Self-oscillating System Research Articles

Phototunable self-oscillating system driven by a self-winding fiber actuator

Self-oscillating systems that enable autonomous, continuous motions driven by an unchanging, constant stimulus would have significant applications in intelligent machines, advanced robotics, and biomedical devices. Despite efforts to gain self-oscillations have been made through artificial systems using responsive soft materials of gels or liquid crystal polymers, these systems are plagued with problems that restrict their practical applicability: few available oscillation modes due to limited degrees of freedom, inability to control the evolution between different modes, and failure under loading. Here we create a phototunable self-oscillating system that possesses a broad range of oscillation modes, controllable evolution between diverse modes, and loading capability. This self-oscillating system is driven by a photoactive self-winding fiber actuator designed and prepared through a twistless strategy inspired by the helix formation of plant-tendrils, which endows the system with high degrees of freedom. It enables not only controllable generation of three basic self-oscillations but also production of diverse complex oscillatory motions. Moreover, it can work continuously over 1270000 cycles without obvious fatigue, exhibiting high robustness. We envision that this system with controllable self-oscillations, loading capability, and mechanical robustness will be useful in autonomous, self-sustained machines and devices with the core feature of photo-mechanical transduction.

Multistability, quasiperiodicity and chaos in a self-oscillating ring dynamical system with three degrees of freedom based on the van der Pol generator

In this paper, we consider a self-oscillating ring system consisting of a nonlinear amplifier and a chain of three linear oscillators. The equations for this system are derived and the results of numerical simulations are presented. The inherent regimes of the self-oscillating system are studied versus the control parameters, and the results of bifurcation analysis are described. It was found that the addition of linear oscillators to the feedback loop of the classical van der Pol generator leads to the appearance of quasiperiodic and chaotic regimes, as well as the formation of multistability. The bifurcation mechanism of the multistability formation determined by two supercritical Andronov - Hopf bifurcations of the steady state and the subcritical Neimark - Sacker bifurcation of the saddle limit cycle is revealed. Transitions to chaos are investigated for each family of multistable states. Transition to chaos is observed through a sequence of doubling bifurcations of torus in a wide range of values of the control parameters.

The Choice of Criteria and Methods to Estimate the Quality of the Angular Sensor Based on the Effect of Nuclear Magnetic Resonance

To adjust the stabilization systems that ensure the operation of the angular position or rate sensor based on the effect of nuclear magnetic resonance, it is required to choose the criteria for the quality assessing of sensor’s operation. The article presents the criteria of the quality of the angular sensor operating as a self-oscillation system. It is shown that the accuracy of the angular sensor increases when the proposed criteria are met.

Динамика генератора с тремя контурами в цепи обратной связи. Формирование мультистабильности и переход к хаосу

Background and Objectives: Studying the dynamical mechanisms of the emergence of nonlinear phenomena that are characteristic for multimode self-oscillating systems consisting of interacting oscillators and an ensemble of passive oscillators or representing active nonlinear systems with complex feedback channels is an important urgent task. The simplest example of a self-oscillating system with a complex feedback is the well-known classical van der Pol oscillator with an additional linear oscillatory circuit included in the feedback channel. We investigate the behavior of the multimode system increasing the number of oscillatory circuits in the oscillator’s feedback loop. The research in this paper can help to better understand the mechanisms of multistability formation in infinite-dimensional self-oscillating systems such as a generator with delayed feedback and a generator with distributed feedback. Materials and Methods: The system equations were derived for the electronic scheme of the self-oscillating system. To describe the existing dynamic modes by numerical simulation methods, the projections of the phase portraits and the Poincare sections were obtained. To study the mechanisms of formation of multistable states, the bifurcation analysis methods were used. Results: It was found that the mechanism underlying the multistability formation is based on a sequence of two supercritical Andronov – Hopf bifurcations and a subcritical Neymark – Saker bifurcation. Therefore, the multistability emerges as a result of gaining stability by the unstable limit set that existed before the multistability appears. Conclusion: The discovered mechanism of multistability formation opens up wide possibilities for managing the multistability, which are inaccessible for systems in which the multistability is realized through tangential bifurcations. In contrast to the tangential bifurcation, the subcritical Neymark – Sacker bifurcation assumes the existence of a limit cycle both before and after the bifurcation. Thus, it is possible to use a wide range of methods and tools to stabilize saddle limit cycles in order to control the boundaries of the multistability region in the space of control parameters of the system.

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.

Designing self-oscillating matter

Designing self-oscillating matter

Self-Sustained Oscillation of a Photothermal-Responsive Pendulum under Steady Illumination

Self-sustained oscillation has the advantages of harvesting energy from the environment and self-control, and thus, the development of new self-oscillating systems can greatly expand its applications in active machines. In this paper, based on conventional photothermal shrinkable material or photothermal expansive material, a simple pendulum is proposed. The light-powered self-sustained oscillation of the simple pendulum is theoretically studied by establishing a dynamic model of the photothermal-responsive pendulum. The results show that there are two motion modes of the simple pendulum, which are the static mode and the oscillation mode. Based on the photothermal-responsive model, this paper elucidates the mechanism of the self-excited oscillation. The condition for triggering self-excited oscillation is further studied. In addition, the influence of the system parameters on the amplitude and frequency is also obtained. This study may have potential applications in energy harvesting, signal monitoring, and soft machines.

Quantum limit cycles and the Rayleigh and van der Pol oscillators

Self-oscillating systems, described in classical dynamics as limit cycles, are emerging as canonical models for driven dissipative nonequilibrium open quantum systems, and as key elements in quantum technology. We consider a family of models that interpolates between the classical textbook examples of the Rayleigh and the van der Pol oscillators, and follow their transition from the classical to the quantum domain, while properly formulating their corresponding quantum descriptions. We derive an exact analytical solution for the steady-state quantum dynamics of the simplest of these models, applicable to any bosonic system---whether mechanical, optical, or otherwise---that is coupled to its environment via single-boson and double-boson emission and absorption. Our solution is a generalization to arbitrary temperature of existing solutions for very-low, or zero, temperature, often misattributed to the quantum van der Pol oscillator. We closely explore the classical to quantum transition of the bifurcation to self-oscillations of this oscillator, while noting changes in the dynamics and identifying features that are uniquely quantum.

Swaying gel: chemo-mechanical self-oscillation based on dynamic buckling

<h2>Summary</h2> Self-oscillating systems are powerful tools for transducing static energy inputs into repetitive motions without the aid of external control units. The challenge in sustaining the far-from-equilibrium motion of an oscillating material is to avoid the tendency of reaching thermodynamic equilibrium or get pinned at steady states in the dynamic process. While living organisms present elegant strategies in myriad self-oscillations (e.g<i>.</i>, peristalsis, cilia motion, homeostasis), current synthetic self-oscillating systems often rely on a fast actuation/reaction, to maintain the far-from-equilibrium motion, which prescribe highly specific chemical reactions and a material microstructure with limited stimuli and movement modes. Here, we present a dynamic buckling-based design for creating self-oscillating systems. The oscillation arises from the self-driven snap-through of a responsive hydrogel between bi-/multi-stable buckling configurations governed by a feedback loop. With broad choices of materials, tunable mechanics, and physical simplicity, this system opens a new venue for unlimited autonomous-oscillating materials applications.

Optimization of transient processes of the pneumatic servo drive taking into account the friction model with the Stribeck effect

The aim of the work is to select the optimal values of the parameters of the digital PID controller to eliminate self-oscillations in systems, as well as to optimize the type of transient processes of the servo pneumatic drive. The reason for the study was the problem of the occurrence of self-oscillations in pneumatic systems when using friction models that are closest to reality. The scientific novelty of the article consists in the creation of a computer model and the application of optimization methods to improve the quality of transient processes of the pneumatic servo drive, taking into account the Striebeck friction model. The authors of the article optimized the transient processes of the pneumatic servo drive taking into account the selected friction model. The optimal parameters of the PID controller were selected using computer simulation. And the instability of the system was eliminated as well. To optimize the system performance, the gradient descent method was chosen. An assessment of the quality indicators of transient processes before and after optimization was made. Based on the simulation results of the pneumatic servo drive system, it can be concluded that the gradient descent method can be used to determine the parameters of the PID controller. The transition from an analog (continuous) system to a digital (discrete) system has been made It is necessary to determine the sampling period for its implementation. The article indicates the main methods for determining the sampling period and shows the disadvantages of these methods. Analysis of the results shows that the methods described in the article should be used only for the first approximation, and the value of the indicated quantity should be selected from the calculation of the minimum error between an analog (continuous) and digital (discrete) system. An error of less than 1% allows the selection of a programmable logic controller. The topic of the article is relevant for scientific research and includes the provision of practical recommendations for determining the parameters of a digital PID controller and selecting a controller for specialists who are inloved in the design of systems that include a pneumatic servo drive.

Method for Predicting the Stability Limit to Acoustic Oscillations in Liquid-Propellant Rocket Engine Combustion Chambers Based on Combustion Noise

An experimental method for determining the critical pressure perturbations leading to acoustic instability in combustion chambers of liquid-propellant rocket engines has been developed and used to estimate the stability of the working process. The method involves statistical processing of recorded noise pressure pulsations near the natural resonant frequency range for all normal modes of acoustic oscillations in cylindrical combustion chambers and gas generators. The oscillation damping coefficient (decrement), characterizing the difference between the generated and dissipated energy, is used as a diagnostic criterion for predicting the stable or unstable states of a dynamic system. The method is based on the theory of self-oscillating dynamic systems and one-dimensional Markov random processes using the Fokker–Planck–Kolmogorov equation. Analysis of a nonlinear differential equation with a symmetrized stochastic right-hand side describing white noise for experimentally determined amplitudes of pressure pulsations and their statistical processing using Mera software allows the state of self-oscillating systems to be identified as stable or unstable. The method is “passive;" it is applicable without using standard external impulse disturbing devices.

Smale-Williams solenoids in autonomous system with saddle equilibrium.

We construct an autonomous low-dimensional system of differential equations by replacement of real-valued variables with complex-valued variables in a self-oscillating system with homoclinic loops of a saddle. We provide analytical and numerical indications and argue that the emerging chaotic attractor is a uniformly hyperbolic chaotic attractor of Smale-Williams type. The four-dimensional phase space of the flow consists of two parts: a vicinity of a saddle equilibrium with two pairs of equal eigenvalues where the angular variable undergoes a Bernoulli map, and a region which ensures that the trajectories return to the origin without angular variable changing. The trajectories of the flow approach and leave the vicinity of the saddle equilibrium with the arguments of complex variables undergoing a Bernoulli map on each return. This makes possible the formation of the attractor of a Smale-Williams type in Poincaré cross section. In essence, our model resembles complex amplitude equations governing the dynamics of wave envelops or spatial Fourier modes. We discuss the roughness and generality of our scheme.

Study of Chaotic and Regular Modes of the Fractional Dynamic System of Selkov

The paper investigates the dynamic modes of the Sel’kov fractional self-oscillating system in order to simulate the interaction of cracks. The spectra of the maximum Lyapunov exponents, constructed depending on the parameters of the dynamic system, are used as a research tool. The maximum Lyapunov exponents were constructed according to the Benettin-Wolf algorithm. It is shown that the existence of chaotic regimes is possible. In particular, the spectrum of the maximum Lyapunov exponents of the order of the fractional derivative contains positive values, which indicates the presence of a chaotic regime. Phase trajectories were also constructed to confirm these results. It was also confirmed that the orders of fractional derivatives are responsible for dissipation in the system under consideration.

APPLICATION OF IMPACT THEORY TO ANALYSIS OF GEAR SHIFTS IN DUAL-CLUTCH TRANSMISSIONS

The article discusses a dynamic model of a transmission containing a dual-clutch gearbox. The absence of a torque converter in such gearboxes, taking into account the short duration of gear shifting (0.2 - 0.5 sec), allows us to present the gear shifting process as an impact. Gear shifting excites the output shaft of the gearbox. Thus, the transmission of the vehicle can beconsidered as a vibro-impact self-oscillating system.

Analytical approximation of a self-oscillatory reaction system using the Laplace-Borel transform

Abstract Time-symmetry breaking bifurcations cause an open system to generate complex structures/patterns, prompting the study of far-from-equilibrium and nonlinear thermodynamics. Specifically, thegeneration of self-organized chemical-wave patterns by the Belousov-Zhabotinsky reaction attractedattention from the academic community, assimilar structureswidely exist in the chemical/biological environment. However, theoretical fundamentals of these self-oscillatory structures are yet to be adequately addressed. This paper introducesa frequency-domain method for approximating the Belousov-Zhabotinskyreaction system.The nonlinear dynamics of the oscillator is estimated using the Laplace-Borel transform, which is an extension of the Laplace transform andutilizesfunctional expansions to approximate the nonlinear terms in the dynamic system.The method is applied to theBelousov-Zhabotinskyreaction model to yieldamplitude, frequency and stability characteristics near theAndronov-Hopf bifurcation points. By studying the emergence of self-oscillatory patternsusing this analytical method, new insights towardsfar-from-equilibrium and nonlinearthermodynamics are explored.

About mixed forced, parametric and self-oscillations by limited excitation and delayed elasticity

Mixed forced, parametric, and self-oscillations are considered if there is a delay in the elastic force in the system. A dynamic model is a friction self-oscillation system describing the frictional self-oscillations that occur in many technical systems for various purposes (metal-cutting machines, textile equipment, brakes and a number of other engineering objects). The operation of the system is supported by the energy source of limited power. For the analysis we used the method of straight linearization which is easier than the known methods of analysis of nonlinear systems, has no time-consuming and complex approximations of different orders, provides an opportunity to obtain the final design ratios regardless of the specific type and degree of nonlinearity, thus reducing labor costs and time by several orders of magnitude. By using this method, we obtained solutions of a nonlinear system of differential equations describing the system's motion. The equations of non-stationary and stationary movements are derived. To analyze the stability of stationary movements, the stability conditions based on the Routh-Hurwitz criteria are compiled. Calculations were performed to obtain information about the effect of delay on the oscillation modes. It is shown that the delay affects both the magnitude of the amplitude and the location of the amplitude-frequency curve in the frequency range depending on the magnitude of the delay, the amplitude curve is shifted to the region of lower frequencies. The stability of stationary oscillations depends both on the energy source characteristics and lag value. The interaction of the oscillating system and the energy source leads to a number of effects, both in the presence and absence of the lag. However, their course may be different depending on the lag value.

Construction and study of the system of differential equations that describes the mutual synchronization of coupled self-oscillating chemical systems

The article constructs and investigates the system of differential equations that describes the mutual synchronization of coupled self-oscillating chemical systems, defines the synchronization bar in which a synchronous mode exists and determines the time of establishment of the synchronous phase difference.

Scientific bases of creation and practical application of digital acoustic model of NPP with VVER

Created acoustic model of nuclear reactor is presented as self-oscillating system belonging to special class of nonlinear dissipative systems capable of generating undamped oscillations with parameters that don’t depend on the initial conditions and are determined only by the properties of the system itself. In open systems, such as coolant circuit, the energy increases over time due to negative friction (negative dissipation). It is known that self-organization, in which a wave order arises spontaneously from turbulent disorder, is possible due to the exchange of energy and mass with the environment, when dissipative losses are compensated from the outside. The creation of this model combined three fundamental scientific results: the Thomson-Kelvin formula for discharge of capacitor in 1853; the properties of acoustic resonator, formulated by Helmholtz in 1869; proof by the author in 1984 of validity of the use of the method of electroacoustic analogies for study of pulsating flows of single-phase and two-phase medium in the presence of negative friction. The acoustic model of nuclear reactor has no analogues in acoustics and is designed to predict, diagnose and prevent the occurrence of unwanted self-oscillations of coolant and resonances with fluctuations of nuclear fuel and equipment in operational and emergency modes.

Determination of Individual Parameters for the Model Mapping of a Boundary Curve in the Phase Diagram of a Stratifying Liquid Mixture

The properties of a model based on the analogy between binary stratifying liquid mixtures and coupled self-oscillating systems is studied. In this paper, an expression representing a curve mapping in the phase diagram of a binary system is derived. The mapping of a boundary curve is presented in the form of the dependence between the ratio of characteristic frequencies assigned to pure components and the mixture concentration. In the framework of this model, the temperature dependence of the squared ratio of frequencies $$({\nu}_{a}/{\nu}_{b})^{2}$$ is also determined. One important aspect of this model is that the temperature-dependent characteristic frequencies $$\nu_{a}$$ and $$\nu_{b}$$ reflect the properties of pure components (instead of solutions). The problem is posed of investigating the physical aspects of the model proposed in this paper in more detail. In the present study, it has been shown that the use of Pade approximants makes it possible to determine the character of the temperature dependence of each characteristic frequency separately on the basis of the temperature dependence derived by linking to experimental data for the ratio $$({\nu}_{a}/{\nu}_{b})^{2}$$ .

Determination of Self-Oscillations in Relay Control Systems

Abstract Some dynamical linear elements including on-off elements such as electro-mechanical relays and electronic components used in switching mode for some feedback control systems can present special features such as the capability to autonomously generate stable self-oscillations. This paper concerns the comparison of two approaches enabling to determine the frequency of self-oscillations in these systems. We examine Tsypkin’s approach which can provide analytical solutions to determining the frequency of existing self-oscillations. On the other hand, we examine the Describing Function (DF) approach which has been developed as an alternative to approximate these solutions. We will compare these two approaches for nonlinear systems of first and second orders. We will examine particularly the possibilities and limits of each approach for calculating the self-oscillations. Simulation of these systems will be performed to visualizes their behaviors. An experimental feedback control system based on electronic circuits used in switching mode has been built as a setup enabling testing and envisioning some applications.