Control Parameter Space Research Articles

Current-Driven Magnetization Reversal in Orbital Chern Insulators.

Graphene multilayers with flat moiré minibands can exhibit the quantized anomalous Hall effect due to the combined influence of spontaneous valley polarization and topologically nontrivial valley-projected bands. The sign of the Hall effect in these Chern insulators can be reversed either by applying an external magnetic field, or by driving a transport current through the system. We propose a current-driven mechanism whereby reversal occurs along lines in the (current I, magnetic-field B) control parameter space with slope dI/dB=(e/h)MA_{M}(1-γ^{2})/γ, where M is the magnetization, A_{M} is the moiré unit cell area, and γ<1 is the ratio of the chemical potential difference between valleys along a domain wall to the electrical bias eV.

Swallowtail-type diffraction catastrophe beams.

We demonstrate a universal approach for generating high-order diffraction catastrophe beams, specifically for Swallowtail-type beams (abbreviated as Swallowtail beams), using diffraction catastrophe theory that was defined by potential functions depending on the control and state parameters. The three-dimensional curved caustic surfaces of these Swallowtail catastrophe beams are derived by the potential functions. Such beams are generated by mapping the cross sections of the high-order control parameter space to the corresponding transverse plane. Owing to the flexibility of the high-order diffraction catastrophe, these Swallowtail beams can be tuned to a diverse range of optical light structures. Owing to the similarity in their frequency spectra, we found that the Swallowtail beams change into low-order Pearcey beams under given conditions during propagation. Our experimental results are in close agreement with our simulated results. Such fantastic catastrophe beams that can propagate along curved trajectories are likely to give rise to new applications in micromachining and optical manipulation, furthermore, these diverse caustic beams will pave the way for the tailoring of arbitrarily accelerating caustic beams.

Role of mixed permutation symmetry sectors in the thermodynamic limit of critical three-level Lipkin-Meshkov-Glick atom models.

We introduce the notion of mixed symmetry quantum phase transition (MSQPT) as singularities in the transformation of the lowest-energy state properties of a system of identical particles inside each permutation symmetry sector μ, when some Hamiltonian control parameters λ are varied. We use a three-level Lipkin-Meshkov-Glick model, with U(3) dynamical symmetry, to exemplify our construction. After reviewing the construction of U(3) unitary irreducible representations using Young tableaux and the Gelfand basis, we first study the case of a finite number N of three-level atoms, showing that some precursors (fidelity susceptibility, level population, etc.) of MSQPTs appear in all permutation symmetry sectors. Using coherent (quasiclassical) states of U(3) as variational states, we compute the lowest-energy density for each sector μ in the thermodynamic N→∞ limit. Extending the control parameter space by μ, the phase diagram exhibits four distinct quantum phases in the λ-μ plane that coexist at a quadruple point. The ground state of the whole system belongs to the fully symmetric sector μ=1 and shows a fourfold degeneracy, due to the spontaneous breakdown of the parity symmetry of the Hamiltonian. The restoration of this discrete symmetry leads to the formation of four-component Schrödinger cat states.

Impact of Electric Vehicle Aggregator with Communication Time Delay on Stability Regions and Stability Delay Margins in Load Frequency Control System

This paper investigates the impact of electric vehicle (EV) aggregator with communication time delay on stability regions and stability delay margins of a single-area load frequency control (LFC) system. Primarily, a graphical method characterizing stability boundary locus is implemented. For a given time delay, the method computes all the stabilizing pro-portional-integral (PI) controller gains, which constitutes a stability region in the parameter space of PI controller. Secondly, in order to complement the stability regions, a frequency-domain exact method is used to calculate stability delay margins for various values of PI controller gains. The qualitative impact of EV aggregator on both stability regions and stability delay margins is thoroughly analyzed and the results are authenticated by time-domain simulations and quasi-polynomial mapping-based root finder (QPmR) algorithm.

Multi-Objective Digital PID Controller Design in Parameter Space and its Application to Automated Path Following

This paper presents a multi-objective digital PID controller design method using the parameter space approach of robust control. Absolute stability is treated first by finding the digital PID controller gain parameter space corresponding to closed loop poles being inside the unit circle. Additionally, phase margin, gain margin and a mixed sensitivity bound are treated as frequency domain constraints. Determination of digital PID controller parameter space regions satisfying these constraints is presented. All of these regions are superimposed to obtain a multi-objective digital PID controller gain parameter space solution region. The path following controller design of an automated driving vehicle is used as an example to illustrate the method. This multi-objective parameter space design approach can be extended to other digital controller forms also.

Power-Synchronization Control for Ultra-Weak AC Networks: Comprehensive Stability and Dynamic Performance Assessment

Power-synchronization control (PSC) is a promising control strategy to improve the stability and performance of voltage-source converters (VSCs) in ultra-weak AC grids. However, evaluation of PSC to date has investigated performance only at single controller operating points, rather than holistically varying multiple controller gains. This paper develops a new methodology, based on small-signal eigenvalue analysis, to comprehensively analyze PSC-VSC stability. The maximum active power transfer of PSC is established across a broad range of controller tunings and the two-way and three-way couplings between the power-synchronization control, AC voltage control and high-pass current filter gains are quantified. A new stable tuning region is introduced, which represents the controller parameter space for stable operation. It is shown that PSC can achieve rated power transfer into an AC grid (short circuit ratio(SCR)=1) at multiple controller operating points, but dynamic performance varies significantly within this region. The robustness of this operating region to SCR changes is also investigated. The stability boundary and dynamic performance are validated using control hardware-in-the-loop experiments with a real-time digital simulator. Practical recommendations arising from this work are a set of controller gains that provide stability and good dynamic performance at high power transfer for ultra-weak grid-connected VSCs employing PSC.

Geometric‐based PID control design with selective harmonic mitigation for DC–DC converters by imposing a norm bound on the sensitivity function

The DC–DC converters usually interfaces renewable energy sources in DC microgrids which may be contaminated by harmonic perturbations that adversely affect performance, creates stability and protection problems in a DC grid system. In this paper, the authors propose the use of the popular proportional–integral–derivative (PID) controller to mitigate selected harmonics. The solution is obtained by computing the complete set of stabilising controllers and imposing a bound on the sensitivity function. Using matrix representation of conic sections, the geometric-based PID controller is derived in the controller parameter space. The main result finds a subset of the stabilising set in which the controller mitigate harmonics with prescribed levels of attenuation which are constructively determined for each frequency of the selected harmonics. Simulation and experimental results using a boost converter are provided for validation.

Wind Reversal in Bubbly Natural Convection

The multi-phase Rayleigh–Bènard convection has been weakly investigated, even though it plays a leading role in the theoretical and applied physics of the heat transfer enhancement. For the case of moderate turbulent convection, a rather unexpected result is an unusual kind of wind reversal, in the sense that the fluid is found to be strongly influenced by the bubbles, whereas the bubbles themselves appear to be little affected by the fluid, despite the relative smallness of the Stokes numbers. The wind reversal induced by the bubbles dispersed in the fluid is a new and remarkable phenomenon in multi-phase flows that provides further perspectives in understanding the complex physics leading the enhancement of thermal convection. For this reason, the fundamental research proposed in this paper aimed to identify a space of control parameters and the physical mechanisms responsible for the wind reversal induced by dispersed bubbles in a confined convective flow. The strength of the following description lies in an innovative numerical approach, based on the multi-scale physics induced by the coupling of the local thermal and mechanical mechanisms arising between each bubble and the surrounding fluid. The continuous phase has been solved numerically using the direct numerical simulation (DNS) technique and each bubble has been tracked by means of a particle Lagrangian model.

Decentralised design of robust multi‐objective PSSs: D ‐decomposition approach

This study addresses the problem of determining the set of all robust three-parameter power system stabilisers having the form . Graphical characterisation of stabilising power system stabilisers (PSSs) is carried out using D-decomposition, whereas the controller–parameter space is subdivided into root-invariant regions. Rather than Hurwitz stability, D-decomposition can parameterise D-stabilising PSSs that enforce pole-clustering in a pre-specified region D to ensure better time-domain specifications. The convex region of D-stabilising PSSs is sketched by mapping the contours from the s-plane onto the controller–parameter plane by two parametric functions and with fixed . The frequency range considered for mapping is initially computed to avoid sweeping over unnecessary frequencies. Based on the geometry of the D-stability region, analytical expressions are derived to compute optimal σ − ζ PSSs for an arbitrary operating point. Parametric uncertainties are captured by an image-set polynomial where the region guarantying robust D-stability of the family is investigated. A computationally effective approach based on stabilising two vertex plants is concluded from the D-stability region. Extension to multi-machine systems is treated where decentralised PSSs are synthesised. An iterative algorithm is suggested to modify a set of initial feasible PSSs sequentially while maximising damping indices. Simulation results confirm the efficacy of the suggested method.

Density resolved wave packet spreading in disordered Gross-Pitaevskii lattices

We perform novel energy and norm density resolved wave packet spreading studies in the disordered Gross-Pitaevskii (GP) lattice to confine energy density fluctuations. We map the locations of GP regimes of weak and strong chaos subdiffusive spreading in the 2D density control parameter space and observe strong chaos spreading over several decades. We obtain a renormalization of the ground state due to disorder, which allows for a new disorder-induced phase of disconnected insulating puddles of matter due to Lifshits tails. Inside this Lifshits phase, the wave packet spreading is substantially slowed down.

Nonlinear dynamics and chaos regularization of one-dimensional pulsating detonations with small sinusoidal density perturbations

In this work, we explore the effect of initial density variation in the combustible mixture on the nonlinear dynamics of one-dimensional gaseous detonation propagation. Studies of nonlinear dynamical behavior of one-dimensional pulsating detonation are frequently based upon the reactive Euler simulations with one-step Arrhenius chemistry. In regions of the control parameters space, i.e., activation energy Ea, the 1-D detonation dynamics are shown to exhibit chaotic behavior at values of 28.5 and 30.0. Using small sinusoidal initial density perturbations, this investigation shows the emergence of various nonlinear temporal patterns as a function of the perturbation wavelength. It demonstrates that the cooperative behavior between the intrinsic instability and imposed small perturbation can lead to regularization of chaotic oscillations in one-dimensional gaseous pulsating detonation. Hence, by means of a small perturbation, an otherwise chaotic motion is rendered more stable and predictable. This result thus has implications for how intrinsically unstable detonation dynamics can be controlled.

Quench dynamics in disordered two-dimensional Gross-Pitaevskii lattices

We numerically investigate the quench expansion dynamics of an initially confined state in a two-dimensional Gross-Pitaevskii lattice in the presence of external disorder. The expansion dynamics is conveniently described in the control parameter space of the energy and norm densities. The expansion can slow down substantially if the expected final state is a non-ergodic non-Gibbs one, regardless of the disorder strength. Likewise stronger disorder delays expansion. We compare our results with recent studies for quantum many body quench experiments.

A Study of Energy Band Rearrangement in Isolated Molecules by Means of the Dirac Oscillator Approximation

Energy band rearrangement along a control parameter in isolated molecules is studied through axially symmetric Hamiltonians describing the coupling of two angular momenta $$\mathbf{S}$$ and $$\mathbf{L}$$ of fixed amplitude. We focus our attention on the case $$S=1$$ which, albeit nongeneric, describes the global rearrangement of a system of energy bands between two well-defined limits corresponding to uncoupled and coupled momenta. The redistribution of energy levels between bands is closely related to the degeneracy of the eigenvalues of the corresponding semiquantum Hamiltonian at isolated points of the three-dimensional Cartesian product of the two-dimensional phase space and the one-dimensional control parameter space. The present paper shows that the band rearrangement for the full quantum system can be quantitatively, rather than qualitatively, reproduced with Dirac oscillator approximations. We also interpret the energy band rearrangement by comparing the evolution of the joint spectra of commuting observables (i. e., energy and axial angular momentum) with that of the image of the energy-momentum map of the completely classical limit of the Dirac oscillator approximations.

Ratchet current in nontwist Hamiltonian systems.

Non-monotonic area-preserving maps violate the twist condition locally in phase space, giving rise to shearless invariant barriers surrounded by twin island chains in these regions of phase space. For the extended standard nontwist map, with two resonant perturbations with distinct wave numbers, we investigate the presence of such barriers and their associated island chains and compare our results with those that have been reported for the standard nontwist map with only one perturbation. Furthermore, we determine in the control parameter space the existence of the shearless barrier and the influence of the additional wave number on this condition. We show that only for odd second wave numbers are the twin island chains symmetrical. Moreover, for even wave numbers, the lack of symmetry between the chains of twin islands generates a ratchet effect that implies a directed transport in the phase space.

A Computational Multicriteria Optimization Approach to Controller Design for Physical Human-Robot Interaction

Physical human-robot interaction (pHRI) integrates the benefits of human operator and a collaborative robot in tasks involving physical interaction, with the aim of increasing the task performance. However, the design of interaction controllers that achieve safe and transparent operations is challenging, mainly due to the contradicting nature of these objectives. Knowing that attaining perfect transparency is practically unachievable, controllers that allow better compromise between these objectives are desirable. In this paper, we propose a multi-criteria optimization framework, which jointly optimizes the stability robustness and transparency of a closed-loop pHRI system for a given interaction controller. In particular, we propose a Pareto optimization framework that allows the designer to make informed decisions by thoroughly studying the trade-off between stability robustness and transparency. The proposed framework involves a search over the discretized controller parameter space to compute the Pareto front curve and a selection of controller parameters that yield maximum attainable transparency and stability robustness by studying this trade-off curve. The proposed framework not only leads to the design of an optimal controller, but also enables a fair comparison among different interaction controllers. In order to demonstrate the practical use of the proposed approach, integer and fractional order admittance controllers are studied as a case study and compared both analytically and experimentally. The experimental results validate the proposed design framework and show that the achievable transparency under fractional order admittance controller is higher than that of integer order one, when both controllers are designed to ensure the same level of stability robustness.

Robust multi-objective PSSs design via complex Kharitonov's theorem

This paper represents a step toward shooting an optimal robust three-parameter power system stabilizer (PSS) with the common form of (x1+x2s)/(1+x3s). The whole set of stabilizing PSSs is graphically characterized using d-decomposition with which the controller-parameter space is subdivided into root-invariant regions. Design is accomplished using the bench mark model of single machine-infinite bus system (SMIB). Rather than Hurwitz stability, d-decomposition is extended to consider d-stability where D refers to a pre-specified damping cone in the open left half of the complex s-plane to enhance time-domain specifications. Pole clustering in damping cone is inferred by enforcing Hurwitz stability of a complex polynomial accounting for the geometry of such cone. Parametric uncertainties of the model imposed by continuous variation in load patterns is captured by an interval polynomial. As a result, computing the set of all robust d-stabilizing PSSs calls for Hurwitz stability of a complex interval polynomial. The latter is tackled by a complex version of Kharitonov's theorem. A less-conservative and computationally effective approach based on only two extreme plants is concluded from the geometry of the stability region in the controller parameter plane. Simulation results affirm the robust stability and performance with the proposed PSSs over wide range of operating points.

Machine-learning approach for constructing control landscape maps of three-dimensional alignment of asymmetric-top molecules

A machine-learning approach to draw landscape maps in a low-dimensional control-parameter space is examined through a case study of three-dimensional alignment control of the asymmetric-top molecule SO2. As a minimal model, we consider the control by using a set of mutually orthogonal, linearly polarized laser pulses that are parameterized by the time delay and fluence ratio. The parameters are represented either by points in the parameter space or by time- and frequency-resolved spectra. Machine-learning models based on convolutional neural networks together with two considerably different representations, which are trained by using a reasonably small number of training samples, construct maps that have sufficient accuracy to predict temperature-dependent control mechanisms.

Relation between the Programmed and Actual Feed Motions in Internal Grinding

A model is proposed for calculating the actual radial feed in internal grinding on a CNC machine. The model establishes the relation between the actual and programmed feed, as a function of the cutting forces, the elastic deformation of the machining system, the cutting conditions, the wheel–workpiece contact geometry, the wheel characteristics, and other parameters. The model is used to predict the change in radius of the machined hole surface in the workpiece, from the initial to the final value for a specified automatic cycle, in various internal-grinding conditions. The model provides the basis for multiparametric optimization of the grinding cycles in multidimensional control-parameter space.

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.