Original Transfer Function Research Articles

Data-driven analysis of parametrized acoustic systems in the frequency domain

A data-driven method combined with the formulations of boundary integral equations is developed for the frequency-domain analysis of parametrized acoustic systems, arising from the spatial discretization of the linear Helmholtz equation. The method derives surrogate models for the approximation of frequency response functions at selected field points via the construction of neural networks with radial basis function interpolation. This requires the offline collection of a training database consisting of discrete frequency-parameter samples and their associated response values, whereas the information about system matrices and interference with boundary element kernels are no longer necessary, leading to a matrix-free and non-intrusive nature. To ensure accurate fitting results, a tensor decomposition technique is employed to decouple the naturally formed tensor grid between the frequency and parameter inputs in the database. After establishing two sets of radial basis networks separately, the final reduced-order solutions as a continuous function of the frequency and parameters are represented by the linear combinations of tensor products. In the online phase, the original transfer function at any testing frequency-parameter location can be quickly predicted as direct output from the compact surrogate model. With the analytical solution, the traditional boundary element method and the fast multipole boundary element method as solvers for the generation of training data, two benchmark problems and one complex system are investigated. In all cases, the simplicity, versatility and efficiency of the proposed method are demonstrated through examples of multi-frequency solutions of acoustic systems with parametrized material and geometric properties.

Interpolation synthesis of thecontrollers for a multi-motorelectric drive system containingan elastically linked element

Partial differential equations, integral, differential, or other equations describe multi-motor automatic electric drive systems containing elastic conveyor belts. Because of the elastic and distributive nature of the system parameters, the transfer function describing them is often a complex expression, containing not only the arguments as a linear system but also the inertial and transcendental components. This makes the precise control of tension and speed synchronously much more complicated than the centralized parameter system. A promising numerical solution based on the real interpolation method will simplify the procedure for synthesizing control loops while preserving the characteristic properties of objects with distributed parameters. The objective of the study is to propose a feasible solution for synthesizing the regulators based on the real interpolation method; it allows direct operation with the original transfer function containing the inertial and transcendental components. In this paper, we proposed an approach to synthesize the control system for objects with distributed parameters using the real interpolation method to reduce computational capacity and synthesis error while preserving the properties of this object class. Building an experimental model of the two-motor electric drive system containing an elastic conveyor to verify the effectiveness of the proposed algorithm. The simulation and experimental results indicate that the control system with the received regulators operating stably and meets the required quality criteria. It proves the efficiency of the synthesis algorithm based on the real interpolation method.

Parallel Binary Rafflesia Optimization Algorithm and Its Application in Feature Selection Problem

The Rafflesia Optimization Algorithm (ROA) is a new swarm intelligence optimization algorithm inspired by Rafflesia’s biological laws. It has the advantages of high efficiency and fast convergence speed, and it effectively avoids falling into local optimum. It has been used in logistics distribution center location problems, and its superiority has been demonstrated. It is applied to solve the problem of continuity, but there are many binary problems to be solved in the actual situation. Thus, we designed a binary version of ROA. We used transfer functions to change continuous values into binary values, and binary values are used to symmetrically represent the meaning of physical problems. In this paper, four transfer functions are implemented to binarize ROA so as to improve the original transfer function for the overall performance of the algorithm. In addition, on the basis of the algorithm, we further improve the algorithm by adopting a parallel strategy, which improves the convergence speed and global exploration ability of the algorithm. The algorithm is verified on 23 benchmark functions, and the parallel binary ROA has a better performance than some other existing algorithms. In the aspect of the application, this paper adopts the datasets on UCI for feature selection. The improved algorithm has higher accuracy and selects fewer features.

Model Order Reduction for Delayed PEEC Models With Guaranteed Accuracy and Observed Stability

In this work, a stable and accurate model order reduction method for large-scale partial element equivalent circuit (PEEC) models with many delays is proposed. The method reduces the dimension of the original model by interpolating the original transfer function. The interpolation points are iteratively selected using a greedy algorithm. An efficient error estimator for the reduced transfer function makes the greedy algorithm very successful in both, properly selecting the interpolation points and tightly measuring the error of the reduced transfer function. The resulting reduced-order model is accurate both in the frequency and in the time domain. Numerical tests have shown that the reduced-order model successfully filters the instability behavior of the original model and exhibits stability over a large time interval.

Modified proportional integral controller for single ended primary inductance converter

The article highlights and optimizes a controller for the single ended primary inductance converter (SEPIC) direct current-direct current (DC-DC) converter. The SEPIC converter adjusts a range of dc input voltages and delivers a constant and stable output voltage. Three different models of the SEPIC converter are presented in order to derive its transfer function. Being a 4th order, an approximation method for the reduction of this transfer function to 2nd and 1st order is implemented. Two methods for controlling the converter are presented, the first one is based on guessing techniques and the second explains the design steps of the controller based on the internal model control (IMC). Furthermore, an improvement on the IMC controller is proposed and results were shown and discussed. IMC is based on integrating the “process model” in the control operation of the actual system. By using an approximation of the original transfer function of the system, it is expected that the IMC control will be able to achieve the desired results. Control schemes of the SEPIC will be presented and results will be shown. The response of the controller was tested with mathematical models for batteries and supercapacitors in MATLAB, as non-ideal DC-sources, and results were presented.

Design of Robust Decentralized Control Systems for Distillation Columns

This paper is devoted to the development of a decentralized control system design method with improved robustness, applicable to distillation columns control problem. The aim is attained by solving the following tasks: selection of representative models of columns; development of an effective transfer function identification algorithm; development of a decentralized controller design algorithm, which takes into account the cross-links impact; verification of the developed method for the selected models of columns. The most important result is the developed design method, which includes two algorithms. The first algorithm can be used to identify simplified models of the effective transfer functions. The second algorithm makes it possible to design a decentralized control system based on the ratio between the diagonals of the original model and effective transfer functions. Modified PI controller is used. The achievement of the distillation column control system robustness to the synchronous technologically conditioned deviation of the model parameters by up to three hundred percent of the nominal value is the paper significant result. The digital implementation of the designed controllers is simple. The analysis of the literature shows that none of the previously proposed methods for designing decentralized automatic control systems solved such a problem. The efficiency of the developed algorithms is illustrated using the known models of dynamics of distillation columns. The analysis of limitations of the method as well as its significant differences to the Biggest Log Tuning and H∞ loop shaping methods is presented.

Order reduction of linear time invariant large-scale system by preserving the impact of dominant poles in the reduced model

ABSTRACT This paper introduces a new reduction method for linear time-invariant continuous and discrete-time systems. The method is created considering only the effect of the dominance pole to get the reduced-order model. The denominator coefficient of reduced order model (ROM) is obtained by conserving the dominant poles of a higher order system while the numerator polynomial of the reduced model is found by comparing the original system transfer function with the transfer function of desired reduced order model. Five standard numeric examples are examined from literature considering single input single output (SISO) and discrete systems. To prove the validity, accuracy and simplicity of the proposed method, the results obtained are compared with other recent established and well-known techniques like Truncation and Routh Stability methods.

An Approximate Transfer Function Model for a Double-Pipe Counter-Flow Heat Exchanger

The transfer functions G(s) for different types of heat exchangers obtained from their partial differential equations usually contain some irrational components which reflect quite well their spatio-temporal dynamic properties. However, such a relatively complex mathematical representation is often not suitable for various practical applications, and some kind of approximation of the original model would be more preferable. In this paper we discuss approximate rational transfer functions G^(s) for a typical thick-walled double-pipe heat exchanger operating in the counter-flow mode. Using the semi-analytical method of lines, we transform the original partial differential equations into a set of ordinary differential equations representing N spatial sections of the exchanger, where each nth section can be described by a simple rational transfer function matrix Gn(s), n=1,2,…,N. Their proper interconnection results in the overall approximation model expressed by a rational transfer function matrix G^(s) of high order. As compared to the previously analyzed approximation model for the double-pipe parallel-flow heat exchanger which took the form of a simple, cascade interconnection of the sections, here we obtain a different connection structure which requires the use of the so-called linear fractional transformation with the Redheffer star product. Based on the resulting rational transfer function matrix G^(s), the frequency and the steady-state responses of the approximate model are compared here with those obtained from the original irrational transfer function model G(s). The presented results show: (a) the advantage of the counter-flow regime over the parallel-flow one; (b) better approximation quality for the transfer function channels with dominating heat conduction effects, as compared to the channels characterized by the transport delay associated with the heat convection.

Digital Compensation of a Resistive Voltage Divider for Power Measurement

The paper presents a method for digital compensation of the ratio and phase angle errors of a resistive voltage divider. The system consists of a separate electrical circuit of a resistive divider, and a digital compensation system based on National Instruments (NI) PCI eXtension for Instrumentation (PXI) PXI-5922 digital acquisition cards (DAQ). A novel approach to the real-time compensation is presented, using digital signal processing. The algorithm is based on Wiener filtering and finite-impulse-response (FIR) filters. The proposed digital compensation, using FIR digital filtration and NI PXI DAQs, gives maximum magnitude error below 400 ppm and the phase angle error below 4500 μrad, in the frequency band 50 Hz–100 kHz. The algorithm allows the fine-tuning of the compensation to adjust to the possible change in the original transfer function due to the aging of the components.

Rational Transfer Function Model for a Double-Pipe Parallel-Flow Heat Exchanger

Transfer functions of typical heat exchangers, resulting from their partial differential equations, usually contain irrational functions which quite accurately describe the spatio-temporal nature of the processes occurring therein. However, such an accurate but complex mathematical representation is often not convenient from the practical point of view, and some approximation of the original model would be more useful. This paper discusses approximate rational transfer functions for a typical thick-walled double-pipe heat exchanger working in the parallel-flow configuration. Using the method of lines with the backward difference scheme, the original symmetric hyperbolic partial differential equations describing the heat transfer phenomena are transformed into a set of ordinary differential equations and expressed in the form of N subsystems representing spatial sections of the exchanger. Each section is described by a rational transfer function matrix and their cascade interconnection results in the overall approximation model expressed by a matrix of rational transfer functions of high order. Based on the rational transfer function representation, the frequency and steady-state responses of the approximate model are evaluated and compared with those resulting from its original irrational transfer function model. The presented results show better approximation quality for the “crossover” input–output channels where the in-domain heat conduction effects prevail as compared to the “straightforward” channels, where the transport delay associated with the heat convection dominates.

MÔ HÌNH HÓA VÀ ƯỚC LƯỢNG PHẦN TỬ LIÊN KẾT ĐÀN HỒI TRONG CÁC HỆ TRUYỀN ĐỘNG ĐIỆN TỰ ĐỘNG NHIỀU ĐỘNG CƠ BẰNG PHƯƠNG PHÁP SỐ

The paper proposes a new approach for solving the problem of determining the optimal estimation model of the elastic linkage element in multi-motor automatic driving systems using the real interpolation method (RIM). Algorithms and programs based on the RIM have been built for a two-motor electromechanical driving model to approximate the original transfer function that describes the elastic linkage element containing inertialand transcendent components by the transfer function in a rational fraction form. Besides,providing a specific function form, the program also calculates estimation errors for different approximate transfer functions, thereby allowing to determine the structure and parameters of the optimal estimation model.

A QSAR model for predicting antidiabetic activity of dipeptidyl peptidase-IV inhibitors by enhanced binary gravitational search algorithm

ABSTRACT Time-varying binary gravitational search algorithm (TVBGSA) is proposed for predicting antidiabetic activity of 134 dipeptidyl peptidase-IV (DPP-IV) inhibitors. To improve the performance of the binary gravitational search algorithm (BGSA) method, we propose a dynamic time-varying transfer function. A new control parameter, , is added in the original transfer function as a time-varying variable. The TVBGSA-based model was internally and externally validated based on , , , , , , Y-randomization test, and applicability domain evaluation. The validation results indicate that the proposed TVBGSA model is robust and not due to chance correlation. The descriptor selection and prediction performance of TVBGSA outperform BGSA method. TVBGSA shows higher of 0.957, of 0.951, of 0.954, of 0.938, and lower and compared to obtained results by BGSA, indicating the best prediction performance of the proposed TVBGSA model. The results clearly reveal that the proposed TVBGSA method is useful for constructing reliable and robust QSARs for predicting antidiabetic activity of DPP-IV inhibitors prior to designing and experimental synthesizing of new DPP-IV inhibitors.

The Integer–Order Approximation of Fractional–Order Systems in The Loewner Framework

Abstract This paper deals with the integer–order (finite–dimensional) approximation of a fractional–order (infinite–dimensional) system using the interpolation approach in the Loewner framework. First given a set of interpolation frequencies and the corresponding values of the original noninteger–order transfer function, a Loewner matrix and a shifted Loewner matrix are created. Then, from these matrices an integer–order model in state–space descriptor form is constructed. Its transfer function matches the original system transfer function at the given frequencies. To avoid singularity problems related to data redundancy, a truncated singular value decomposition may finally be applied. Numerical simulations show that the suggested approach to fractional–order system approximation compares favourably with alternative techniques recently presented in the literature to the same purpose.

A Clustering Based Transfer Function for Volume Rendering Using Gray-Gradient Mode Histogram

Volume rendering is an emerging technique widely used in the medical field to visualize human organs using tomography image slices. In volume rendering, sliced medical images are transformed into attributes, such as color and opacity through transfer function. Thus, the design of the transfer function directly affects the result of medical images visualization. A well-designed transfer function can improve both the image quality and visualization speed. In one of our previous paper, we designed a multi-dimensional transfer function based on region growth to determine the transparency of a voxel, where both gray threshold and gray change threshold are used to calculate the transparency. In this paper, a new approach of the transfer function is proposed based on clustering analysis of gray-gradient mode histogram, where volume data is represented in a two-dimensional histogram. Clustering analysis is carried out based on the spatial information of volume data in the histogram, and the transfer function is automatically generated by means of clustering analysis of the spatial information. The dataset of human thoracic is used in our experiment to evaluate the performance of volume rendering using the proposed transfer function. By comparing with the original transfer function implemented in two popularly used volume rendering systems, visualization toolkit (VTK) and RadiAnt DICOM Viewer, the effectiveness and performance of the proposed transfer function are demonstrated in terms of the rendering efficiency and image quality, where more accurate and clearer features are presented rather than a blur red area. Furthermore, the complex operations on the two-dimensional histogram are avoided in our proposed approach and more detailed information can be seen from our final visualized image.

The generalised singular perturbation approximation for bounded real and positive real control systems

The generalised singular perturbation approximation (GSPA) is considered as a model reduction scheme for bounded real and positive real linear control systems. The GSPA is a state-space approach to truncation with the defining property that the transfer function of the approximation interpolates the original transfer function at a prescribed point in the closed right half complex plane. Both familiar balanced truncation and singular perturbation approximation are known to be special cases of the GSPA, interpolating at infinity and at zero, respectively. Suitably modified, we show that the GSPA preserves classical dissipativity properties of the truncations, and existing a priori error bounds for these balanced truncation schemes are satisfied as well.

Converting Infinite Impulse Response Filters to Parallel Form [Tips & Tricks

Discrete-time rational transfer functions are often converted to parallel second-order sections due to better numerical performance compared to direct form infinite impulse response (IIR) implementations. This is usually done by performing partial fraction expansion over the original transfer function. When the order of the numerator polynomial is greater or equal to that of the denominator, polynomial long division is applied before partial fraction expansion resulting in a parallel finite impulse response (FIR) path.

Reservoir computing using dynamic memristors for temporal information processing

Reservoir computing systems utilize dynamic reservoirs having short-term memory to project features from the temporal inputs into a high-dimensional feature space. A readout function layer can then effectively analyze the projected features for tasks, such as classification and time-series analysis. The system can efficiently compute complex and temporal data with low-training cost, since only the readout function needs to be trained. Here we experimentally implement a reservoir computing system using a dynamic memristor array. We show that the internal ionic dynamic processes of memristors allow the memristor-based reservoir to directly process information in the temporal domain, and demonstrate that even a small hardware system with only 88 memristors can already be used for tasks, such as handwritten digit recognition. The system is also used to experimentally solve a second-order nonlinear task, and can successfully predict the expected output without knowing the form of the original dynamic transfer function.

Un Nuevo Método de Identificación Basado en la Respuesta Escalón en Lazo Abierto de Sistemas Sobre-amortiguados

In this paper a new process identification method based in open loop step response of overdamped systems is presented. Initially the transient behavior of transfer functions with multiple real poles is analyzed, establishing analytical formulas to estimate the time it takes for these systems to reach certain points of his reaction curve to stimuli of the step type, including settling time for error criteria of 2% and 5%. Subsequently developed a method of identification using 3 points characteristic of the reaction curve (tk, yk), allowing estimate the order process N, the time constant T of multiple poles and delay time L of the approximate model. To evaluate the performance of the proposed method, 3 minimum phase and 1 non mimium phase transfer functions are used to compare the proposed method with other of identification methods found in the literature, as well as also, one model of a non-isothermal chemical reactor; establishing as efficiency index the root mean square error (RMSE) of the transient response and the frequency resposne of the identified models with respect to the original transfer functions with different signal to noise ratio (SNR) values. From the results obtained show that the proposed method achieves excellent approximation of the transient responses and frequency compared to other methods. From the results, it was observed that the proposed method obtains good approximations of the transient and frequency responses, being a simple method and requires a low computational load compared with others methods.

Implicit Volterra series interpolation for model reduction of bilinear systems

We propose a new interpolatory framework for model reduction of large-scale bilinear systems. The input–output representation of a bilinear system in frequency domain involves a series of multivariate transfer functions, each representing a subsystem of the bilinear system. If a weighted sum of these multivariate transfer functions associated with a reduced bilinear system interpolates a weighted sum of the original multivariate transfer functions, we say that the reduced system satisfies a Volterra series interpolation (Flagg and Gugercin, 2015). These interpolatory conditions can also ensure the necessary conditions for H2-optimal model reduction (Flagg and Gugercin, 2015; Benner and Breiten, 2012). We observe that, by carefully selecting the weights of the series, the Volterra series interpolatory conditions are transformed to the problem of interpolating a linear system with an affine parameter dependence. Such linear parametric systems can then be reduced by some method for parametric model order reduction.Linear systems where the affine parameter dependence is given as low-rank variation in the state matrix can be mapped into a non-parameterized multi-input multi-output linear system. This allows us to utilize the standard (non-parametric) linear IRKA (Gugercin et al., 2008) for the problem of parameterized/bilinear interpolation. Numerical results show that the approximations are of comparable accuracy to those obtained from the bilinear iterative rational Krylov algorithm (Benner and Breiten, 2012). The proposed approach, however, has the advantage that it reduces the computational costs as it involves computations associated with solving linear systems only.

Wide area network discrete feedback control on FastADR of a cluster of building air‐conditioning facilities

Building air‐conditioning facilities are promising resources of the fast automated demand response (FastADR) aggregation. However, designing a closed‐loop control includes problems of strong nonlinear dynamic properties of the facility and large sampling period due to building facility communications. This paper proposes an original aggregated transfer function that approximates hundreds of air‐conditioners with large wide area network communication delays. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.