Control Parameter Space Research Articles

Catastrophe theory in the phenomenological description of the avalanche effect in dc-biased microwave HTSC transmission lines

Within the framework of the proposed generalization of the phenomenological model of a microwave nonlinear HTSC transmission line, the effects of direct current on the transmission line are studied. Taking into account the next term in the expansion of the nonlinear dependence of the resistance on current allows us to explain the anomalous dependence of the insertion loss on the input power level observed in the experiment at subcritical temperatures. An additional direct current through the microwave waveguide can lead to the appearance of a bifurcation region in the space of control parameters. This is manifested in the possibility of an abrupt change in the properties of the waveguide at the boundaries of this region and the transition of the HTSC waveguide to a strongly dissipative state. The qualitative correspondence of the properties of the generalized phenomenological model to the data of experimental studies of the HTSC coplanar waveguide is obtained.

Dynamics of non-autonomous oscillator with a controlled phase and frequency of external forcing

The dynamics of a non-autonomous oscillator in which the phase and frequency of the external force depend on the dynamical variable is studied. Such a control of the phase and frequency of the external force leads to the appearance of complex chaotic dynamics in the behavior of oscillator. A hierarchy of various periodic and chaotic oscillations is observed. The paper studies the structure of the space of control parameters. It is shown that in the dynamics of the system there are oscillatory modes similar to those of a non-autonomous oscillator with a potential in the form of a periodic function, but there are also significant differences.

Chaotic Dynamics of a Simple Population Model under the Allee Effect

We look at the population dynamics of an ecological system considering the Allee effect across different levels of population growth rates. The model is described by the growth and degradation of population size by multiplying a threshold term by the Allee effect. When the population of a species is low, the population of the system is not maintained and collapses to extinction. A wide survival region is observed in the dynamics of the Allee effect, and we report a bifurcation diagram for selected control parameters. We identify the chaotic region based on Lyapunov exponents. We obtain a phase diagram distinguishing extinction, periodic oscillation, the chaotic region, and the unstable region in the control parameter space. We observe two sets of chaotic bands one for low and the other for high values of the Allee effect. The Allee effect diversifies the dynamic region in parameter space.

Order by disorder: saving collective motion from topological defects in a conservative model

Using analytic and numerical methods, we study a 2d Hamiltonian model of interacting particles carrying ferro-magnetically coupled continuous spins which are also locally coupled to their own velocities. This model has been characterised at the mean field level in a parent paper. Here, we first obtain its finite size ground states, as a function of the spin-velocity coupling intensity and system size, with numerical techniques. These ground states, namely a collectively moving polar state of aligned spins, and two non-moving states embedded with topological defects, are recovered from the analysis of the continuum limit theory and simple energetic arguments that allow us to predict their domains of existence in the space of control parameters. Next, the finite temperature regime is investigated numerically. In some specific range of the control parameters, the magnetisation presents a maximum at a finite temperature. This peculiar behaviour, akin to an order-by-disorder transition, is explained by the examination of the free energy of the system and the metastability of the states of minimal energy. The robustness of our results is checked against the geometry of the boundary conditions and the dimensionality of space.

Modelling of correlation of actual and program feeds in the automatic cycle

The article presents a model for calculating the current values of the actual radial feed in the internal grinding process controlled in an automatic cycle on a CNC machine. The model establishes the correlation of actual and program feeds with cutting forces, elastic deformation of the technological system, cutting modes, geometrical parameters of the contact area between the wheel and the workpiece, wheel characteristics and other technological parameters and conditions of processing in a wide range of their variation. The obtained model is used for predicting radii changes of the machined hole surface starting from the workpiece to the final size for a given automatic cycle and various technological conditions of the internal grinding operation. The model described in this article is the basis for the development of methodology for multiparameter optimization of grinding cycles in a multidimensional space of control parameters.

A Current Sensorless Delay–Based Control Scheme for MPPT–Boost Converters in Photovoltaic Systems

The results presented in this paper deal with the design of a current sensorless delay–based controller for the closed–loop stabilization of a photovoltaic system under an MPPT scheme using a boost dc/dc converter. Some applications of such topology are dc microgrids, solar vehicles, or stand-alone systems, to mention a few. The basis of this control scheme relies on the feedback linearization control technique coupled with a delay–based low-order controller. In order to study the stability, the proposed approach uses a geometric point of view which allows the partitioning of the controller parameters space into regions with similar stability characteristics (same number of unstable characteristic roots). The most important contribution of the paper relies on providing practical guidelines to tune the gains of the proposed delay–based controller, ensuring asymptotic stability of the closed–loop system and fulfilling the requirements for photovoltaic applications. In addition, the proposed approach allows the design a non-fragile controller with respect to the controller gains. Furthermore, in order to test the effectiveness of the control scheme presented, experimental results evaluating the closed–loop system performance under set-point changes and abrupt irradiance disturbances are addressed using a solar array simulator and a battery bank as load.

Architectures and algorithms of an autonomous small-scale drilling agent

This paper describes the core architectures and algorithms of an autonomous small-scale drilling agent. The agent operates in a laboratory rig, demonstrating drilling scenarios with limited or even no human intervention. The work illustrates its performance through self-coordinating state transition, Rate of Penetration (ROP, drilling speed) optimization capability, formation classification, and drilling incidents management. The agent is an original rule-based system, and its control architecture utilizes finite states automation. The novel ROP optimization strategy employs a gradient search in Weight on Bit (WOB)-rotational speed (RPM, Revolutions per Minute) control parameter space. It generates an increasing ROP trend with time and requires re-iteration at abrupt formation changes. Several drilling incidents are managed using ‘if-then’ logic-based activity decomposition. A key learning outcome from the study is the comprehension of the requirement of standard software architecture and Applications Programming Interfaces (API) for continuous research and development of the agent. Such interfaces enhance interoperability between systems and stimulate innovative thinking among independent developers to produce a better-faster set of algorithms. Laboratory testing and evaluation is an essential part of promoting the adaptation of digital technologies for drilling automation. Such studies are a useful, safe, and cost-effective solution for testing, integrating and improving hardware, software, and data management before expensive full-scale testing and integration.

Spatial dynamics of predator-prey system with hunting cooperation in predators and type I functional response

In this paper, we have investigated a spatial predator-prey system with hunting cooperation in predators and type-I functional response. Using linear stability analysis, we obtain the stipulations for diffusive instability and identify the corresponding domain in the space of control parameters. Using qualitative and quantitative analysis, we obtain complex patterns, namely, spotted pattern, stripe pattern and mixed pattern in the Turing domain, by varying the rate of hunting cooperation in predators and diffusion coefficients of prey and predators. The results focus on the effect of hunting cooperation in pattern dynamics of a diffusive predator-prey model and help us in better understanding of the dynamics of the predator-prey interaction in real environment.

Computation of stability regions for load frequency control systems including incommensurate time delays

This article studies the impact of incommensurate communication time delays on stability regions defined in proportional-integral (PI) controller parameter space for a two-area load frequency control (LFC) system. Distributed power generations and large power plants increase the complexity and control issues of interconnected power systems. In interconnected power systems, LFC systems need to have complex communication networks to exchange data between control center and geographically dispersed generations. The receiving/transmitting of remote measuring data through communication infrastructures causes inevitable time delays, which adversely affect controller performance and stability of the LFC system. Time delays introducing feedback control loops of a multiarea LFC system could exhibit incommensurate characteristics. In this study, a simple graphical method based on extracting a stability boundary locus is implemented to get PI controller parameters responsible for stabilizing the LFC system having incommensurate delay values. The boundaries of the stability regions in the PI controller parameter space are confirmed by time-domain simulations and a numerical algorithm known as the quasipolynomial mapping-based root finder algorithm. Results illustrate that incommensurate delays have remarkable effects on the stability region.

Additional Food Supplements as a Tool for Biological Conservation of Biosystems in the Presence of Inhibitory Effect of the Prey

Provision of additional food supplements for the purpose of biological conservation has been widely researched both theoretically and experimentally. The study of these biosystems is usually done using predator-prey models. In this paper, we consider an additional food provided predator-prey system in the presence of the inhibitory effect of the prey. This model is analyzed in the control parameter space using the control parameters, quality and quantity of additional food. The findings suggest that with appropriate choice of additional food to predators, the biosystem can be controlled and steered to a desirable state. It is also possible to eliminate either of the interacting species. The vital role of the quality and quantity of the additional food in the system dynamics cautions the eco manager on the choice of the additional food for realizing the goal in the biological conservation programme.

A randomised algorithm for computing static-output-feedbacks for large-scale systems

ABSTRACTA randomised algorithm is proposed for computing globally optimal static-output-feedbacks for large-scale systems. The algorithm is based on the Ray-Shooting Method and involves some heuristics to accelerate the search. We also improve the basic Ray-Shooting Algorithm and make the search in the controller parameter-space (which generally, is much more smaller than the certificate parameter-space), thus enabling its efficient use for large-scale systems.

Computation of Robust PI-Based Pitch Controller Parameters for Large Wind Turbines

This paper deals with the computation of all proportional-integral (PI)-based pitch controllers which achieve the desired frequency-domain specifications, namely, gain and phase margins (GPMs) of a large wind turbine (LWT) with communication delays. An efficient graphical method based on extracting the boundaries of stability regions in PI controller parameter space having user-defined GPMs has been employed to determine GPM-based stability regions for a wide range of time delays. The theoretical region boundaries are validated by using a powerful numerical method known as the quasi-polynomial mapping-based root finder (QPmR) and time-domain simulations. Results indicate that the proposed scheme gives an improved dynamic response compared to the recently developed scheme based on stability only for the pitch control of LWTs with communication delays.

Measuring complex-partition-function zeros of Ising models in quantum simulators

Studying the zeroes of partition functions in the space of complex control parameters allows to understand formally how critical behavior of a many-body system can arise in the thermodynamic limit despite various no-go theorems for finite systems. In this work we propose protocols that can be realized in quantum simulators to measure the location of complex partition function zeroes of classical Ising models. The protocols are solely based on the implementation of simple two-qubit gates, local spin rotations, and projective measurements along two orthogonal quantization axes. Besides presenting numerical simulations of the measurement outcomes for an exemplary classical model, we discuss the effect of projection noise and the feasibility of the implementation on state of the art platforms for quantum simulation.

Non-Abelian Geometric Dephasing.

We study the adiabatic dynamics of degenerate quantum states induced by loop paths in a control parameter space. The latter correspond to noisy trajectories if the system is weakly coupled to environmental modes. On top of conventional dynamic dephasing, we find a universal non-Abelian geometric dephasing (NAGD) contribution and express it in terms of the non-Abelian Berry connection and curvature. We show that NAGD implies either decay or amplification of coherences as compared to the coherences when only dynamic dephasing is present. The full NAGD matrix structure can be probed through interference experiments. We outline such a detection scheme for modified Majorana braiding setups.

Non-Abelian Berry phase for open quantum systems: Topological protection versus geometric dephasing

We provide a detailed theoretical analysis of the adiabatic evolution of degenerate open quantum systems, where the dynamics is induced by time-dependent fluctuating loop paths in control parameter space. For weak system-bath coupling, the fluctuations around a deterministic base path obey Gaussian statistics, where we assume that the quantum adiabatic theorem is also satisfied for fluctuating paths. We show that universal non-Abelian geometric dephasing (NAGD) contributions are contained in the fluctuation-averaged evolution operator. This operator plays a key role in all experimental protocols proposed in this work for the detection of NAGD. In particular, we formulate interference measurements providing full access to NAGD. Apart from a factor due to the dynamic phase and its fluctuations, the averaged evolution operator contains the averaged Berry matrix. A polar decomposition of this non-unitary matrix into the product of a unitary, $V$, and a positive semi-definite Hermitian matrix, $R$, reveals the physics of the NAGD contributions. Unlike the conventional dynamic dephasing rate, the NAGD eigenrates encoded by $R$ depend on the loop orientation sense and, in particular, change sign under a reversal of the direction. A negative rate then implies amplification of coherences as compared to the ones when only dynamic dephasing is present. The non-Abelian character of geometric dephasing is rooted in the non-commutativity of $V$ and $R$ and causes smoking-gun signatures in interference experiments. We also clarify why systems subject to topological protection do not show geometric dephasing. Without full protection, however, geometric dephasing can arise and has to be taken into account. As concrete application, we propose spin-echo NAGD detection protocols for modified Majorana braiding setups.

Numerical studies on passive suppression of one and two degrees-of-freedom vortex-induced vibrations using a rotative non-linear vibration absorber

This paper presents a numerical investigation on the use of a rotative non-linear vibration absorber (NVA) as a passive suppressor for the vortex-induced vibrations phenomenon (VIV). The structural model consists of rigid cylinders mounted on elastic supports and the hydrodynamic loads are calculated using phenomenological models. The NVA is defined as a rigid bar, fitted with a tip-mass and hinged to the cylinder. Energy is dissipated by means of a linear dashpot linked to the bar.Two major groups are studied, the first one being that in which the cylinder is constrained to oscillate in the cross-wise direction (1-dof VIV). The second group, herein named 2-dof VIV, refers to the condition in which simultaneous oscillations in the cross-wise and in-line directions are allowed.Characteristic oscillation amplitude curves are obtained as functions of reduced velocities covering the lock-in for different values of the control parameters that define the NVA (namely, its mass, radius and dashpot constant). In addition, quantitative and qualitative aspects of cylinder and suppressor responses are explored in the form of colormaps defined in the space of control parameters for three specific reduced velocities.The systematic study shows that the mass parameter of the NVA has more influence on the VIV suppression for both 1-dof VIV and 2-dof VIV. In general, the suppression has proved to be greater in the 1-dof VIV case.

Quasi-periodic bursters and chaotic dynamics in a shallow arch subject to a fast–slow parametric excitation

In this paper, various nonlinear dynamics of a one-degree-of-freedom shallow arch model are investigated. The arch is subject to an imposed displacement of its support that is composed of slow and fast harmonic motions. The corresponding mathematical model consists of a nonlinear quasi-periodic Mathieu–Duffing equation. The dynamics are analyzed using the singular perturbation theory and the Melnikov method. It is shown that invariant slow manifolds of the averaged system, over the fast dynamics, are slaving the dynamics of the system under the condition of non-hyperbolicity of the undeformed state of the arch. These manifolds correspond to the buckled, the unbuckled and the undeformed solutions of the arch. Various kinds of quasi-periodic and chaotic bursters relating these slow manifolds are obtained, and quasi-periodic bursters doubling and tripling sequences leading to hysteretic chaos are observed. Using the Melnikov method and the Lyapunov exponents computations, it was demonstrated that chaos induced by the slow excitation can be suppressed by the fast harmonic excitation in large domains of the control parameters space, especially in the regions where the undeformed configuration of the arch is not hyperbolic.

Spatiotemporal Model of a Predator–Prey System with Herd Behavior and Quadratic Mortality

In this paper, we have investigated a diffusive predator–prey model with herd behavior. Also, we considered that the mortality of predators is linear as well as quadratic. Using linear stability analysis, we obtain the condition for diffusive instability and identify the corresponding domain in the space of control parameters. Using extensive numerical simulations, we obtain non-Turing spatiotemporal patterns in the model with linear mortality of predators, and Turing pattern formation, namely, spotted pattern and mixed pattern (spots-stripes) in model with quadratic mortality of predators. The results focus on the effect of the changing mortality rates of predator in pattern dynamics of a diffusive predator–prey model and help us in the better understanding of the dynamics of the predator–prey interaction in real environment.

Two-parameter areal scaling in the Hénon map

We study a bifurcation cascade whose proper unfolding requires tuning more than one parameter simultaneously. Specifically, we investigate metric properties of extended self-similar triangular areas observed recently in the control parameter space of flows (lasers and electronic circuits), and maps. Such areas are delimited by shrimplike stability islands, seem to arise in unbounded quantities, and to accumulate in narrow intervals of control parameters. Numerically, we find their asymptotic rate of accumulation to be unity. The asymptotic properties of triangle vertices and their centroids are also investigated.

Geometric Speed Limit of Accessible Many-Body State Preparation

We analyze state preparation within a restricted space of local control parameters between adiabatically connected states of control Hamiltonians. We formulate a conjecture that the time integral of energy fluctuations over the protocol duration is bounded from below by the geodesic length set by the quantum geometric tensor. The conjecture implies a geometric lower bound for the quantum speed limit (QSL). We prove the conjecture for arbitrary, sufficiently slow protocols using adiabatic perturbation theory and show that the bound is saturated by geodesic protocols, which keep the energy variance constant along the trajectory. Our conjecture implies that any optimal unit-fidelity protocol, even those that drive the system far from equilibrium, are fundamentally constrained by the quantum geometry of adiabatic evolution. When the control space includes all possible couplings, spanning the full Hilbert space, we recover the well-known Mandelstam-Tamm bound. However, using only accessible local controls to anneal in complex models such as glasses or to target individual excited states in quantum chaotic systems, the geometric bound for the quantum speed limit can be exponentially large in the system size due to a diverging geodesic length. We validate our conjecture both analytically by constructing counter-diabatic and fast-forward protocols for a three-level system, and numerically in nonintegrable spin chains and a nonlocal SYK model.