Frequency Domain Description Research Articles

Robust internal model control based on a novel generalized extended state observer and its application on a two-inertia system

Disturbance observer (DOB) and extended state observer (ESO) are extensively utilized to handle external disturbances and model uncertainties in the control system. Nevertheless, the integration of these two methods to improve disturbance suppression remains an open question. In this research, the disturbance compensation mechanism of DOB is employed to compensate the disturbance estimation error of ESO, thereby achieving an effective integration of DOB and ESO. Additionally, a generalized ESO (GESO) is proposed to replace ESO. A robust internal mode control (RIMC) scheme is then developed by incorporating GESO into a two-degree-of-freedom internal mode control (TDF-IMC) framework. Moreover, the equivalence of RIMC and classical TDF-IMC is given by a rigorous derivation under the frequency domain description. Finally, the RIMC is applied to the control of a two-inertia system to verify its superiority in terms of robustness, disturbance rejection, and resonance suppression.

Temporal Dynamics of Collective Resonances in Periodic Metasurfaces.

Temporal dynamics of confined optical fields can provide valuable insights into light-matter interactions in complex optical systems, going beyond their frequency-domain description. Here, we present a new experimental approach based on interferometric autocorrelation (IAC) that reveals the dynamics of optical near-fields enhanced by collective resonances in periodic metasurfaces. We focus on probing the resonances known as waveguide-plasmon polaritons, which are supported by plasmonic nanoparticle arrays coupled to a slab waveguide. To probe the resonant near-field enhancement, our IAC measurements make use of enhanced two-photon excited luminescence (TPEL) from semiconductor quantum dots deposited on the nanoparticle arrays. Thanks to the incoherent character of TPEL, the measurements are only sensitive to the fundamental optical fields and therefore can reveal clear signatures of their coherent temporal dynamics. In particular, we show that the excitation of a high-Q collective resonance gives rise to interference fringes at time delays as large as 500 fs, much greater than the incident pulse duration (150 fs). Based on these signatures, the basic characteristics of the resonances can be determined, including their Q factors, which are found to exceed 200. Furthermore, the measurements also reveal temporal beating between two different resonances, providing information on their frequencies and their relative contribution to the field enhancement. Finally, we present an approach to enhance the visibility of the resonances hidden in the IAC curves by converting them into spectrograms, which greatly facilitates the analysis and interpretation of the results. Our findings open up new perspectives on time-resolved studies of collective resonances in metasurfaces and other multiresonant systems.

Frequency-domain modelling of reset control systems using an impulsive description

The ever-increasing industry desire for improved performance makes linear controller design run into fundamental limitations. Nonlinear control methods such as Reset Control (RC) are needed to overcome these. RC is a promising candidate since, unlike other nonlinear methods, it easily integrates into the industry-preferred PID design framework. Thus far, RC has been analysed in the frequency domain either through describing function analysis or by direct closed-loop numerical computation. The former computes a simplified closed-loop RC response by assuming a sufficient low-pass behaviour. In doing so it ignores all harmonics, which literature has found to cause significant modelling prediction errors. The latter gives a precise solution, but by its direct closed-loop computation does not clearly show how open-loop RC design translates to closed-loop performance. The main contribution of this work is aimed at overcoming these limitations by considering an alternative approach for modelling RC using state-dependent impulse inputs. This permits accurately computing closed-loop RC behaviour starting from the underlying linear system, improving system understanding. A frequency-domain description for closed-loop RC is obtained, which is solved analytically by using several well-defined assumptions. This analytical solution is verified using a simulated high-precision stage, critically examining sources of modelling errors. The accuracy of the proposed method is further substantiated using controllers designed for various specifications.

Precisely computing bound orbits of spinning bodies around black holes. II. Generic orbits

In this paper, we continue our study of the motion of spinning test bodies orbiting Kerr black holes. Non-spinning test bodies follow geodesics of the spacetime in which they move. A test body's spin couples to the curvature of that spacetime, introducing a "spin-curvature force" which pushes the body's worldline away from a geodesic trajectory. The spin-curvature force is an important example of a post-geodesic effect which must be modeled carefully in order to accurately characterize the motion of bodies orbiting black holes. One motivation for this work is to understand how to include such effects in models of gravitational waves produced from the inspiral of stellar mass bodies into massive black holes. In this paper's predecessor, we describe a technique for computing bound orbits of spinning bodies around black holes with a frequency-domain description which can be solved very precisely. In that paper, we present an overview of our methods, as well as present results for orbits which are eccentric and nearly equatorial (i.e., the orbit's motion is no more than $\mathcal{O}(S)$ out of the equatorial plane). In this paper, we apply this formulation to the fully generic case -- orbits which are inclined and eccentric, with the small body's spin arbitrarily oriented. We compute the trajectories which such orbits follow, and compute how the small body's spin affects important quantities such as the observable orbital frequencies $\Omega_r$, $\Omega_\theta$ and $\Omega_\phi$.

Frequency Domain Repercussions of Instantaneous Granger Causality.

Using directed transfer function (DTF) and partial directed coherence (PDC) in the information version, this paper extends the theoretical framework to incorporate the instantaneous Granger causality (iGC) frequency domain description into a single unified perspective. We show that standard vector autoregressive models allow portraying iGC’s repercussions associated with Granger connectivity, where interactions mediated without delay between time series can be easily detected.

Universal SAR and optical image registration via a novel SIFT framework based on nonlinear diffusion and a polar spatial-frequency descriptor

Due to severe speckle noise in synthetic aperture radar (SAR) images and the large nonlinear intensity differences between SAR and optical images, the registration of SAR and optical images is a challenging problem that remains to be solved. In this paper, an improved nonlinear scale-invariant feature transform (SIFT)-framework-based algorithm that combines spatial feature detection with local frequency-domain description for the registration of SAR and optical images is proposed. First, multiscale representations of the SAR and optical images are constructed based on nonlinear diffusion to better preserve edges and obtain consistent edge information. The ratio of exponentially weighted averages (ROEWA) operator and the Sobel operator are utilized in the process of scale space construction to calculate consistent gradient information. Then, a new feature detection strategy based on the Harris–Laplace ROEWA and Harris–Laplace Sobel techniques is proposed to detect stable and repeatable keypoints in the scale space. Finally, a novel descriptor, called the rotation-invariant amplitudes of log-Gabor orientation histograms (RI-ALGH), and a simplified version, ALGH, are proposed. The proposed descriptors are built based on the amplitudes of multiscale and multiorientation log-Gabor responses and utilize an improved spatial structure of the gradient location and orientation histogram (GLOH) descriptor, which is robust to local distortions. The experimental results on both simulated and real images demonstrate that the proposed method can achieve better results than other state-of-the-art methods in terms of registration accuracy.

Structural vibration control using delayed state feedback via LMI approach: with application to chatter stability problems

This paper considers the problem of active vibration control in machining processes to prevent dynamic instability and chatter. A method for robust delayed-state feedback control is presented based on Lyapunov–Krasovskii functionals (LKFs). For fast computation and realizability, a partial state feedback approach based on a reduced order model of structural vibration is considered that matches available sensors and captures the main vibratory modes that impact on stability limits. Robustness to neglected dynamics and other model errors are accounted for by a frequency domain description of model uncertainty, augmented with the basic LKF stability condition. The controller synthesis problem is formulated as a set of linear matrix inequality equations that can be solved numerically using convex optimization methods. Evaluations on a hardware-in-the-loop flexible structure test-bed show that feedback controllers optimized via the LKF stability condition provide significant improvements in stability regions compared with optimized PD control and quadratic regulation. The results confirm the methodology as a useful approach for robust chatter control based on combined flexible structure and cutting process models.

Frequency-domain Methods and Polynomial Optimization for Optimal Periodic Control of Linear Plants

We consider the problem of periodic trajectory design for single-output systems which may be subject to periodic external disturbances. We show how trajectories optimizing a possibly nonquadratic and nonconvex polynomial performance objective can be found by using the frequency-domain description of the plant by converting the problem to a polynomial optimization problem (POP) in the Fourier coefficients of the external input signals. The method is suited for distributed-parameter systems, since the system transfer functions are not required to be rational; the computational complexity of the method depends on the order of the polynomial nonlinearities in the performance objective as well as the number of required harmonics, but is independent of the underlying system dimension.

Polarization-Sensitive Electro-Optic Sampling of Elliptically-Polarized Terahertz Pulses: Theoretical Description and Experimental Demonstration

We review our recent works on polarization-sensitive electro-optic (PS-EO) sampling, which is a method that allows us to measure elliptically-polarized terahertz time-domain waveforms without using wire-grid polarizers. Because of the phase mismatch between the employed probe pulse and the elliptically-polarized terahertz pulse that is to be analyzed, the probe pulse senses different terahertz electric-field (E-field) vectors during the propagation inside the EO crystal. To interpret the complex condition inside the EO crystal, we expressed the expected EO signal by “frequency-domain description” instead of relying on the conventional Pockels effect description. Using this approach, we derived two important conclusions: (i) the polarization state of each frequency component can be accurately measured, irrespective of the choice of the EO crystal because the relative amplitude and phase of the E-field of two mutually orthogonal directions are not affected by the phase mismatch; and, (ii) the time-domain waveform of the elliptically-polarized E-field vector can be retrieved by considering the phase mismatch, absorption, and the effect of the probe pulse width. We experimentally confirm the above two conclusions by using different EO crystals that are used for detection. This clarifies the validity of our theoretical analysis based on the frequency-domain description and the usefulness of PS-EO sampling.

Time- and frequency-domain linear viscoelastic modeling of highly damped aerospace structures

Abstract The numerical modeling of highly damped viscoelastic materials is critical for aerospace applications such as dynamic analysis of solid rocket motors – showing high damping ratios due to the presence of solid propellant – and design of passive damping devices for minimizing vibrations in aeronautical and space systems. Time-domain viscous damping models – giving damping forces proportional to velocities – are directly applicable in transient simulations, but they give a frequency-linear dissipative behavior which has no experimental evidence. On the other hand, frequency-domain hysteretic damping models – giving damping forces proportional to displacements – result in a frequency-constant dissipation that better describes the behavior of certain materials. However, using such models in transient analyses may give unphysical, non–Hermitian and non-causal system response. This paper reviews a class of first-principle-based damping models commonly used in structural dynamics by deriving them as particular cases of a general continuum mechanics formulation. The proposed damping models are tuned, in their frequency-domain description, on material experimental data so providing a Hermitian and causal time-domain responses, and they are applied to highly damped, practical aerospace structures via Finite Element models. The proposed model is applied to two aerospace systems: a scaled-down test article dynamically representative of a solid rocket motor launch-vehicle stage and a two-dimensional airfoil with passive viscoelastic dampers for flutter suppression.

Invariance With Dynamic Multipliers

This paper focusses on the robust or absolute stability analysis of feedback interconnections consisting of a linear time-invariant system and an uncertain linear or nonlinear component. Building on the framework of integral quadratic constraints, we establish a novel local stability result using general dynamic multipliers that enables the verification of hard time-domain state and output constraints. This is achieved by merging frequency-domain descriptions of uncertainties with time-domain dissipation arguments as they typically arise in Lyapunov theory. The general applicability of the results provided in this paper is illustrated by means of several examples that demonstrate the effectiveness of the presented approach, even if compared to techniques that are tailored to particular uncertainty classes.

Heat exchanger dynamic analysis

• Energy balance model yielding the system governing, partial differential equations. • The multivariable, multi-dimensional, Laplace transformed formulation of heat exchanger representations. • A frequency domain description of the system model is derived enabling the recovery of rationality. • The system is irrational in terms of s for both parallel and counter flow heat exchanger models. The modeling and dynamic analysis of shell and tube heat exchangers will be considered in this contribution. Procedures which incorporate the heat transfer and the fluid flow system properties, for these processes, will be developed. An incremental, energy balance yielding the system, partial differential equations presents the governing process. The multivariable, multi-dimensional, Laplace transformed, distributed parameter formulation of heat exchanger representations, are provided. A frequency domain description of the system model is derived enabling the recovery of Laplace function rationality for both parallel and counter flow heat exchanger models. Suitable feedback control techniques are identified, as a prelude to closed loop design studies. The dynamics, for tubular heat exchangers are computed, for purposes of comparison with alternative response and regulation approaches. A typical application study is outlined.

Consensus controllers for general integrator multi‐agent systems: analysis, design and application to autonomous surface vessels

This study addresses the distributed H ∞ and H 2 consensus control problems for multi-agent systems with general integrator dynamics and undirected topology. First, based on the frequency domain description of linear multi-agent systems, a sufficient and necessary condition is imposed on each controller to achieve consensus. Second, both H ∞ and H 2 optimal controllers are computed analytically according to the corresponding performance indices. The novel controllers not only can optimise the reference tracking performance but also has a simple tuning way to trade off the nominal performance and robustness. Finally, by application to the formation control of autonomous surface vessels shows the effectiveness of the proposed two control strategies.

Iterative Frequency Domain Equalization for MIMO-GFDM Systems

This paper proposes a new iterative frequency domain equalization (FDE) algorithm for multiple-input multiple-output (MIMO)-frequency division multiplexing (GFDM) systems. This new FDE scheme is capable of enhancing the system fidelity by considering the complete frequency-domain second order description of the received signal. In addition, a new nulling filter design is also proposed for MIMO-GFDM systems to remove the residual interference, which further improves the system fidelity compared with the traditional scheme. Simulation results are presented to verify the effectiveness and efficiency of the proposed FDE algorithm.

Pharmacodynamic modeling of propofol-induced general anesthesia in young adults.

Target controlled infusion (TCI) of intraveneous anesthetics can assist clinical practitioners to provide improved care for General Anesthesia (GA). Pharmacokinetic/Pharmacodynamic (PK/PD) models help in relating the anesthetic drug infusion to observed brain activity inferred from electroencephalogram (EEG) signals. The parameters in popular population PK/PD models for propofol-induced GA (Marsh and Schnider models) are either verified based on proprietary functions of the EEG signal which are difficult to correlate with the neurophysiological models of anesthesia, or the marker itself needs to be estimated simultaneously with the PD model. Both these factors make these existing paradigms challenging to apply in real-time context where a patient-specific tuning of parameters is desired. In this work, we propose a simpler EEG marker from frequency domain description of EEG and develop two corresponding PK/PD modeling approaches which differ in whether they use existing population-level PK models (approach 1) or not (approach 2). We use a simple deterministic parameter estimation approach to identify the unknown PK/PD model parameters from an existing human EEG data-set. We infer that both approaches 1 and 2 yield similar and reasonably good fits to the marker data. This work can be useful in developing patient-specific TCI strategies to induce GA.

Computing the Stochastic ${H} ^\infty $ -Norm by a Newton Iteration

The stochastic $H^\infty $ -norm is defined as the $L^{2}$ -induced norm of the input-output operator of a stochastic linear system. Like the deterministic $H^\infty $ -norm it is characterized by a version of the bounded real lemma, but without a frequency domain description or a Hamiltonian condition. Therefore, we base its computation on a parametrized algebraic Riccati-type matrix equation and a Newton iteration. For large dimensions, our algorithm outperforms LMI-methods.

Nonlinear data-driven identification of polymer electrolyte membrane fuel cells for diagnostic purposes: A Volterra series approach

In this work, a data-driven identification method, based on polynomial nonlinear autoregressive models with exogenous inputs (NARX) and the Volterra series, is proposed to describe the dynamic and nonlinear voltage and current characteristics of polymer electrolyte membrane fuel cells (PEMFCs). The structure selection and parameter estimation of the NARX model is performed on broad-band voltage/current data. By transforming the time-domain NARX model into a Volterra series representation using the harmonic probing algorithm, a frequency-domain description of the linear and nonlinear dynamics is obtained. With the Volterra kernels corresponding to different operating conditions, information from existing diagnostic tools in the frequency domain such as electrochemical impedance spectroscopy (EIS) and total harmonic distortion analysis (THDA) are effectively combined. Additionally, the time-domain NARX model can be utilized for fault detection by evaluating the difference between measured and simulated output. To increase the fault detectability, an optimization problem is introduced which maximizes this output residual to obtain proper excitation frequencies. As a possible extension it is shown, that by optimizing the periodic signal shape itself that the fault detectability is further increased.

Modelling pollution dynamics of longitudinally ventilated road tunnels

This paper develops a mathematical model in various forms to describe the dynamic response between vehicle exhaust emissions, air flow and the resulting pollutant concentrations in a longitudinally ventilated tunnel. Starting with the well-known “advection-diffusion” partial differential equation, several innovations in analysis are presented to finally create a simple estimator usable in predictive control algorithms. These innovations include;i)a variable time step numerical method of solution,ii)a discrete time (z- domain) model of the system,iii)a linear analytical solution for harmonic inputs which leads to a frequency domain description of the system dynamics for small perturbations about a mean operating condition,iv)a continuous time (s- domain) transfer function model, derived from the frequency domain analysis.

Reprint of: Coulomb field strength measurement by electro-optic spectral decoding system at the CALIFES beam line

Electro-optic (EO) techniques are increasingly used for longitudinal bunch profile measurements. A bunch profile monitor, based on electro-optic spectral decoding (EOSD), has been developed and demonstrated on the CALIFES beam line at CERN. The EO response is analysed using a frequency domain description, and two methods for extraction of absolute Coulomb field strengths from the electron bunch are demonstrated. Measurements at field strengths up to 1.3MV/m agree with the expectation based on independent charge measurements.

Coulomb field strength measurement by electro-optic spectral decoding system at the CALIFES beam line

Electro-optic (EO) techniques are increasingly used for longitudinal bunch profile measurements. A bunch profile monitor, based on electro-optic spectral decoding (EOSD), has been developed and demonstrated on the CALIFES beam line at CERN. The EO response is analysed using a frequency domain description, and two methods for extraction of absolute Coulomb field strengths from the electron bunch are demonstrated. Measurements at field strengths up to 1.3MV/m agree with the expectation based on independent charge measurements.