Coefficients Of Transfer Function Research Articles

Complementary Metal Oxide Semiconductor Circuit Realization of Inverse Chebyshev Low-Pass Filter of Order (1 + α)

This paper presents the CMOS circuit realization of a low-pass Inverse Chebyshev fractional-order filter (FOF) of order (1 + α) using the inverse-follow-the-leader feedback (IFLF) topology. A nonlinear least squares optimization routine is used to determine the coefficients of the fractional-order transfer function to approximate the stop-band characteristics. The Inverse Chebyshev FOF of orders 1.3, 1.6, and 1.9 using cross-coupled operational transconductance amplifier (OTA) was designed in united microelectronics corporation (UMC) 180 nm complementary metal–oxide–semiconductor process. The MATLAB and Cadence Spectre simulations are used to validate the implementation of the fractional-order filter of orders 1.3, 1.6 and 1.9. The dynamic range (DR) of the filter is found to be 83.04 dB, 86.13 dB, and 84.71 dB, respectively, for order of 1.3, 1.6, and 1.9. The simulation results such as magnitude response, transient plot, Monte Carlo, and PVT plots, have justified the design accuracy.

Scaled Sensitivity of Pavement–Mechanistic-Empirical Transfer Function Coefficients for Flexible and Rigid Pavements

The American Association of State Highway and Transportation Officials (AASHTO)Ware Pavement–Mechanistic-Empirical (ME) transfer functions need local calibration for reliable performance predictions. It is often not viable to calibrate all coefficients at the same time. Therefore, it is crucial to identify the most sensitive transfer function coefficients. Moreover, the sensitivity also indicates the impact of each coefficient on the performance prediction. Several studies have shown the sensitivity of the Pavement-ME design inputs, but limited research is available on the sensitivity of transfer function coefficients. Typically, the sensitivity is obtained using a normalized sensitivity index (NSI). This paper estimated the sensitivity of the Pavement-ME transfer function coefficients using scaled sensitivity coefficients (SSCs). NSI values are compared with the SSCs. Ten sections, each from flexible and rigid pavements, were used to calculate the NSI values. These are existing pavement sections from the Michigan Department of Transportation (MDOT) pavement management system (PMS) database, designed using the 1993 AASHTO design guide. Results show that SSCs provide a more reliable sensitivity on a range of independent variables rather than a point estimate, unlike NSI. NSI values showed variability among different sections and magnitudes of predicted performance. Calculation of SSCs is a forward problem and does not require any input data. A mathematical model (transfer function) is needed; therefore, SSCs can be calculated on any range of independent variables. It also shows the potential correlation between different coefficients and accuracy in estimation.

Adaptive identification of linear infinite-dimensional systems

We propose an adaptive algorithm for identifying the unknown parameter (possibly vector-valued) in a linear stable single-input single-output infinite-dimensional system. We assume that the transfer function of the infinite-dimensional system can be expressed as a ratio of two infinite series in s (the Laplace variable). We also assume that certain identifiability conditions, which include a persistency of excitation condition, hold. For a fixed integer n, we propose an adaptive update law (a differential equation in time) driven by real-time input-output data for estimating the first n + 1 coefficients in the numerator and the denominator of the transfer function. We show that the estimates for the transfer function coefficients generated by the update law are close to the true values at large times provided n is sufficiently large (the estimates converge to the true values as time and n tend to infinity). The unknown parameter can be reconstructed using the transfer function coefficient estimates obtained with n large and the algebraic expressions relating the transfer function coefficients to the unknown parameter. We also provide a numerical scheme for verifying the identifiability conditions and for choosing n sufficiently large so that the value of the reconstructed parameter is close to the true value. The class of systems to which our approach is applicable includes many partial differential equations with constant/spatially-varying coefficients and distributed/boundary input and output. We illustrate the efficacy of our approach using three examples: a delay system with four unknown scalars, a 1D heat equation with two unknown scalars and a 1D wave equation with an unknown linearly-varying (in space) coefficient.

Design of Optimal Control Systems in the Frequency Domain by the Functional of the Generalized Work

The paper considers the problem of analytical design of optimal controllers (ADOC) for one-dimensional linear stationary objects according to the functional of generalized work (FGW) A. A. Krasovsky. The use of FGW in comparison with the quadratic performance functional greatly simplifies the calculation of the optimal controller — the calculation of its matrix of coefficients mainly consists in solving the linear matrix Lyapunov equation, which, in contrast to the nonlinear matrix Riccati equation, fundamentally reduces the amount of calculations. In addition, the use of FGW provides the best stability margins of the designed system in terms of amplitude and phase. This work is devoted to the development of a method for solving the ADOC problem A. A. Krasovsky in the frequency (complex) domain, which reduces the determination of the transfer function coefficients of the optimal controller for an object of order n to the solution of the corresponding system of n linear algebraic equations. In this regard, the proposed method for solving the ADOC problem by A. A. Krasovsky differs by a much smaller amount of calculations in comparison with the standard method, in which the Lyapunov equation is solved with the desired matrix of dimensions n * n. The proposed method for the synthesis of optimal control systems, which has an analytical nature, became the basis for solving the inverse problem ADOC A. A. Krasovsky, which consists in determining the values of the weight coefficients of the FGW, which provide the given primary quality indicators of the synthesized control system. Using its relations, a relatively simple method for calculating the FGW coefficients based on the given values of the error coefficients for the designed dynamic system has been developed.

Tribological Behaviour of Hypereutectic Al-Si Composites: A Multi-Response Optimisation Approach with ANN and Taguchi Grey Method

An optimisation model for small datasets was applied to thixocasted/compocasted composites and hybrid composites with hypereutectic Al-18Si base alloys. Composites were produced with the addition of Al2O3 (36 µm/25 nm) or SiC (40 µm) particles. Based on the design of experiment, tribological tests were performed on the tribometer with block-on-disc contact geometry for normal loads of 100 and 200 N, a sliding speed of 0.5 m/s, and a sliding distance of 1000 m. For the prediction of the tribological behaviour of composites, artificial neural networks (ANNs) were used. Three inputs were considered for ANN training: type of reinforcement (base alloy, Al2O3 and SiC), amount of Al2O3 nano-reinforcement (0 and 0.5 wt.%), and load (100 and 200 N). Various ANNs were applied, and the best ANN for wear rate (WR), with an overall regression coefficient of 0.99484, was a network with architecture 3-15-1 and a logsig (logarithmic sigmoid) transfer function. For coefficient of friction (CoF), the best ANN was the one with architecture 3-6-1 and a tansig (hyperbolic tangent sigmoid) transfer function and had an overall regression coefficient of 0.93096. To investigate the potential of ANN for the prediction of two outputs simultaneously, an ANN was trained, and the best results were from network 3-5-2 with a logsig transfer function and overall regression coefficient of 0.99776, but the predicted values for CoF in this case did not show good correlation with experimental results. After the selection of the best ANNs, the Taguchi grey multi-response optimisation of WR and CoF was performed for the same combination of factors as the ANNs. For optimal WR and CoF, the combination of factors was as follows: composite with 3 wt.% Al2O3 micro-reinforcement, 0.5 wt.% Al2O3 nano-reinforcement, and a load of 100 N. The results show that developed ANN, the Taguchi method, and the Taguchi grey method can, with high reliability, be used for the optimisation of wear rate and coefficient of friction of hypereutectic Al-Si composites. Microstructural investigations of worn surfaces were performed, and the wear mechanism for all tested materials was light abrasion and adhesion. The findings from this research can contribute to the future development of hypereutectic Al-Si composites.

Data-driven modeling and regression analysis on ship resistance of in-service performance

This study employs operational data to model ship resistance, aiming to bridge the gap between controlled experiments and real-world conditions. It comprehensively analyzes wind, waves, and currents, employing nonlinear regression and z-score filtering. The model is validated using data from three identically designed ships operating on the similar servicevoyages. Key findings reveal significant impacts of wind and waves on the added resistance, variability in resistance across different loading conditions, and discrepancies between in-service performance and model test results, especially at medium to low speeds. Calm water resistance results are reliable, varying within 5%–10% of the average, though in-service performance is generally higher, indicating a need for further research. The added resistance due to wind is significant, with variations within 5%–10%, and the transverse projected area does not always proportionally affect resistance. Head winds have a greater impact on resistance than following winds at the same speed. The analysis of added resistance due to waves shows significant, but sometimes inconsistent, transfer function coefficients, suggesting simpler model structures could be more effective. The added resistance due to current if found to typically fall within a 2–3% range, indicating that significant changes are rare and localized. For large ships, short waves dominate, with resistance increasing proportionally with the non-dimensionalized wave length. While head currents can increase resistance by up to 20% and following currents can reduce it by 5–10%, these larger changes are infrequent. Segmenting data by loading conditions, routes, and speeds improves regression analysis accuracy, though excessive segmentation reduces data diversity and reliability.

Frequency-Domain Identification of Discrete-Time Systems using Sum-of-Rational Optimization

This paper proposes a new computationally tractable method to fit coefficients of a fixed-order discrete-time transfer function to a measured frequency response, with stability guaranteed. The problem is formulated as a non-convex global sum-of-rational optimization problem whose objective function is the sum of weighted squared residuals at each observed frequency datapoint. Stability is enforced using a polynomial matrix inequality constraint. The problem is solved by a moment-sum-of-squares hierarchy of semidefinite programs through a framework for sum-of-rational-functions optimization. Convergence of the moment-sum-of-squares program is guaranteed as the bound on the degree of the sum-of-squares polynomials approaches infinity. The performance of the proposed method is demonstrated using numerical simulation examples.

External Positivity of Discrete-Time Linear Systems: Transfer Function Conditions and Output Feedback

This paper develops an optimization-based synthesis procedure for fixed-order output-feedback controllers, ensuring a stable closed-loop system with a monotonic step response and rejection of persistent disturbances. This result is based on a unified set of external positivity conditions for discrete-time linear systems. The conditions are derived using an alternative technique for the inverse <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathcal {Z}}$</tex-math></inline-formula> -transform of rational transfer functions based on Bell polynomials and a convenient recurrence relation for the impulse response. Our approach yields a necessary and sufficient condition expressed as polynomial inequalities in the transfer function coefficients. Under additional assumptions, we derive a sequence of weaker but numerically more tractable conditions, leading to an efficient controller synthesis procedure.

An Approximation Method for Fractional-Order Models Using Quadratic Systems and Equilibrium Optimizer

System identification is an important methodology used in control theory and constitutes the first step of control design. It is known that many real systems can be better characterized by fractional-order models. However, it is often quite complex and difficult to apply classical control theory methods analytically for fractional-order models. For this reason, integer-order models are generally considered in classical control theory. In this study, an alternative approximation method is proposed for fractional-order models. The proposed method converts a fractional-order transfer function directly into an integer-order transfer function. The proposed method is based on curve fitting that uses a quadratic system model and Equilibrium Optimizer (EO) algorithm. The curve fitting is implemented based on the unit step response signal. The EO algorithm aims to determine the optimal coefficients of integer-order transfer functions by minimizing the error between general parametric quadratic model and objective data. The objective data are unit step response of fractional-order transfer functions and obtained by using the Grünwald-Letnikov (GL) method in the Fractional-Order Modeling and Control (FOMCON) toolbox. Thus, the coefficients of an integer-order transfer function most properly can be determined. Some examples are provided based on different fractional-order transfer functions to evaluate the performance of the proposed method. The proposed method is compared with studies from the literature in terms of time and frequency responses. It is seen that the proposed method exhibits better model approximation performance and provides a lower order model.

Adaptive Control Based on LMS Algorithm for Grid-Connected Inverters

The grid-connected inverter is the key component for the reliable and safe operation of grid-interconnected renewable energy systems. In order to ensure that the inverter output current is in-phase synchronized with the grid voltage, a highly efficient and fast control strategy is required. This paper proposes an algorithmically driven approach for designing the adaptive controller for a grid-connected DC/AC inverter. The controller consists of two adaptive IIR filters based on the LMS algorithm and has two modes of operation. During the learning mode, the controller uses the filters to estimate the coefficients of the inverse transfer function of the PWM-driven inverter at several grid frequencies within a specific range. During the online mode, the controller generates the driving signal for the inverter block using a set of learned coefficients corresponding to the current grid frequency. By constantly monitoring the grid voltage and reconfiguring the controller accordingly, a fast adaptation of the inverter output current to grid frequency variations is achieved. For grid frequency variations in the range of 48 to 52 Hz, the MATLAB simulation results show that the phase difference between the grid voltage and inverter output current waveforms becomes less than 1 degree after at most four periods.

Wave force identification for a large-scale quasi-elliptical cylinder from monitored wave elevation

Based on the potential theory, the wave force on a large-scale quasi-elliptical cylinder was identified using monitored wave elevation data. Expressions with underdetermined coefficients of quadratic transfer functions for a noncircular cylinder are presented. The linear wave forces, second-order wave forces, and hydrostatic forces on the cylinder are identified using recursive least squares in real time. A comparison between the experimental and identified results of wave forces demonstrates the effectiveness of the identification method for a noncircular cylinder. The identified wave force consisted of several force components that correspond to the Fourier coefficients of the radius function. Generally, at a low wave number, the force components corresponding to the Fourier coefficient of the radius function decrease as the order of the harmonic term increases. With increasing wave number, the force components at the high-order harmonic term may significantly increase and become the dominant components of the wave force. The phase difference between the force components was studied, in which the phase difference of the first two main components was zero in the short-side direction and is π in the long-side direction. Phase jumps occur when the force components are zero.

Определение дискретной передаточной функции приведенной непрерывной части цифровой следящей системы

Предложен способ вычисления коэффициентов дискретной передаточной функции, не требующий трудоемкого получения описывающих их аналитических выражений. Способ основан на совпадении значений переходной характеристики дискретной приведенной непрерывной части и дискретных значений переходной характеристики непрерывной части (НЧ). Последние можно вычислить любым известным способом. Разработан алгоритм вычислений, позволяющий по заданным постоянным времени НЧ и периоду дискретизации рассчитать значения дискретной передаточной функции при единичном коэффициенте преобразования. Приведен пример составления Matlab-программы вычислений. Применение программы дало результат, совпавший с расчетом по формулам, полученным классическим методом.

СЕМЕЙСТВО АКТИВНЫХ RC-ФИЛЬТРОВ ВТОРОГО ПОРЯДКА (ФНЧ, ФВЧ, ПФ) С НЕЗАВИСИМОЙ ПОДСТРОЙКОЙ ОСНОВНЫХ ПАРАМЕТРОВ

A bank of circuit design solutions for active RC filters of the second order is considered - alow-pass filter, a high-pass filter and band-pass filters, in which independent tuning of the mainparameters - the pole frequency, the quality factor of the pole and the transmission coefficient isprovided. From these positions, the requirements for three special transfer functions of a multipolefrequency-setting RC circuit, which contains two resistors and two capacitors, are formulated.By choosing the coefficients of the numerator of the first transfer function, the type of the requiredfilter (LPF, HPF, BPF) is implemented. The coefficients of the second transfer function are chosenso that they affect only the frequency of the pole. It should be noted that, depending on the set ofcoefficients of the transfer function numerator polynomial, the developed circuits have the propertyof lowering the pole frequency or increasing the pole frequency. In this case, the choice of parametersof the third transfer function provides the necessary attenuation of the pole. Using theThe introduction describes a generalized architecture of second-order active RC filters, whichallows implementing an algorithm for step-by-step tuning of the main parameters and can be usedas the basis for the synthesis of many other modifications of active RC filters. For correct independentadjustment, the following sequence must be observed: the frequency of the pole, the secondstage is the adjustment of the quality factor of the pole, and the third stage is the scalingfactor. The stages of synthesis of this class of active RC filters are considered, the coefficients ofthe transfer functions of the presented circuits of 12 band-pass filters, a high-pass filter and a lowpassfilter, confirmed by 14 patents of the Russian Federation, are given.

Automatic Regionalization of Model Parameters for Hydrological Models.

Parameter estimation is one of the most challenging tasks in large-scale distributed modeling, because of the high dimensionality of the parameter space. Relating model parameters to catchment/landscape characteristics reduces the number of parameters, enhances physical realism, and allows the transfer of hydrological model parameters in time and space. This study presents the first large-scale application of automatic parameter transfer function (TF) estimation for a complex hydrological model. The Function Space Optimization (FSO) method can automatically estimate TF structures and coefficients for distributed models. We apply FSO to the mesoscale Hydrologic Model (mHM, mhm-ufz.org), which is the only available distributed model that includes a priori defined TFs for all its parameters. FSO is used to estimate new TFs for the parameters "saturated hydraulic conductivity" and "field capacity," which both influence a range of hydrological processes. The setup of mHM from a previous study serves as a benchmark. The estimated TFs resulted in predictions in 222 validation basins with a median NSE of 0.68, showing that even with 5years of calibration data, high performance in ungauged basins can be achieved. The performance is similar to the benchmark results, showing that the automatic TFs can achieve comparable results to TFs that were developed over years using expert knowledge. In summary, the findings present a step toward automatic TF estimation of model parameters for distributed models.

IIR Cascaded-Resonator-Based Filter Design for Recursive Frequency Analysis

The cascaded-resonator (CR)-based filter structure has been proposed in previous works as a convenient approach to the dynamic harmonic analysis. This CR filter can be with multiple resonator (MR) poles or ones dispersed properly. In all previous papers the resulting filters of the CR structure are finite-impulse-response (FIR)-type. In this letter, the aim is to use the infinite-impulse-response (IIR) CR-based filters for a full spectrum estimation. Thanks to the linearized model, including stability conditions, filter coefficients of the IIR filter transfer function are derived through the minimax optimization using a linear programming. This way, the frequency responses of the harmonic analyzer can be improved in accordance with actual requirements, sometimes even without any increase of computational burden.

Neural Network With Fourier Series-Based Transfer Functions for Filter Modeling

The Fourier series is introduced as a transfer function (TF) in the artificial neural network (ANN) for parametric modeling of microwave filters in this letter. The reported pole-residue-based TF leads to an order-changing problem of input samples from vector fitting, which is usually solved with an order-tracking technique or data classification. The proposed Fourier series-based TF does not have to carry out the time-consuming operation because the only coefficient order can be determined for all input samples in an iterative process. Compared with the pole-residue-based TF, moreover, the ANN training involves a small number of TF coefficients in the proposed method. The predicted electromagnetic (EM) response is obtained from the coefficients of the ANN output. An example of the ultrawideband (UWB) filter is employed to verify the effectiveness of the Fourier series-based TF.

Correlation between the sum of the flux conduction transfer function coefficients and a dimensionless function of the thermal properties of building walls

The estimation of the conduction transfer function (CTF) coefficients is the main step to obtain the transient heat flows on the inside and outside surfaces of a multilayer wall, and thus the heating and cooling loads in a building. Taking a wide variety of construction types, 76 walls from the ASHRAE Handbooks of Fundamentals, it is demonstrated that the aspects of wall transient thermal behaviour can be summarised by a non-dimensionalised function V of the thermal capacity and resistance of the layers of the wall. The sum of the flux CTFs, Σdk, is highly correlated with this measure and the correlation coefficient increases when the sampling time interval decreases. The current interest for nearly zero energy buildings demand management techniques requires the calculation of the CTFs for highly insulated walls and short sampling intervals. The study is extended to the possibility of the CTFs with shorter time steps but longer time steps are needed for thick walls. The theory of the plain slab runs as a thread through the study: the scatter of wall Σdk values cluster around the Σdk:V relation for a slab; the response factor function (exit flux following imposition of a temperature change at the other surface) follows readily from a classical expression in transient thermal response (and from which the slab CTF’s readily follow), and an appendix presents the slab’s recently discovered exact Σdk:V relation.

Parameterized Modeling Incorporating MOR-Based Rational Transfer Functions With Neural Networks for Microwave Components

Neuro-transfer function (neuro-TF) methods are deemed as powerful tools in modeling the electromagnetic (EM) behavior of microwave passive components. Existing neuro-TF methods either endure the issue of &#x201C;order-changing&#x201D; or the issue of mismatch of poles/zeros, both calling for specific algorithms to process the data of the transfer function coefficients as a part of model development. This letter proposes a novel neuro-TF method to eliminate the two issues simultaneously by using combined neural networks and model-order reduction (MOR)-based rational transfer functions. In the proposed method, the coefficients of the transfer function are computed by the MOR technique instead of vector fitting. The use of MOR allows the order of the transfer function to remain constant in different regions in the design parameter space, thereby avoiding the issue of &#x201C;order-changing.&#x201D; Additionally, the coefficients of the rational transfer function resultant from MOR are naturally sorted according to the order of frequency, which eliminates the issue of mismatch of poles/zeros and subsequently improves modeling accuracy. Compared with existing neuro-TF methods, the proposed method achieves better modeling accuracy for the same geometrical variations. Two microwave examples are utilized to demonstrate the advantages of the proposed method.

The flame displacement speed: A key quantity for turbulent combustion and combustion instability

Future combustion power and propulsion systems may operate in premixed regime enabling reduced fuel burn and reduced pollutant emissions. The turbulent premixed regime in those future combustion systems is likely to be in the corrugated regime where modeling the flame as a thin interface propagating into the fresh gas is made possible. The flame displacement speed is thus a key quantity for turbulent combustion in this regime. This quantity is also important for combustion instabilities. Indeed, the flame displacement speed [Formula: see text] combined to the flow speed [Formula: see text] determines the flame surface location by determining the flame surface speed [Formula: see text]. The flame surface location has shown to play a major role on combustion instabilities. Research work have also demonstrated the role of the flame displacement speed on the flame response which is used for subsequent combustion instability prediction. In this context, the derivation of flame speed models and flame transfer function models based on this quantity are required. This paper presents the theoretical derivation of flame transfer function coefficients for swirling premixed flames in this context. The derivation is based on the definition of the flame speed for turbulent flame, its perturbed form for oscillating flow, and the kinematic flame-flow speed budget. The obtained results are compared to previous literature data and discussed. The effect of the flame angle, id est the effect of the swirl number on the flame response is also investigated. This works motivates detailed local measurements and simulations to evaluate flow-flame speed budget terms.

Integrated improvement of the efficiency of computer control system of spatial orientation settings of drilling facilities

Purpose. Improving the efficiency of the system by increasing the accuracy in determining the drilling objects spatial orientation, as well as adjusting the system components to more accurately isolate the information signal from the angle transducer. Methodology. A comprehensive increase in the angle transducer accuracy is based on taking into account the influence of factors and errors in determining the drilling objects spatial orientation, as well as a possibility of smoothly tuning the characteristics of the receiving part due to the departure of the information modulated signal frequency from the angle transducer. Findings. Given the converters operating condition, the error in measuring the zenith angle (deviation angle from the vertical) does not exceed 0.3, the installation angle of the deflector is 3. In addition, restructuring the frequency-dependent components characteristics of the systems receiving part allows one to make changes quickly and improve the overall system. Originality. A comprehensive solution to the problem of increasing the control system efficiency is to increase the converter characteristics, by taking into account its errors and operating conditions, as well as increasing the smoothness and tuning the characteristics efficiency of the receiving part, due to the possibility of calculating the transfer function coefficients using simplified ratios, which will greatly simplify the process of processing information and improve the quality of inclinometric work. Practical value. This complex solution is brought to the design, manufacture and experimental converter verification, and algorithms and programs for tuning frequency-dependent components are proposed and brought to implementation.