Sustained Oscillations Research Articles

Computational Methods for Nonlinear Analysis of Hopf Bifurcations in Power System Models

Hopf bifurcations can occur in power systems when a system mode experiences low damping because of changes in system operating conditions and they can lead to the emergence of limit cycles and oscillations. There are two types of Hopf bifurcations, namely, supercritical and subcritical, and they are determined by the sign of a cubic normal form coefficient. This paper discusses the two types of Hopf phenomena in test power system models where both types could be seen under changes in system and control parameters. The paper proposes an efficient computational method for carrying out the higher-order center manifold and normal form calculations for a general power system model and discusses the implications of the normal form coefficients for power system dynamics. Distinguishing between subcritical versus supercritical is important since they lead to very different types of oscillatory phenomena, divergence versus sustained oscillations, respectively.

Cascaded Control for Building HVAC Systems in Practice

Actuator hunting is a widespread and often neglected problem in the HVAC field. Hunting is typically characterized by sustained or intermittent oscillations, and can result in decreased efficiency, increased actuator wear, and poor setpoint tracking. Cascaded control loops have been shown to effectively linearize system dynamics and reduce the prevalence of hunting. This paper details the implementation of cascaded control architectures for Air Handling Unit chilled water valves at three university campus buildings. A framework for implementation the control in existing Building Automation software is developed that requires only a single line of additional code. Results gathered for more than a year show that cascaded control not only eliminates hunting in control loops with documented hunting issues, but provides better tracking and more consistent performance during all seasons. A discussion of efficiency losses due to hunting behavior is presented and illustrated with comparative data. Furthermore, an analysis of cost savings from implementing cascaded chilled water valve control is presented. Field tests show 2.2–4.4% energy savings, with additional potential savings from reduced operational costs (i.e., maintenance and controller retuning).

Computational modeling predicts regulation of central pattern generator oscillations by size and density of the underlying heterogenous network.

Central pattern generators are characterized by a heterogeneous cellular composition, with different cell types playing distinct roles in the production and transmission of rhythmic signals. However, little is known about the functional implications of individual variation in the relative distributions of cells and their connectivity patterns. Here, we addressed this question through a combination of morphological data analysis and computational modeling, using the pacemaker nucleus of the weakly electric fish Apteronotus leptorhynchus as case study. A neural network comprised of 60-110 interconnected pacemaker cells and 15-30 relay cells conveying its output to electromotoneurons in the spinal cord, this nucleus continuously generates neural signals at frequencies of up to 1kHz with high temporal precision. We systematically explored the impact of network size and density on oscillation frequencies and their variation within and across cells. To accurately determine effect sizes, we minimized the likelihood of complex dynamics using a simplified setup precluding differential delays. To identify natural constraints, parameter ranges were extended beyond experimentally recorded numbers of cells and connections. Simulations revealed that pacemaker cells have higher frequencies and lower within-population variability than relay cells. Within-cell precision and between-cells frequency synchronization increased with the number of pacemaker cells and of connections of either type, and decreased with relay cell count in both populations. Network-level frequency-synchronized oscillations occurred in roughly half of simulations, with maximized likelihood and firing precision within biologically observed parameter ranges. These findings suggest the structure of the biological pacemaker nucleus is optimized for generating synchronized sustained oscillations.

Plasma instability in graphene field-effect transistors with a shifted gate

We present detailed numerical analysis of the Dyakonov–Shur (DS) plasma instability in a DC biased graphene field-effect transistor (FET) with the gate shifted with respect to the middle of the transistor conducting channel. We show that the geometric asymmetry is sufficient to trigger the DS instability in the two-dimensional electron gas in the transistor channel. We demonstrate sustained plasma oscillations in the instability end point and analyze the properties of these oscillations for different positions of the gate and at different values of other physical and geometric FET parameters. The obtained results show the possibility of designing a tunable on-chip source of terahertz electromagnetic radiation based on the graphene FET with shifted gate.

Parameterization of voice onset for automatic assessment of Parkinson’s disease

Acoustic analysis of Parkinson’s disease (PD) usually focuses on sustained oscillations of the vocal folds; however, the voice onset (transition from the rest state to a saturation value) is often neglected. In this study, we investigated the parameterization of the voice onset for the objective evaluation of PD. 50 PD patients (25 females) and 50 healthy controls (25 females) performed the sustained phonation of the vowels /ah/, /ih/, and /uh/. Three experts listened to the recordings and assessed the dysarthria level according to a modified version of the Frenchay dysarthria assessment scale (mFDA). We extracted the voice onset automatically, considering the time needed for the amplitude envelope of the acoustic signal to go from 10% up to 90% of the maximum value. Then, we computed filter bank features from the voice onset and pitch, loudness, and perturbation features from the sustained phonation. We performed automatic classification and regression analyses using support vector machines. We obtained a classification accuracy of 89% (AUC: 0.93) when we used feature importance analysis to reduce the feature set. In addition, the regression analysis showed a significant correlation (r: 0.583, p-value < 0.001) between the acoustic features and the mFDA scale. These results show the suitability of the voice onset for objective clinical evaluation of PD.

Broad tunable photonic microwave signal generation using optically-injected 1310 nm spin-VCSELs

We theoretically propose and demonstrate photonic microwave signal generation with a very broad tunability range from below 2.5 GHz to around 100 GHz. The proposed scheme is based on sustained oscillation dynamics produced in spin-VCSELs under right circularly polarized optical injection. The generated microwave frequencies can be tuned by detuning the frequency of the optical injection signal. The system also takes the advantage of polarization switching phenomena to generate broader microwave frequencies where the generated frequencies are equal to the sum of the absolute detuning frequency and the birefringence split between the spin-VCSEL modes which is 47.7 GHz. Sustained oscillation dynamics provokes tunable periodical oscillations through the adjustment of the frequency detuning and injection strength which can be used as a microwave signal generator. Enhancement of the RF power of the oscillations can be achieved by increasing the injection strength towards the locking regions. The microwave linewidth is reduced from 58 MHz to a medium linewidth of about 14 MHz under optical injection technique. This simple configuration paves the way for potential uses of spin-VCSELs in Radio-over-Fiber (RoF) applications and future technologies.

Flow-induced self-sustained oscillations in a straight channel with rigid walls and elastic supports

This work considers the two-dimensional flow field of an incompressible viscous fluid in a parallel-sided channel. In our study, one of the walls is fixed whereas the other one is elastically mounted, and sustained oscillations are induced by the fluid motion. The flow that forces the wall movement is produced as a consequence that one of the ends of the channel is pressurized, whereas the opposite end is at atmospheric pressure. The study aims at reducing the complexity of models for several physiological systems in which fluid-structure interaction produces large deformation of the wall. We report the experimental results of the observed self-sustained oscillations. These oscillations occur at frequencies close to the natural frequency of the system. The vertical motion is accompanied by a slight trend to rotate the moving mass at intervals when the gap height is quite narrow. We propose a simplified analytical model to explore the conditions under which this motion is possible. The analytical approach considers asymptotic solutions of the Navier–Stokes equation with a perturbation technique. The comparison between the experimental pressure measured at the midlength of the channel and the analytical result issued with a model neglecting viscous effects shows a very good agreement. Also, the rotating trend of the moving wall can be explained in terms of the quadratic dependence of the pressure with the streamwise coordinate that is predicted by this simplified model.

Sustaining Rabi oscillations by using a phase-tunable image drive

Recent electron spin resonance experiments on CaWO_4:Gd^{3+} and other magnetic impurities have demonstrated that sustained Rabi oscillations can be created by driving a magnetic moment with a microwave field frequency slightly larger than the Larmor frequency and tuned to the Floquet resonance, together with another microwave field (image drive) with a frequency smaller than the Larmor frequency. These observations are confirmed by the new experimental results reported in this paper. We use numerical and analytical techniques to study the interplay between the microwave drives and three different mechanisms of relaxation. The first model describes a magnetic moment subject to microwave fields, interacting with a bath of two-level systems which acts as a source of decoherence and dissipation. The second model describes identical, interacting magnetic moments, subject to the same microwave fields. The decay of the Rabi oscillations is now due to the interactions. Third, we study Rabi oscillation decay due to the inhomogeneity of the microwave radiation. We show that under appropriate conditions, and in particular at the Floquet resonance, the magnetization exhibits sustained Rabi oscillations, in some cases with additional beatings. Although these two microscopic models separately describe the experimental data well, a simulation study that simultaneously accounts for both types of interactions is currently prohibitively costly. To gain further insight into the microscopic dynamics of these two different models, we study the time dependence of the bath and system energy and of the correlations of the spins, data that are not readily accessible experimentally.Graphic abstract

Cryptochrome 1 as a state variable of the circadian clockwork of the suprachiasmatic nucleus: Evidence from translational switching

The suprachiasmatic nucleus (SCN) of the hypothalamus is the principal clock driving circadian rhythms of physiology and behavior that adapt mammals to environmental cycles. Disruption of SCN-dependent rhythms compromises health, and so understanding SCN time keeping will inform management of diseases associated with modern lifestyles. SCN time keeping is a self-sustaining transcriptional/translational delayed feedback loop (TTFL), whereby negative regulators inhibit their own transcription. Formally, the SCN clock is viewed as a limit-cycle oscillator, the simplest being a trajectory of successive phases that progresses through two-dimensional space defined by two state variables mapped along their respective axes. The TTFL motif is readily compatible with limit-cycle models, and in Neurospora and Drosophila the negative regulators Frequency (FRQ) and Period (Per) have been identified as state variables of their respective TTFLs. The identity of state variables of the SCN oscillator is, however, less clear. Experimental identification of state variables requires reversible and temporally specific control over their abundance. Translational switching (ts) provides this, the expression of a protein of interest relying on the provision of a noncanonical amino acid. We show that the negative regulator Cryptochrome 1 (CRY1) fulfills criteria defining a state variable: ts-CRY1 dose-dependently and reversibly suppresses the baseline, amplitude, and period of SCN rhythms, and its acute withdrawal releases the TTFL to oscillate from a defined phase. Its effect also depends on its temporal pattern of expression, although constitutive ts-CRY1 sustained (albeit less stable) oscillations. We conclude that CRY1 has properties of a state variable, but may operate among several state variables within a multidimensional limit cycle.

Detection and Analysis of Critical Dynamic Properties of Oligodendrocyte Differentiation

In this paper, we derive a four-dimensional ordinary differential equation (ODE) model representing the main interactions between Sox9, Sox10, Olig2 and several miRNAs, which drive the process of (olygodendrocyte) differentiation. We utilize the Lyapunov–Andronov theory to analyze its dynamical properties. Our results indicated that the strength of external signaling (morphogenic gradients shh and bmp), and the transcription rate of mOlig2 explain the existence of stable and unstable (sustained oscillations) behavior in the system. Possible biological implications are discussed.

Enhanced spin wave coupling between array of spin torque nano oscillators in magnonic crystal cavities

Spin wave coupling between nano contact spin torque nano oscllators in asymmetric and symmetric array of antidot MC cavities to obtain sustained spin wave oscillations using supercell plane wave method and micromagnetics is discussed. The SWs were excited by injecting a spin-polarized current into a single nano contact in a L3 magnonic crystal cavity(MCC) and radiate like an end-fire antenna. The SW oscillations are then coupled into one of the guided modes of a magnonic crystal waveguide (MCW). The MCC acts as a SW resonator and spin-torque injection as gain. Together they achieve sustainable oscillations in a manner analogous to the behavior of a laser cavity. The phase locking of arrays of cavities arranged symmetrically and asymmetrically on both sides of a MCW is also discussed. Spin waves are radiated like a broadside antenna. The PSD of the broadside case is 28 dB lower than that of the end-fire case. The obtained value from the micromagnetic simulation is used to find the corresponding point in the guided mode of MCW, and this occurs nearer to the edge of the Brillouin zone. We also investigated the point in dispersion where the maximum energy is coupled from MCC to MCW. The spectral characteristics of the broadside coupling were correlated with frequency pulling effects in the laser cavity. Asymmetric spin-torque excitations on either sides of the MCW cause odd frequency peaks in the PSD characteristics. This can be mitigated when we use MC cavities placed symmetrically on both sides of the MCW, and excite spin waves in each cavity. However, spin waves excited in an asymmetric array of cavities add in phase, yielding a power enhancement with an increase in the number of cavities. Spin waves excited in a symmetric array of cavities add out of phase and result in spin-wave decoherence with an increase in the number of cavities.

Improved sequential autotuning of PI controllers for industrial-scale polymerization (ISP) reactor

Abstract This current work proposes a refined investigation on the improved sequential relay autotuning method to compute the optimal parameters of the decentralized PI controller for Two Input Two Output (TITO) system using relay feedback method. The sustained oscillation occurring in the relay response with the sequential relay autotuning and the simultaneous relay autotuning method is analyzed by taking the higher-order harmonics into consideration and the efficient performance results of the decentralized PI control systems are obtained. These methods have been applied to an Industrial-Scale Polymerization (ISP) reactor transfer function model. In closed-loop studies, comparative analysis of autotuning methods has been carried out using simulation. The effect of measurement noise and robustness are studied in the proposed work. The robustness performance of the system using improved sequential relay autotuning is enhanced by 5–25% for servo operation and 11–40% for regulatory operation. The performance of the systems with the effect of measurement noise using improved sequential relay autotuning is enhanced by 2–24% for servo operation. Comparative analysis has been carried out with the improved sequential relay autotuning and the simultaneous relay autotuning method. It is observed that the proposed method provides improved closed-loop performances and less sum of Integral square error even in presence of robustness and effect of measurement noise.

Model-Based Design of a Synthetic Oscillator Based on an Epigenetic Methylation Memory System.

Oscillations are an important component in biological systems; grasping their mechanisms and regulation, however, is difficult. Here, we use the theory of dynamical systems to support the design of oscillatory systems based on epigenetic control elements. Specifically, we use results that extend the Poincaré-Bendixson theorem for monotone control systems that are coupled to a negative feedback circuit. The methodology is applied to a synthetic epigenetic memory system based on DNA methylation that serves as a monotone control system, which is coupled to a negative feedback. This system is generally able to show sustained oscillations according to its structure; however, a first experimental implementation showed that fine-tuning of several parameters is required. We provide design support by exploring the experimental design space using systems-theoretic analysis of a computational model.

A novel adaptive SMC strategy for sustained oscillations in nonlinear sandwich systems based on stable limit cycle approach

This paper deals with the problem of creating stable oscillations in the class of nonlinear sandwich systems with dead-zone nonlinearity and unknown disturbances by creating the stable limit cycle. Due to the presence of the non-smooth dead-zone nonlinearity in the middle of the separate subsystems in the sandwich systems' structure, the control synthesis of such systems is complex. In this paper, to deal with the complexities, the control design process is implemented in two steps and a robust adaptive controller is presented by utilizing the sliding mode control (SMC) method. To achieve the control purpose through the SMC, a novel sliding surface is introduced regarding the structure of the admissible limit cycle, which is associated with some characteristics such as frequency, shape, and the amplitude of the desired sustained output oscillations. Simultaneously, the adaptive scheme is employed through the controller design process to extract the proper adaptive laws to estimate the upper bounds of unknown terms. The proposed method guarantees that the admissible limit cycle is generated in the phase plane of the controlled system and consequently verifies that the desired sustained oscillation (with the prescribed properties) is produced at the system's output. It also ensures that all variables in the resulting closed-loop system keep bounded. Finally, to show the effectiveness of the presented method, the given approach is applied to a practical system, and simulation results are given.

Insights into Chemically Fueled Supramolecular Polymers.

Supramolecular polymerization can be controlled in space and time by chemical fuels. A nonassembled monomer is activated by the fuel and subsequently self-assembles into a polymer. Deactivation of the molecule either in solution or inside the polymer leads to disassembly. Whereas biology has already mastered this approach, fully artificial examples have only appeared in the past decade. Here, we map the available literature examples into four distinct regimes depending on their activation/deactivation rates and the equivalents of deactivating fuel. We present increasingly complex mathematical models, first considering only the chemical activation/deactivation rates (i.e., transient activation) and later including the full details of the isodesmic or cooperative supramolecular processes (i.e., transient self-assembly). We finish by showing that sustained oscillations are possible in chemically fueled cooperative supramolecular polymerization and provide mechanistic insights. We hope our models encourage the quantification of activation, deactivation, assembly, and disassembly kinetics in future studies.

Analysis and Suppression of Oscillation in V/F Controlled Induction Motor Drive Systems

V/F control has been widely applied for induction motor drive systems because of its simplicity and reliability. However, sustained oscillation often occurs under light load, which leads to undesirable faults. This article focuses on the causes of oscillation and proposes an oscillation suppression solution. Based on the small-signal model, an open-loop transfer function of the induction motor is derived. The resonant peak, which is related to system parameters, such as frequency and inertia, is obtained from the transfer function and leads to unstable regions. The oscillation effects are discussed in detail. Then, the current feedback compensation method without any motor parameter is proposed to suppress the oscillation by decreasing the resonant peak. The feedback gain is optimized and designed. Finally, three current feedback paths are tested and compared in simulation and experiment. Simulation and experimental results have demonstrated the correctness of the theoretical analysis and the effectiveness of the proposed methods. The feedback path from current to voltage in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> -axis is the best suppression solution for its wider gain range and higher stability in the application.

Improved functional–weight approach to oscillatory patterns in excitable networks

Studies of sustained oscillations on complex networks with excitable node dynamics received much interest in recent years. Although an individual unit is non-oscillatory, they may organize to form various collective oscillatory patterns through networked connections. An excitable network usually possesses a number of oscillatory modes dominated by different Winfree loops and numerous spatiotemporal patterns organized by different propagation path distributions. The traditional approach of the so-called dominant phase-advanced drive method has been well applied to the study of stationary oscillation patterns on a network. In this paper, we develop the functional–weight approach that has been successfully used in studies of sustained oscillations in gene-regulated networks by an extension to the high-dimensional node dynamics. This approach can be well applied to the study of sustained oscillations in coupled excitable units. We tested this scheme for different networks, such as homogeneous random networks, small-world networks, and scale-free networks and found it can accurately dig out the oscillation source and the propagation path. The present approach is believed to have the potential in studies competitive non-stationary dynamics.

Describing Function Analysis of Sustained Oscillations in Grid-Tied Voltage-Source Converter With Double Saturation Limiters

Recently, with the fast development of renewable energy, various power-electronic-based devices have been widely incorporated in power systems, and controller saturation limiters have been broadly utilized, such as in voltage-source converter. It has been well recognized that these saturation limiters make sustained oscillations possible. To study the impact of saturation limiters, by considering the dynamical response of double saturation limiters in both the d-axis and q-axis of the alternating current control, this paper establishes single-input-single-output models for two novel phenomena including the double-clipped oscillation and single-clipped oscillation, based on the describing function. Then the describing-function-based Nyquist criterion is used to obtain the amplitude and frequency of the sustained oscillations. The model accuracy is verified by the electromagnetic transient simulation, and the influences of control parameters are extensively studied. All these findings clearly demonstrate that the saturation limiters play an active role in sustained oscillations in power-electronic-based power systems.

Feedbacks and non-linearity of silicate glass alteration in hyperalkaline solution studied by in operando fluid-cell Raman spectroscopy

Mechanisms, feedbacks and resulting non-linearity during silicate glass alteration in a hyperalkaline carbonate solution were studied through hyperspectral Raman imaging of heated fluid-cells. Our experimental setup enabled in operando visualization and rate measurements of glass dissolution and secondary phase precipitation, complemented by spectral characterization of the phases involved and semi-quantitative monitoring of the ionic strength of the solution close to the glass interface. After initial congruent dissolution of the Ba-bearing soda-lime boroaluminosilicate glass, the formation of a crystalline, saponite-based surface alteration layer (SAL), as well as subsequent zeolite precipitation, witherite coating, and carbonate precipitation within pore spaces of the saponite layer were observed. Two in operando experiments were conducted at ∼ 90 °C for 180 and 260 h that otherwise solely differed in the solution volume (SV) while keeping the surface area constant. The high SV experiment exhibited a transient upward excursion of initial dissolution rates, followed by continuously rapid glass dissolution along with slow SAL growth and sustained oscillations in ionic strength. Contrastingly, in the low SV experiment, glass dissolution monotonically decreased after the onset of rapid SAL growth and no sustained oscillations were observed. We find that growth conditions and resulting properties of the SAL exert dominant, non-linear effects on the evolution of glass dissolution rates. In turn, SAL formation depends on nucleation/growth kinetics and the accumulation of glass-derived solutes at the reaction front. Both, dissolution and precipitation, feedback with solution chemistry and transport processes, together controlling the evolution of the corrosion process. Additionally, fracturing, delamination, and the evolution of surface morphology may affect glass dissolution rates and transport pathways. Such interpretations of decelerating reaction rates in response to the growth of a protective layer are consistent in micro-scale experiments and in outcrop- to global-scale observations, as is the accelerating effect of surface area creation by physical disruption and morphology. Thus, these µm-scale mechanistic insights could help elucidating local to global environmental feedbacks (e.g., erosion or weathering patterns) as well as process dynamics in engineered environments (e.g., nuclear waste disposal) and may assist the improvement predictive models.

Convective effects on columnar dendritic solidification – A multiscale dendritic needle network study

Gravity-induced buoyancy, inevitable in most solidification processes, substantially alters the dynamics of crystal growth, such that incorporating fluid flow in solidification models is crucial to understand and predict key aspects of microstructure selection. Here, we present a multi-scale Dendritic Needle Network (DNN) model for directional solidification that includes buoyant flow in the liquid, and apply it to a range of alloys and growth conditions. After a brief presentation of the model, we study the selection of stable primary dendrite arm spacings in Al-4at.%Cu and in Ti-45at.%Al alloys under different gravity levels, comparing both applications to published phase-field results and experimental measurements. Then, we simulate the oscillatory growth behavior recently reported via X-ray in situ imaging of directional solidification of nickel-based superalloy CMSX-4. In this last application, the DNN simulations manage to reproduce the oscillatory growth behavior, and hence permit identifying the fundamental mechanisms behind the oscillatory growth regime. In particular, we show that sustained oscillations occur when the average liquid flow velocity is close to the crystal growth velocity, and that primary dendritic spacings also play a crucial role in the oscillatory behavior.