Finite Frequency Band Research Articles

Model-free finite frequency H∞ control for active chatter suppression in turning

Regenerative chatter is an extremely harmful phenomenon in machining, which generally results in overcut and rapid tool wear. This paper presents the design, analysis, and verification of a novel model-free finite frequency band (MFFFB) H∞ control algorithm, which is dedicated to chatter suppression of turning process. The proposed MFFFB H∞ controller is established by utilizing the reinforcement Q-learning along with the generalized Kalman-Yakubovich-Popov (GKYP) lemma. Unlike available entire frequency domain (EFD) H∞ controllers, the proposed approach facilitates a less conservative implementation since the H∞ performance index is only designed for the concerned frequency band which implies the limited energies of the actuator are mainly focused on this band, and users can specify optimized frequency band according to the actual turning conditions. Furthermore, it permits the construction of H∞ controller without any knowledge of the dynamic model of turning process, only the data measured from the system state and input are required. Besides, an iterative solution algorithm for H∞ control on the basis of policy iteration is presented, which decreases the burden on manual parameter adjustment and capable of achieving the optimal solution. Simulation and experiment results demonstrate that the proposed MFFFB H∞ controller generates significant improvement in chatter-free region compared with EFD H∞ controller and conventional FFB H∞ controller.

DIRECT IMAGE RECONSTRUCTION IN MULTI-ELEMENT INTERFEROMETRY

The Ukrainian VLBI system of decameter radio telescopes URAN successfully solves many scientific problems, but implementing aperture synthesis technology has a number of difficulties. One of them is significant phase distortions in this range caused by an inhomogeneous propagation environment. Therefore, the task arose to develop an alternative technology with the conventional name "Interferovision", which would allow us to restore radio images with a limited number of antennas, operate with broadband signals, not require flatness of the objects scene, and have an extended field of view. A method of direct image reconstruction when observing objects in space, using a multi-element interferometer, is proposed. This method is based on a physically based principle that is similar to holography. The wave front is registered by the antennas of the interferometer, and further processing is equivalent to its playback in reverse and registration of the resulting spatial interference image. There are no special requirements for the radiation of individual points of the source, except for its delta correlation. A finite frequency band is considered, and each point can be characterized by its own spectrum, that is, its own autocorrelation function of radiation. The resolution of the direct reconstruction method depends on its width. With the quasi-monochromatic approximation, the autocorrelation functions of the radiation of all the source points degenerate into sinusoids, and the restoration of the image becomes possible only with the use of the Fourier transformation. A theoretical justification of the method for spaces of different dimensions has been obtained. Interferometric systems of the same rank with many antennas are reduced to a same canonical form with fixed number of virtual antennas placed at the origin of the coordinates and at unit distances on the coordinate axes. The ambiguity of the obtained solution is eliminated by using an additional antenna. A simulation of the proposed method of direct image reconstruction for two-dimensional space was carried out. Despite the low conditionality of the system for estimating the distance, when it increases, the angular characteristics are preserved. Therefore, the method is promising for restoring radio images of space radio sources.

Design and analysis of a tunable electromagnetic lever-type anti-resonant vibration isolator

To broaden the effective vibration suppression band of a typical dynamic anti-resonant vibration isolator (DAVI), a tunable lever-type anti-resonant vibration isolator has been designed, theoretically investigated, and experimentally verified. An anti-resonant frequency occurs within the device when the inertial force generated by the levered mass cancels the spring force. By controlling the electromagnetic spring so as to adjust the system’s equivalent stiffness, the anti-resonant frequency of the electromagnetic lever-type anti-resonant vibration isolator (EM-LVI) can be tuned to coincide with the excitation frequency in real time. A broad stopband where the vibration is sufficiently suppressed can be provided by the EM-LVI for low-frequency applications. Due to the lever’s amplifying effect, the EM-LVI can modify the equivalent stiffness of the system with a small electromagnetic stiffness, which provides a viable approach to the design of lightweight isolators. Theoretical and experimental results demonstrate that the tuning bandwidth increases along with the lever amplification ratio. With the advantages of a wide stopband and a high vibration suppression level, the proposed EM-LVI exhibits significant advantages in suppressing low-frequency vibration in a finite-frequency band and has been successfully validated by experimental prototypes for its beneficial performance in low-frequency vibration suppression.

Topology optimization of a thermal cloak in the frequency domain

Designing wideband thermal cloaks remains a challenge, especially at high frequencies. We propose an optimization approach for the design of a thermal cloak for an arbitrary object with large thermal conductivity (copper), in a given frequency band and for a specific diffusion direction. Cloaking performance is assessed as a function of frequency (in the optimal direction) and as a function of angle (at the optimal frequency). Near-perfect cloaking is achieved over a finite frequency band, and, moreover, the thermal cloak performs well in the time domain, including in the transient regime, irrespective of the initial temperature distribution. Interestingly, this specially optimized cloak also works fairly well for other objects with large thermal conductivity but breaks down for those of low thermal conductivity.

Phase synchronization between neurons under nonlinear coupling via hybrid synapse

Biological neurons and nonlinear circuits contain certain inner field energy, and an equivalent Hamilton energy function can be obtained to discern the dependence of firing modes on the energy flow. In this paper, a voltage-controlled resistor is used to connect two neural circuits, and hybrid synapse is activated to control the synchronization stability and mode transition in neurons under phase lock. Realistic stimuli can be combined signals within certain frequency band rather than simple periodic stimulus, and the firing patterns will show multiple modes by applying mixed signals. Similar coherence resonance is detected in an isolated neuron driven by the filtered signals. Therefore, chaotic signals are encoded to represent filtered waves with finite frequency band, and then the mixed signals are used to excite two neural circuits via nonlinear coupling. Hamilton energy for the coupled neurons via hybrid synapse is estimated to detect the controllability of synchronization between neurons. The nonlinear resistor along the coupling channel can reproduce the biophysical property of hybrid synapse accompanying with field coupling, which mainly contributes the energy exchange between neurons. It is confirmed that this hybrid synapse is effective to control the synchronization stability and phase lock even the neurons presenting with different firing patterns/modes. The results confirmed that nonlinear coupling via specific components is helpful to design hybrid synapse, and it is effective to block the bursting synchronization between neurons driven by filtered chaotic signals. Therefore, activation of this hybrid synapse can prevent the occurrence of seizure in nervous system.

Mechanism of low frequency spectral scattering by a side-branch electromagnetic device with switching shunt

Sound waves are reflected and absorbed by a passive side-branch device in a duct. The performance is limited at low frequencies if the cavity is compact. In this study, an electro-magnetic mechanism to enhance such low-frequency performance is examined. A common loudspeaker diaphragm, with its moving-coil immersed in the magnetic field, is used as a passive interface to the cavity, and a shunt analogue circuit is periodically connected and disconnected by a MOSFET. When the diaphragm is driven to vibrate by the incident wave, the reactive Lorentz force exerts extra acoustic impedance, which almost stops the diaphragm vibration if the shunt is close to a short circuit. The repeated transition between system damping of very low and high values scatters a significant portion of the incident sound energy to frequencies other than the source frequency. The peak energy scattering efficiency is found when the switching is twice the frequency of the incident. The sudden removal of the Lorentz force by MOSFET switch-off creates a boost in the diaphragm response, which is otherwise suppressed by the cavity stiffness, leading to much enhanced sound reflection. When the incident wave is random with a finite frequency band, scattering effect is found to offer a positive virtual mass, which counters the high system stiffness in the low frequencies.

Parameter Estimation for Robotic Manipulator Systems

In this paper, a novel methodology for estimating the parameters of robotic manipulator systems is proposed. It can be seen that, for the purpose of parameter estimation, the input torque to each joint motor is designed as a linear combination of sinusoids. After the transient responses of joint angles exponentially converge to zero, the steady states of joint angle outputs can be extracted. Since the steady states of joint angles are the equivalent finite Fourier series, the coefficients of the steady state components of joint angles can be further extracted in a fundamental period. With the amazing finding that the steady states contain all dynamic information of manipulator systems, all unknown parameters of the system model can be accurately estimated with the extracted coefficients in finite frequency bands. The simulation results for a two-link manipulator are carried out to illustrate the effectiveness and robustness against measurement noise of the proposed method.

A Universal Framework of the Generalized Kalman–Yakubovich–Popov Lemma for Singular Fractional-Order Systems

The well-known generalized Kalman–Yakubovich–Popov lemma is widely used in system analysis and synthesis. However, the corresponding theory for singular systems, especially singular fractional-order systems (SFOSs), is lacking. Therefore, many control problems for this type of systems cannot be optimized in limited frequency ranges. In this article, a universal framework of the finite frequency band generalized Kalman–Yakubovich–Popov lemma for SFOSs is established, the bounded real lemma in the sense of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${L_{\infty }}$ </tex-math></inline-formula> -norm is derived for different frequency ranges, and the corresponding controller is designed to improve the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${L_{\infty } }$ </tex-math></inline-formula> performance index of SFOSs. Three illustrative examples are given to demonstrate the correctness and effectiveness of the theoretical results.

Robust feedback controller in finite frequency based on H∞ performance for a variable speed wind turbine

The modern wind turbine system is modelled as a flexible structure operating in the presence of wind speed turbulences. Furthermore, it's highly nonlinear and its dynamic changes rapidly with the change of wind speed. A sophisticated control system is needed to allow wind turbines to generate power in a wide variety of wind conditions. This paper investigates a system control in finite frequency based on H∞ performance in order to maximise the extracted energy from the wind while mitigating aerodynamic loads. The finite frequency approach is used to design a robust feedback control to stabilise the system when the disturbances occur in a finite frequency band due to the stochastic nature of the wind flow. The controller gains are given in terms of linear matrices inequality (LMIs) which can be solved easily using existing numerical tools. The performance of the proposed control strategy is investigated in terms of stability and robustness under variable wind speed, and illustrated by tests simulation using MATLAB® software.

Metasurfaces for efficient digital noise absorption

We numerically demonstrate two types of metasurface absorbers to efficiently absorb digital signals. First, we show that the digital waveforms used in this study contain not only a fundamental wave but also nonnegligible harmonic waves, which limits the absorption performance of a conventional metasurface absorber operating in only a single, finite frequency band. The first type of the proposed absorbers is designed using two kinds of unit cells, each of which absorbs either a fundamental frequency or third harmonic of an incident digital waveform. This dual-band metasurface absorber exhibits absorption performance exceeding that of the conventional metasurface absorber and more strongly dissipates the energy of a digital waveform. In addition, the second type of absorber exploits the concept of nonlinear analogous circuits to convert an incoming wave to a different waveform, specifically, a triangular waveform that has a larger magnitude at a fundamental frequency. Therefore, the incoming waveform is more effectively absorbed by this waveform-conversion metasurface absorber as well. Although still there remain some issues to put these digital signal absorbers into practice, including experimental validation, our results contribute to mitigating electromagnetic interference issues caused by digital noise and realising physically smaller, lighter digital signal processing products for the next generation.

The Langmuir probe measurements in a low-pressure discharge supported by hollow cathode using the combined periodic and noise sweep signals

Тhe newly developed electronic set-up for working with Langmuir probes was used in measurements of the properties of the electronic component in the discharge with a hollow rectangular cathode. For the formation of current-voltage characteristics for the first time, it was proposed to use noise voltage signals in combination with traditional sawtooth or sinusoidal ones. The noise voltage can be applied to obtain the electron energy distribution functions (EEDF) both in the whole energy range and for its selected energy intervals. This improves the accuracy and reproducibility of measurements of distributions at the finite frequency band of the equipment. Measurements of the electron energy distributions, concentrations, mean energies, and plasma potentials were carried out with spatial resolution for the discharge in helium and its mixtures with water molecules and other rare gases which are of interest for optical actinometry. The EEDF dynamic is of not less (3–3.5) orders range All parameters are substantially inhomogeneous. An increase in He pressure (1–4) Torr leads to a drop in the plasma potential throughout the space and at the same time increases its gradient. The typical EEDF is of the two-peak shape. This correlates with the redistribution of electrons from the low-energy region to the high-energy region, which is apparently due to the nonlocality of the processes of the formation of distributions in an inhomogeneous electric field. The additives of molecules prevent such energy transfer.

Feedback Resonating Control for a Wave Energy Converter

Through the use of advanced control techniques, wave energy converters (WECs) can achieve substantial increases in energy absorption. The motion of the WEC device is a significant contribution to the energy absorbed by the device. Reactive (complex conjugate) control maximizes the energy absorption due to the impedance matching. The issue with complex conjugate control is that, in general, the controller is noncausal, which requires prediction of the incoming waves. This article explores the potential of employing system identification techniques to build a causal transfer function that approximates the complex conjugate controller over a finite frequency band of interest. This approach is quite viable given the band-limited nature of ocean waves. The resulting controller is stable, and the average efficiency of the power captured by the causal controller in realistic ocean waves is 99%, when compared to the noncausal complex conjugate.

On the physical meaning of time-domain constitutive models with complex parameters

This paper revisits the physical meaning of linear, time-domain constitutive models with complex parameters that have been presented in the literature and concludes that such models are not physically realizable. While complex-parameter phenomenological models (including those with complex-order time derivatives) may be efficient in capturing in the frequency domain the frequency-dependent behavior of viscoelastic materials over a finite frequency band, they do not possess physically acceptable time-response functions. The paper first reviews the intimate relation between the causality of a physically realizable constitutive model and the analyticity of its frequency-response function and explains that in theory it is sufficient to conduct a nonlinear regression analysis for estimating the model parameters either on only the real part or on only the imaginary part of its frequency-response function, given that they are related with the Hilbert transform. Consequently, the resulting model-parameters are real-valued; therefore, there is no theoretical justification to conduct the nonlinear regression analysis for estimating the model parameters in the complex space. The paper concludes with an example by showing that the relaxation modulus of the complex-coefficient Maxwell model is a divergent function at all positive times; therefore it is not a physically realizable constitutive model.

Exactness of the Born approximation and broadband unidirectional invisibility in two dimensions

Achieving exact unidirectional invisibility in a finite frequency band has been an outstanding problem for many years. We offer a simple solution to this problem in two dimensions that is based on our solution to another more basic open problem of scattering theory, namely finding scattering potentials $v(x,y)$ in two dimensions whose scattering problem is exactly solvable for energies not exceeding a critical value $E_c$. This extends the notion of quasi-exact solvability to scattering theory and yields a simple condition under which the first Born approximation gives the exact expression for the scattering amplitude whenever the wavenumber for the incident wave is not greater than $\alpha:=\sqrt{E_c}$. Because this condition only restricts the $y$-dependence of $v(x,y)$, we can use it to determine classes of such potentials that have certain desirable scattering features. This leads to a partial inverse scattering scheme that we employ to achieve perfect broadband unidirectional invisibility in two dimensions. We discuss an optical realization of the latter by identifying a class of two-dimensional isotropic active media that do not scatter incident TE waves with wavenumber in the range $(\alpha/\sqrt 2,\alpha]$ and source located at $x=\infty$, while scattering the same waves if their source is relocated to $x=-\infty$.

Chatter detection in robotic drilling operations combining multi-synchrosqueezing transform and energy entropy

Robotic drilling shows higher efficiency and precision than the manual drilling, which has great application prospects in the aviation manufacturing. Nevertheless, due to the detrimental effects on surface quality, tool wear, the safety of the robot and machining efficiency, chatter vibration has been a major obstacle to achieve stable and efficient robotic drilling. Therefore, it is particularly significant to detect and manage to suppress the chatter as early as possible. This paper presents a novel approach to identify the chatter in robotic drilling process based on multi-synchrosqueezing transform (MSST) and energy entropy. To begin with, matrix notch filters are designed to effectively eliminate the interference of spindle rotating frequency and its harmonics to the measured vibration signal. Subsequently, the filtered signal is processed by the MSST to obtain concentrated time-frequency representation. Then, the signal is divided equally into finite frequency bands and the subcomponent corresponding to each frequency band is reconstructed through the reverse MSST. Finally, in consideration of the change of the vibration signal in frequency and energy distribution when chatter occurs, the energy entropy is computed as the chatter detection indicator. The proposed chatter detection method was validated by robotic drilling experiments with different tools, machining parameters, and workpiece material, and the results indicate that the proposed method can effectively detect the chatter before it is fully developed and recognize the chatter earlier than the synchroextracting-based method.

Achievable simultaneous time and frequency domain energy concentration for finite length sequences

For numerous applications in the field of signal processing, it is desired to design a compact window that can simultaneously concentrate maximum energy in finite time interval and frequency band. Although zero-order discrete prolate spheroidal sequence (DPSS) meets this requirement, it is of infinite support. Limiting this sequence to finite support no longer guarantees the optimality property. This study aims at designing a discrete finite length window that can maximise the energy simultaneously in narrow time interval and frequency band. A multi-objective optimisation approach is adopted to obtain the upper bound of maximum achievable time and frequency domain energy concentrations for finite length sequences. The optimal sequence thus obtained is termed as the optimal window with finite support (OWFS), and its various associated properties are discussed. It is shown analytically that as the support of OWFS approaches infinity, it converges to zero-order DPSS. In order to illustrate its optimality, the compactness of the proposed OWFS is compared with those of various window functions. Extending the proposed OWFS, this study also discusses the formulation and associated properties of the zero-order periodic DPSS. Further, the closed form expression for the upper bound of achievable time and frequency domain energy concentrations is also derived.

Bandlimited Distortionless Material Design by an Approximation of the Heaviside Condition

The distortionless propagation of signals in a medium offers a way to preserve the signal integrity. There exists a condition for distortionless propagation on a transmission line known as the Heaviside condition. This paper proposes the use of the Heaviside condition to characterize and design magneto-dielectric materials that provide distortionless propagation in a specified finite frequency band. Plane wave propagation in a magneto-dielectric material is modeled by a transmission line model, thereby assuming transverse electromagnetic mode propagation. Then, the Heaviside condition is employed to derive the frequency-dependent permittivity and permeability functions of the material in rational form, so they satisfy the condition in a specified frequency interval. A procedure to design such materials is described. A numerical example of the design process is provided and an illustration of the effectiveness of modeled material in fulfilling the Heaviside condition in a specified frequency interval both in the time and frequency domains is given, indicating the validity of the approximation. The design procedure is as such a suitable preliminary design guide for deriving a realizable description of a magnetodielectric, exhibiting the distortionless property in the desired frequency interval, with certain specified requirements put on the loss, or the permeability and permittivity values satisfied. The obtained results may initiate further investigations into the bandwidth restrictions of the approximation, on closed-form design solutions, and the practical realization of such materials.

Tuning of vibration absorbers and Helmholtz resonators based on modal density/overlap parameters of distributed mechanical and acoustic systems

This paper presents a study on the tuning of vibration absorbers and Helmholtz resonators used to control at target resonance frequencies respectively the flexural response of lightly damped distributed structures and the acoustic response of lightly damped cavities subject to broadband stochastic excitations. The vibration and acoustic control effects of these two devices are assessed considering the broadband flexural response and acoustic response of typical structures and enclosures encountered in practical applications, that is: beam, thin plate and thin walled cylinder structures and one-dimensional duct, two-dimensional slender volume, three-dimensional volume enclosures. The herein proposed multi-mode tuning approaches are based on the H2 cost functions of the total flexural kinetic energy of the three structures and of the total acoustic potential energy of the three enclosures. The H2 cost functions are defined within finite frequency bands centred at the target structural or acoustic resonance frequencies respectively. A comprehensive overview of the modal density and modal overlap functions for the flexural response of the three structures and for the acoustic response of the three enclosures is also presented to provide physical interpretations and practical guidelines on the performance and applicability of classical single-mode and the proposed multi-mode tuning approaches. The study shows that classical tuning laws can be straightforwardly employed to control the response at low resonance frequencies such that the modal overlap is not greater than one, whereas to control the response at higher resonance frequencies, where the modal overlap is significantly greater than one, the proposed multi-mode tuning approach should be adopted.

Nonfragile H∞ Control of Delayed Active Suspension Systems in Finite Frequency Under Nonstationary Running

The vehicle active suspension has drawn considerable attention due to its superiority in improving the vehicle dynamic performance. This paper investigates the nonfragile H∞ control of delayed vehicle active suspension in a finite frequency range under nonstationary running. The control objective is to improve ride quality in a finite frequency band and ensure suspension constraints, and a quarter car model of the active suspension is established for a controller design. Then, the input delay, actuator uncertainty, and external disturbances are considered in the controller design. Moreover, a further generalization of the strict S-procedure is utilized to derive a sufficient condition in terms of linear matrix inequality (LMI) to capture performance in the concerned frequency range. Furthermore, a multi-objective controller is designed based on projection lemma in the framework of the solution of LMIs. A nonstationary road profile is established, and numerical simulations are also conducted to show the effectiveness and robustness of the proposed controller. Finally, experimental tests on a quarter-car test rig are implemented to examine the performance of the proposed controller for real applications.

Multi-Objective H-/H∞ Fault Detection Filter Design For T-S Fuzzy Systems With Finite Frequency Specifications

This study aims to synthesize a fault detection filter for continuous-time T-S fuzzy systems. The proposed filter is designed in finite frequency domain in as much as the frequency ranges of the fault and unknown disturbances are assumed to be known beforehand and to belong in finite frequency bands. The generated residual is ensured to be as sensitive as possible to faults and as robust as possible against unknown disturbances by means of two finite frequency performance indices such as H_ and H∞ norms. By the use of the Generalised Kalman-Yakubovich-Popov (GKYP) lemma and the Lyapunov method, sufficient design conditions are derived in LMI terms. Finally, simulation study is introduced to validate the developed approach.