accuracy; (2) margins of stability against self-oscillation; (3) temperature variations; (4) aging; (5) static errors drift errors, and transient errors, (6) classical frequency and time domain characteristics; and (7) the equivalent noise at the input of the comparater operational amplifier. The DC feedback loop of the torque current generator was approximated as a second-order system. Stability calculations for gain margins are discussed. Circuit diagrams are shown and block diagrams showing the implementation of the torque current generator are discussed.

Mcknight, R. D.↗

Stochastic thermodynamic cycles of a mesoscopic thermoelectric engine

Here, we analyze a steady-state thermoelectric engine, whose working substance consists of two capacitively coupled quantum dots. One dot is tunnel-coupled to a hot reservoir serving as a heat source, the other one to two electrically biased reservoirs at a colder temperature, such that work is extracted under the form of a steady-state current against the bias. In single realizations of the dynamics of this steady-state engine autonomous, four-stroke cycles can be identified. The cycles are purely stochastic, in contrast to mechanical autonomous engines which exhibit self-oscillations. In particular, these cycles fluctuate in direction and duration and occur in competition with other spurious cycles. Using a stochastic thermodynamic approach, we quantify the cycle fluctuations and relate them to the entropy produced during individual cycles. We identify the cycle mainly responsible for the engine performance and quantify its statistics with tools from graph theory. We show that such stochastic cycles are made possible because the work extraction mechanism is itself stochastic instead of the periodic time dependence in the working-substance Hamiltonian which can be found in conventional mechanical engines. Our investigation brings new perspectives about the connection between cyclic and steady-state engines.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Optomechanical interaction in fibre lasers with micro-optomechanical resonance structures

We report the results of studies of fibre lasers with passive modulators based on light-excited micro-optomechanical resonance structures (micro-oscillators). It is shown that in fibre lasers based on active fibres doped with rare-earth elements (Er, Er/Yb, Yb, Nd), the optomechanical interaction of laser radiation with micro-oscillators of various types (fibre-optic, microvolume) leads to self-oscillations of the characteristics of laser radiation at frequencies of relaxation oscillations and intermode beats synchronised with the frequencies of elastic eigenoscillations of micro-oscillators. It is found that in an ultra-long erbium – ytterbium fibre laser with a nonlinear mirror based on a microcantilever, laser photothermal excitation of the second mode of elastic transverse oscillations of the microcantilever makes it possible to perform passive mode locking exclusively due to Q-switching of the laser cavity. Pulsed lasing with a controlled repetition rate (∼76 kHz), a pulse duration of 2 – 5 μs and an output energy of 0.1 μJ per pulse is implemented. Based on a simplified physical model of the indicated fibre lasers with micro-oscillators, we have developed an approximate mathematical model describing the regimes of passive mode locking of fibre lasers with micro-oscillators that play the role of mirrors with a nonlinear reflection coefficient in the laser cavity. The prospects for the development and application of the considered laser systems are discussed. (control of laser radiation parameters)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Phase-field model of coupled insulator-metal transitions and oxygen vacancy redox reactions

A predominant ubiquitous feature of strongly correlated oxides is the possible presence of oxygen vacancies, which has recently been shown to have profound effects on their electronic phase transitions. Here, we formulate a comprehensive phase-field model of intercoupled insulator-metal transitions and oxygen vacancy redox reactions, taking into account the valence electron state of oxygen vacancies. We use the model to study the voltage self-oscillation phenomenon in a prototypical strongly correlated oxide, VO 2 , and discover the mutual activation of the insulator-metal transition and oxygen vacancy redox reactions leading to systematic enhancement of the oscillation frequency. Furthermore, the established methodology and the mutual activation mechanism are generally applicable to understanding any insulator-metal transition dynamics in oxygen-deficient correlated oxides and improving the performance of voltage self-oscillation-based artificial neurons.

36 MATERIALS SCIENCE↗