Transfer Function Matrix Research Articles

Numerical and experimental analysis on helicopter's main rotor transmission for predicting structure-borne noise (SBN) using CB-TPA methods

A large number of a vehicle's mechanical systems are responsible for tonal vibrations, which propagate through the connected structures to radiate structure-borne noise into the cabin. In the literature, transfer path analysis (TPA) methods make it possible to solve vibro-acoustic problems using sub-structuring applications. This paper presents a case study of a heavy-active component connected to a plate backed cavity, using Component-Based transfer path analysis methods. The studied academic system is representative of a helicopter's main transmission. Both numerical and the experimental characterization are used to discuss the effect of several parameters, such as coupling (in-situ) vs decoupling (sub-structuring), completeness of the used transfer function matrix, the accuracy of the inversion method, as well as the rigidity of the test bench used to identify the equivalent forces. It is shown both numerically and experimentally that by using part of the frequency response functions matrix, one can reconstruct the response of both vibration and acoustic targets locations, even by decoupling the system and characterizing the equivalent forces on a test bench.

Dynamic matrix theory for resonance response of plasmonic metamaterial lattice

In this paper, a lattice dynamics method, named M-K matrix method, is proposed to investigate the near-field resonance response of a plasmonic metamaterial lattice under an oblique incident field with an arbitrary incident angle. By considering the electric, magnetic and field-dipole interactions, we construct a dissipative many-body Lagrange model for a reference lattice. A collective forced vibration equation, with the degree of freedom equals to the number of nanoparticles in a cell, is introduced to describe the lattice resonance under a polarized field. The resonance frequencies can be conveniently obtained from the poles of transfer function matrix. Based on this elegant matrix differential equation, one can calculate the amplitude-frequency and phase-frequency responses of plasmonic lattice, and analysis the normal modes from dispersion relations. The analytical results, which are from three examples: simple square lattice, binary chain and chessboard lattice, are perfectly matched with numerical simulations in a large frequency band, proving it to be an effective tool to calculate the dynamic response of plasmonic lattice.

A Method for Evaluating the Impact of Controllers and Wind Turbine Generators on Low-Frequency Oscillation

Based on the celebrated Generalized Nyquist Criterion, this paper presents a new frequency-domain method to analyze the impact of governor-turbine systems (GTSs), power system stabilizers (PSSs) and wind turbine generators (WTGs) on small disturbance stability in power systems. Compared with other common analysis method, the new method can avoid the calculations of eigenvalues, eigenvectors and residues, and the impact of multiple controllers or WTGs can be obtained using simple matrix operations. In addition, the method is intuitive for users since the stability analysis results can be displayed in the complex plane directly. The new method indicates that the impact of controllers and WTGs on power system is determined by the phase of certain elements in the transfer function matrices of controllers, WTGs and synchronous grid. Based on the information provided by the afore-mentioned transfer function matrices, the parameters of controllers can be optimized properly. The proposed method has been tested using the data of a four-machine two-area system and a regional power grid in China. The results demonstrate that the effect of controllers and WTGs can be conveniently identified, and the effectiveness of parameter tuning for controllers is verified.

Innerization and Singular LQ Control Problem for Linear Discrete-Time Systems

In this paper, we discuss the LQ problem for discrete-time linear systems with singular weight. The interactor with all-pass property is used in order to make a given strictly proper system be proper. In our approach, the type of Riccati equation to be solved is different from the result for a square transfer function matrix case, where the input weight equals to zero. The relation between our approach and the singular weight case is discussed. Unlike the square case, the explicit solution to the problem cannot be obtained and a recursive method to solve the Riccati equation is shown. An application to the finite settling-time control is also discussed.

2-D lossless FIR filter design using synthesis of the paraunitary transfer function matrix

2-D lossless FIR filter design using synthesis of the paraunitary transfer function matrix

Extended Approach to Analytical Triangular Decoupling Internal Model Control of Square Stable Multivariable Systems With Delays and Right-Half-Plane Zeros

The Analytical Triangular Decoupling Internal Model Control (ATDIMC) technique for 2×2 systems is generalized to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> × <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> systems ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> ≥2) with delays and right-half-plane (RHP) transmission zeros. The formulation is done by first creating a triangular closed-loop transfer function matrix corresponding to the achievement of the triangular decoupling objective of restraining inverse-response and control-loop-interaction characteristics to a single plant output. Subsequently, the corresponding multivariable internal model controller is calculated, with transfer-function approximations made using optimization algorithm that minimizes the Integral Time-Weighted Absolute Error (ITAE) of the difference between the step responses of the original and reduced expressions. It is shown that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> ATDIMC designs emerge that achieve the shifting of inverse responses and interactions to a least-desired output, with delays retained for all outputs and asymptotic tracking of setpoints achieved for all <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> outputs of each design. To mitigate the possible effect of severe interaction on the least-desired output, a modification of this formulation is performed to spread inverse-response behavior to a second output, while minimizing the interaction of that output with the initial least-desired output. Simulation results for selected 3×3 and 4×4 systems show the effectiveness of these propositions.

An Improved Quantitative Analysis Method of Oscillation Mode for DFIG-Based Wind Power Base With LCC-HVDC Transmission Considering Frequency Coupling Characteristic

The line-commutated converter-based high-voltage direct-current (LCC-HVDC) transmission has become one of the main forms to deliver wind power in China. However, due to the connections of a large number of power electronic devices (PEDs), there emerges a risk of sub/super-synchronous oscillations in the DFIG-based wind power base with LCC-HVDC transmission. The existing multi-node system analysis methods have ignored the frequency coupling characteristic (FCC) of PEDs, unable to obtain accurate oscillation characteristics. Besides, the relationship between the oscillation and multi-level factors has not been revealed yet. Therefore, this paper proposes an improved quantitative analysis method of oscillation mode which considers the FCC on the basis of the system admittance network model. Firstly, the impedance model of the system considering the FCC is established. Then, the improved quantitative analysis method of the oscillation mode considering the FCC is proposed and its steps are as follows. 1) To establish the system transfer function matrix considering the FCC, and determine the system stability accurately by the dominant oscillation mode; 2) To define the node oscillation participation factor, considering the effect of the coupling frequency, and quantify the participation degree of each node and identify the origin and weak point of oscillation; 3) To carry out multi-level oscillation mode sensitivity analysis. Finally, the oscillation characteristics and laws of the DFIG-based wind power base with LCC-HVDC transmission are studied, and the time-domain simulations in MATLAB/Simulink validate the analytical results.

Синтез нейросетвого регулятора для линеаризованной модели объекта – два перевернутых маятника на тележке

This article demonstrates the procedure for the synthesis of a neural network controller for a linearized model of the plant «two inverted pendulums on a cart». A feature of this plant can be considered its nonsquare matrix transfer function and the number of input effects is less than the number of output effects. The task of the control is to stabilize the angles of the inverted pendulums in a stable position and transfer the position of the cart to a set value. A distinctive feature of the demonstrated procedure for the synthesis of a neuroregulator is the deterministic choice of architecture and initialization of the weighting coefficients of the neural network. Data on the choice of architecture and on the values of initialized weighting coefficients for the neural network controller are obtained based on information about the transfer function of the controller obtained by the modal method using the polynomial matrix decomposition of the system. Recommendations for structural transformations of a neural network regulator containing recurrent connections are given. They are necessary for further training of a neural network controller with a deterministic approach to initialization of weight coefficients used in the demonstrated synthesis procedure. As a result of the complexity of the structure and further training of the neural network controller obtained, it is possible to increase the efficiency of the automatic control system compared with the system using the controller obtained by the modal method.

Investigating the effect of edge modifications on networked control systems: Stability analysis

This paper investigates the impact of addition/removal/reweighting of edges in a complex networked linear control system. For networks of positive edge weights, we show that when adding edges leads to the creation of new cycles, these in turn may lead to instabilities. Dynamically, these cycles correspond to positive feedback loops. Conditions are provided under which the modified network is guaranteed to be stable. These conditions are related to the steady state value of the transfer function matrix of the newly created positive feedbacks. The tools we develop in the paper can be used to investigate the fragility of a network, i.e., its robustness to structured perturbations.

Structure Identifiability of an NDS With LFT Parametrized Subsystems

Requirements on subsystems have been made clear in this paper for a linear time invariant (LTI) networked dynamic system (NDS), under which subsystem interconnections can be estimated from external output measurements. In this NDS, subsystems may have distinctive dynamics, and subsystem interconnections are arbitrary. It is assumed that system matrices of each subsystem depend on its (pseudo) first principle parameters (FPPs) through a linear fractional transformation (LFT). It has been proven that if in each subsystem, the transfer function matrix (TFM) from its internal inputs to its external outputs is of full normal column rank (FNCR), while the TFM from its external inputs to its internal outputs is of full normal row rank (FNRR), then the structure of the NDS is identifiable. Moreover, under some particular situations like there are no direct information transmission from an internal input to an internal output in each subsystem, a necessary and sufficient condition is established for NDS structure identifiability. A matrix valued polynomial (MVP) rank based equivalent condition is further derived, which depends affinely on subsystem (pseudo) FPPs and can be independently verified for each subsystem. From this condition, some necessary conditions are obtained for both subsystem dynamics and its (pseudo) FPPs, using the Kronecker canonical form (KCF) of a matrix pencil.

Application of matrices for transfer function values calculation in mechanical systems

The paper describes the formalism and methodology that can be employed for calculation of transfer function in distributed parameter elastic mechanical systems. Generalized formalism for derivation of transfer function matrices is presented as developed in accordance with the Hilbert-Schmidt theorem. Matrix-based method to determine elastic mechanical system transfer function is offered. The solution of the problem of forced harmonic oscillations of an elastic body of a mechanical system with the presence of friction is considered. The described technique can be applied to find the transfer functions of technological equipment in order to determine the dynamic characteristics of the system.

HVAC multivariable system modelling and control

Heating, Ventilation and Air Conditioning (HVAC) is a multivariable process where any alteration with one system input affects most or all of the system’s outputs simultaneously. Owing to its comprehensiveness, a readily derived multivariable HVAC mathematical model is selected for this work, mainly a hybrid distributed-lumped parameters model. As the transfer function matrix was not established in the selected HVAC model, it was exclusively developed in this study, using the time domain graphical responses of the chosen model. Based on the developed transfer function matrix, a conceptual two-step approach was followed to control HVAC model performance. The first was decoupling the interactions that affect all the system outputs, and the second was designing proper PID controllers for each decoupled loop similar to those used for single input single output (SISO) systems. A direct Nyquist Array (DNA) multivariable control strategy was used for this purpose and successfully decoupled the HVAC system into three separate (SISO) loops. Three PID controllers afterwards were applied for each decoupled loop. The results showed quite decoupled system outputs with a minor coupling percentage so that any change in a system input only affected the corresponding system output. The output responses are also underdamped with almost zero steady-state error confirming the effectiveness of the selected PID parameters. The values of steady-state responses are obtained in (10–15) s compared with (200–600) s of open-loop response time. However, various overshoot percentages in the responses are encountered but are relatively small, with a short settling time, so they don’t affect the thermal comfort of the ventilated volume. System stability using the Nyquist criterion has also been examined and found to satisfy the criterion. The multivariable DNA control technique and the SISO closed-loop PID controllers have shown the capability to suppress external disturbances and restore the system to its original functional steady-state values.

Robust control of water quality in intensive aquaculture using multi‐variable quantitative feedback theory: From an Indian context

AbstractThis paper addresses the problem of controlling turbidity, dissolved oxygen, ammonium‐ion concentration, and water‐temperature to maintain the desired water quality in an intensive aquaculture plant. The research is carried out to fit into the present scenario of intensive aquaculture in India. The plant model along with uncertain parameters are derived using physical laws and the data acquired from an aquaculture pond in Assam, India. A pre‐compensated multi‐variable quantitative feedback theory (QFT)‐based fully populated robust matrix controller is proposed to mitigate the control challenge. A novel method is used to design the pre‐compensator to enhance the diagonal dominance of plant transfer function matrix. The desired robust stability, reference tracking, and sensitivity specifications are fulfilled by the proposed QFT‐based robust controller despite the parametric uncertainty. The effectiveness of the proposed method is validated through numerical simulation. A comparative study against a controller shows that the proposed controller strategy gives a satisfactory performance compared to it.

Robust method for the identification of dynamical anisotropic flexible bearing parameters using multi-objective optimization and structural modification technique

In this paper, a deterministic multi-objective design optimization problem is addressed in order to identify the dynamical joint parameters such as mass, stiffness, damping and cross-coupling parameters. The proposed formulation uses directly the measured frequency transfer functions of the constrained system (with supports) and the mode of the unconstrained system (without supports) to predict the joint dynamic parameters. Since measurement noise often leads to erroneous identifications, the deterministic multi-objective optimization (DMOO) is used to eliminate the redistribution and amplification of noise due to the inversion of the frequency transfer function matrices. The proposed optimization design gives satisfactory results when using noise-free data as well as under realistic noise levels. A parametric study was also performed in order to assert the sensitivity of dynamical joints parameters against the level of noise. The results show also that the constrained non-dominated sorting genetic algorithm (C-NSGA-II) was capable to generate well-distributed reliable Pareto solutions.

Study on mechanism analysis, specimen influence, and compensation control of large compound shaking table

In order to realize the wide frequency excitation and high accuracy control of a new type of large load-capacity seismic simulation shaking table (named large compound shaking table, LCST), it is necessary to study the in-depth mechanism, influence factors, and compensation algorithm of the LCST. In this paper, the mechanism model of LCST was established by transfer function matrix and the coupling characteristics were analyzed by Bristol method. Then, the three-variable control simulation analysis was carried out by Simulink. The specimen influence on the LCST was tested by setting different mass, frequencies, and damping ratios of the specimen. A series of simulation studies suggest that the control accuracy of LCST is most sensitive to the frequency of the specimen, and high natural frequency could even lead to system instability. For the sake of high-precision control, this paper proposed a feedforward decoupling compensation control (FDCC) strategy. Through numerical studies, the improved tracking of the FDCC strategy was demonstrated. In addition, the mature compensation methods in the conventional shaking table can be introduced reasonably into the control loop by FDCC strategy so that the LCST can more accurately replicate the characteristics of synthetic and historic earthquakes.

Design of discrete-time matrix all-pass filters using subspace Nevanlinna pick interpolation

Unitary matrix-valued functions of frequency are matrix all-pass systems, since they preserve the norm of the input vector signals. Typically, such systems are represented and analyzed using their unitary-matrix valued frequency domain characteristics, although obtaining rational realizations for matrix all-pass systems enables compact representations and efficient implementations. However, an approach to obtain matrix all-pass filters that satisfy phase constraints at certain frequencies was hitherto unknown. In this paper, we present an interpolation strategy to obtain a rational matrix-valued transfer function from frequency domain constraints for discrete-time matrix all-pass systems. Using an extension of the Subspace Nevanlinna Pick Interpolation Problem (SNIP), we design a construction for discrete-time matrix all-pass systems that satisfy the desired phase characteristics. An innovation that enables this is the extension of the SNIP to the boundary case to obtain efficient time-domain implementations of matrix all-pass filters as matrix linear constant coefficient difference equations, facilitated by a rational (realizable) matrix transfer function. We also show that the derivative of matrix phase constraints, related to the group delay at the interpolating points, can be optimized to control the all-pass transfer matrices at the unspecified frequencies. Simulations show that the proposed technique for unitary matrix filter design performs as well as traditional DFT based interpolation approaches, including Geodesic interpolation and the popular Givens rotation based matrix parameterization.

Research on acoustic reconstruction methods of the hull vibration based on the limited vibration monitor data

The prediction of hull vibration response is the basis for the quantitative control of cabin noise and underwater radiated noise, which has an important engineering value to obtain vibration characteristics accurately. In this paper, a new method is proposed to reconstruct hull vibration by some monitoring data in low frequencies. The hull vibration response is reconstructed by the monitoring data and the transfer function, and the ill-posed problem of inversion for the transfer function matrix is solved by the total least-squares regularization. A P-GRU (Peak-based Gated Recurrent Unit) neural network correction model is proposed to improve the prediction accuracy of vibration response. Taking a certain cabin structure as an example, some research such as the hull vibration data monitoring, the vibration transfer function calculation, vibration response reconstruction, and correction based on experimental data were carried out, and the simulation calculations and verification of experiment models were obtained. The multi-parameter comprehensive method is adopted to quantitatively evaluate the results between the simulation and the experiment. The results show that the acoustic reconstruction results are in good agreement with the experimental data. The overall level error is within 3 dB, the main peak value correlation coefficient is above 0.9, and the main peak difference is within 4 dB. The mechanism of the rapid and accurate prediction of the low-frequency vibration for the hull based on limited monitoring data is discussed by using a semi-physical simulation method combining the simulation calculation, vibration monitoring, and machine learning. The problem of phase asynchrony was solved, and strong support was provided for the construction of the ship's acoustic digital twin.

Physics-Based Greedy Algorithm for Reliable Fast Frequency Sweep in Electromagnetics via the Reduced-Basis Method

A reliable fast frequency sweep model order reduction (MOR) process is detailed. A reduced-basis approximation is taken into account to accurately and efficiently describe the electromagnetic field in a frequency band of analysis. The reduced-basis space is made up of snapshots of the electric field adaptively chosen on a physics-based greedy algorithm. Following a theoretical analysis starting from time-harmonic Maxwell’s equations, in- band eigenresonances are shown to significantly contribute to the electric field in the band of analysis. An impedance matrix transfer function description of the microwave circuit is used and a pole-residue expansion of this matrix-valued impedance transfer function is detailed. A fundamental physical property is identified, from which a straightforward a posteriori error estimator arises, namely, matrix residues in the pole-residue expansion of the impedance transfer function must be rank-1. This cheap computation is well-suited for fast greedy algorithm strategies in adaptive construction of the reduced-basis approximation. Contrary to what has been previously done, a straightforward physics-based greedy algorithm that does not need to scan the whole frequency band of interest to enrich the reduced-basis approximation is proposed. Finally, actual microwave applications illustrate the capabilities and efficiency of the new physics-based a posteriori error estimator in the proposed methodology.

Integrating Vernier spectrum with Fano resonance for high sensitivity of an all-optical sensor

Vernier and Fano resonances are promising approaches for enhancing the sensitivity of an all-optical sensor. A theoretical analysis was performed to integrate a Fano-like resonance shape with a Vernier resonance by considering the presence of partially reflective end facets at a double microring resonator waveguide. The system was developed based on scattering matrix and optical transfer function. The all-pass racetrack microring resonator (ARMRR) and the double racetrack microring resonator (DRMRR) were compared with and without the end facet at the waveguide to analyze the dynamic change of the output resonance spectrum. The spectrum was analyzed based on the free spectral range and resonance pattern. The resonator systems were applied to a refractive index-based sensing protocol, which was operated by a resonance wavelength shift with a refractive index change. The sensitivity was optimized by varying the configuration parameters such as the radius of the ring, the distance between the end facet, and the coupling coefficients. Integrating Vernier spectrum with Fano resonance improved the sensitivity for ARMRR configuration by 5.16% and the sensitivity for DRMRR configuration by 6.31%. The recorded limit of detection (LOD) of the DRMRR was 3.30 × 10-5.

Long-distance mid-wave infrared super-resolution compressive imaging

Super-resolution imaging (SRI) for mid-wave infrared (MWIR) has attracted increasing attention in recent years due to the expensive price for a large number of pixels MWIR cameras. Investigation of the compressed sensing method can partially improves the resolution. However, the quality of SRI is highly related to the transfer function matrix of the optical system, which is difficult to be accurately measured because of the noise existed in MWIR detection, especially in long-distance systems. In this work, we propose a transfer function matrix calculation method which overcomes the issues of low imaging contrast and signal-to-noise ratio compared with previous studies. And we further establish a long-distance focal plane array-based compressive imaging system with a resolution of two digital micro-mirror device pixels which just satisfies the system diffraction limit. In addition, we achieve the 4 × 4 times super-resolution high-quality reconstruction of long-distance digital and physical objects with only six measurements.