Polynomial Transfer Research Articles

Sparse plus low-rank identification for dynamical latent-variable graphical AR models

This paper focuses on the identification of graphical autoregressive models with dynamical latent variables. The dynamical structure of latent variables is described by a matrix polynomial transfer function. Taking account of the sparse interactions between the observed variables and the low-rank property of the latent-variable model, a new sparse plus low-rank optimization problem is formulated to identify the graphical auto-regressive part, which is then handled using the trace approximation and reweighted nuclear norm minimization. Afterwards, the dynamics of latent variables are recovered from low-rank spectral decomposition using the trace norm convex programming method. Simulation examples are used to illustrate the effectiveness of the proposed approach.

A Gray-Box Stability Analysis Method of Grid-Connected Inverter Considering Synchronization Dynamics

The Grid-Connected Inverter (GCI) can be considered a gray box when circuit and controller parameters are missing due to intellectual property rights or parameter variations caused by aging, which poses an impediment to assessing the stability of the system. This paper presents a gray-box stability analysis method based on impedance identification of GCI considering the synchronization dynamics. The impedance frequency responses of GCI are measured by the frequency scanning method on the dq-frame. Meanwhile, the influence of synchronization dynamics and background harmonics is theoretically investigated. A vector fitting (VF) algorithm, co-designed with impedance identification, is then applied to generate polynomial transfer functions. Based on the obtained transfer functions, the stability of the GCI can be judged by the distance relationship between the prohibited area boundary and the center of the gershgorin-circle through the distance formula. Finally, the experiments of both RT-LAB and experimental prototypes are conducted to verify the feasibility of the proposed method.

On designing good doppler tolerance waveform with low PSL of ambiguity function

Although the thumbtack-type ambiguity functions (AF) of the existing phase-coded signals are of good range-Doppler resolutions, they are not suitable for detection of high-speed targets due to their poor Doppler tolerance. In this paper, we address the design of waveform with good Doppler tolerance, which is expected to be of both diagonal-ridge-type AF and also local low peak sidelobe level (PSL). First we formulate the design model of Doppler tolerant waveform via minimizing the ratio of PSL to the minimum mainlobe level. Then, we solve the resulting fractional programming problem via quartic polynomial transfer and high-order polynomial optimization. Numerical results demonstrate the excellent Doppler tolerance and low PSL performance of our design.

A Co-driven Functional Electrical Stimulation Control Strategy by Dynamic Surface Electromyography and Joint Angle.

Functional electrical stimulation (FES) is widely used in neurorehabilitation to improve patients’ motion ability. It has been verified to promote neural remodeling and relearning, during which FES has to produce an accurate movement to obtain a good efficacy. Therefore, many studies have focused on the relationship between FES parameters and the generated movements. However, most of the relationships have been established in static contractions, which leads to an unsatisfactory result when applied to dynamic conditions. Therefore, this study proposed a FES control strategy based on the surface electromyography (sEMG) and kinematic information during dynamic contractions. The pulse width (PW) of FES was determined by a direct transfer function (DTF) with sEMG features and joint angles as the input. The DTF was established by combing the polynomial transfer functions of sEMG and joint torque and the polynomial transfer functions of joint torque and FES. Moreover, the PW of two FES channels was set based on the muscle synergy ratio obtained through sEMG. A total of six healthy right-handed subjects were recruited in this experiment to verify the validity of the strategy. The PW of FES applied to the left arm was evaluated based on the sEMG of the right extensor carpi radialis (ECR) and the right wrist angle. The coefficient of determination (R2) and the normalized root mean square error (NRMSE) of FES-included and voluntary wrist angles and torques were used to verify the performance of the strategy. The result showed that this study achieved a high accuracy (R2 = 0.965 and NRMSE = 0.047) of joint angle and a good accuracy (R2 = 0.701 and NRMSE = 0.241) of joint torque reproduction during dynamic movements. Moreover, the DTF in real-time FES system also had a nice performance of joint angle fitting (R2 = 0.940 and NRMSE = 0.071) and joint torque fitting (R2 = 0.607 and NRMSE = 0.303). It is concluded that the proposed strategy is able to generate proper FES parameters based on sEMG and kinematic information for dynamic movement reproduction and can be used in a real-time FES system combined with bilateral movements for better rehabilitation.

A digraph approach to the state-space model realization of MIMO non-commensurate fractional order systems

This paper proposes a novel approach that can generate a state-space model with low inner dimension for an MIMO non-commensurate fractional order (NCFO) system. Specifically, the notion of an admissible digraph is firstly introduced associated with a fractional order transfer (function column) vector. Then, new state-space model realization conditions and corresponding procedures based on this admissible digraph are proposed for the state-space model realization of an NCFO polynomial transfer matrix. Finally, a new necessary and sufficient state-space model realization condition is proposed for the rational transfer matrix of an MIMO NCFO system, and it is shown, based on a matrix fractional description (MFD) of the given rational transfer matrix, a state-space model realization can be obtained by firstly converting it to the polynomial case and then utilizing the digraph approach for polynomial case. Symbolic and numerical examples are provided to demonstrate the main ideas and effectiveness of the proposed digraph approach.

Optimized Gaussian Pulse Design for UWB System Using Particle Swarm Optimization Based-on Generalized Bessel Polynomials

The ultrawideband system operates a very short pulse with enormous bandwidth to provide high data rates for data transmission. To design the UWB pulse, considering the pulse shape is very necessary, and a spectral emission mask of the designed pulse should meet the FCC spectral mask requirement between frequency range 3.1 GHz to 10.6 GHz. The traditional UWB pulse design is based on the Gaussian derivative. However, the frequency spectrum is not satisfied the FCC spectral mask requirement. In this study, the Gaussian pulse can be designed from the mathematical characteristic of the generalized Bessel polynomial. The spectral efficiency of the proposed pulse can be improved by the combination of the derivative of Gaussian pulse with a weight coefficient optimization with particle swarm optimization (PSO). PSO is a population-based optimization algorithm inspired by animal behavior. PSO is applied with generalized Bessel polynomial transfer function to gain the best weight coefficient, we proposed to optimize its weight vector to design a pulse that exceeds to FCC spectral mask. The results were found in MATLAB software show that generalized Bessel polynomials can approximate the proposed pulse with combination method and PSO. The spectral efficiency is improved to 89.30% and the spectrum is greater close to the FCC spectral mask requirement. To confirm an improved spectral efficiency compared to the previous works.

An Explicit Analytical Solution for Transient Two-Phase Flow in Inclined Fluid Transmission Lines

Due to the complex nonlinearity characteristics, analytical modeling of compressible flow in inclined transmission lines remains a challenge. This paper proposes an analytical model for one-dimensional flow of a two-phase gas-liquid fluid in inclined transmission lines. The proposed model is comprised of a steady-state two-phase flow mechanistic model in-series with a dynamic single-phase flow model. The two-phase mechanistic model captures the steady-state pressure drop and liquid holdup properties of the gas-liquid fluid. The developed dynamic single-phase flow model is an analytical model comprised of rational polynomial transfer functions that are explicitly functions of fluid properties, line geometry, and inclination angle. The accuracy of the fluid resonant frequencies predicted by the transient flow model is precise and not a function of transmission line spatial discretization. Therefore, model complexity is solely a function of the number of desired modes. The dynamic single-phase model is applicable for under-damped and over-damped systems, laminar, and turbulent flow conditions. The accuracy of the overall two-phase flow model is investigated using the commercial multiphase flow dynamic code OLGA. The mean absolute error between the two models in step response overshoot and settling time is less than 8% and 2 s, respectively.

A Robust Circuit and Controller Parameters’ Identification Method of Grid-Connected Voltage-Source Converters Using Vector Fitting Algorithm

This article presents a vector fitting (VF) algorithm-based robust circuit and controller parameters’ identification method for grid-connected voltage-source converters (VSCs). The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula> -domain impedance frequency responses (IFRs) of the VSCs are first measured using the frequency scanning method, based on which the corresponding measured phasor-domain IFRs are calculated. Then, polynomial transfer functions are generated by applying the VF algorithm on the measured phasor-domain IFRs, from which the circuit and controller parameters, i.e., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$LCL$ </tex-math></inline-formula> filter parameters, digital sampling time, current controller parameters, and phase-locked loop parameters, are identified. The influence of measurement noise on parameters’ identification accuracy and corresponding countermeasure to mitigate the adverse influence are also theoretically investigated. The proposed method is able to identify the circuit and controller parameters when detailed parameters are missing due to industrial secrecy or parameters variation caused by operating condition change, temperature fluctuation, or aging. The effectiveness of the proposed circuit and controller parameters’ identification method is validated by theoretical demonstration, OPAL-RT-based real-time simulation, and experimental validation.

A Functionalized Paper Strip‐Based Platform for Rapid Detection of Anticancer Drug Concentrations

This article presents a compact, low‐cost, robust, and flexible test platform for determining the concentration of drugs in fluids. This device is based on a PVC foil card containing copper conductive foils in which disposable paper test strips are inserted. The paper test strips are overlaid with deposition of multiwalled carbon nanotubes (MWCNTs) acting as a sensing layer. When a paper test strip is inserted into the test card, the conductive path between two copper lines is established. A drop of test fluid on the sensing MWCNT layer changes the conductivity in a concentration‐dependent manner, enabling calculation of the drug concentration after measurement of the electrical resistance at the copper terminals. An equivalent electrical circuit was also proposed to model the response of the fabricated sensor. It was shown that model parameters are dependent on the concentration of the cytostatic drug methotrexate. Additionally, the fabricated sensor demonstrated the ability to differentiate the same concentration of methotrexate and cyclophosphamide. The complete readout electronics and polynomial transfer function for calculating drug concentrations were also developed and are presented.

PID Controller Simulator Design for Polynomials Transfer Function

PID controller is a controller used to determine precision of a system instrument employing feedback of the system. The component of PID control can be applied simultaneously or singly depends on the response we desired from a plant. However, there is problem in analyzing planned system response; how to get transfer function from a system and analyze it quickly and easily. As of today, control system engineers still encounter difficulty in analyzing system response especially for transfer function using polynomial equations of degree greater than two and employing trial and error method when analyzing response in the simulation. Thus, the writers design a simulator to solve this problem by using Graphical User Interface. The design of the program can be used for polynomial transfer function and installed directly to computer with smaller memory capacity. Hence, it is more user-friendly and not slowing down the operating system of computer. To ensure that the output of simulation correctly generated, we implemented block diagram modeling in simulink. In the future, the result of this research can be implemented as reference to easily understand the characteristics of PID controller especially for polynomials transfer function.

Improving eye-tracking calibration accuracy using symbolic regression.

Eye tracking systems have recently experienced a diversity of novel calibration procedures, including smooth pursuit and vestibulo-ocular reflex based calibrations. These approaches allowed collecting more data compared to the standard 9-point calibration. However, the computation of the mapping function which provides planar gaze positions from pupil features given as input is mostly based on polynomial regressions, and little work has investigated alternative approaches. This paper fills this gap by providing a new calibration computation method based on symbolic regression. Instead of making prior assumptions on the polynomial transfer function between input and output records, symbolic regression seeks an optimal model among different types of functions and their combinations. This approach offers an interesting perspective in terms of flexibility and accuracy. Therefore, we designed two experiments in which we collected ground truth data to compare vestibulo-ocular and smooth pursuit calibrations based on symbolic regression, both using a marker or a finger as a target, resulting in four different calibrations. As a result, we improved calibration accuracy by more than 30%, with reasonable extra computation time.

Simulation of parallel mechanisms for motion cueing generation in vehicle simulators using AM-FM bi-modulated signals

The use of robotic motion platforms in vehicle simulators is relatively common. However, the process of testing and tuning the so-called washout algorithms, used for motion cueing generation in motion-based vehicle simulators, is complex. This process can be reduced in cost, simplified, improved, shortened and performed safer if virtual motion platforms are used instead of real devices. This paper deals with identifying a method to perform a fast but reliable simulation of parallel mechanisms to be used for motion cueing generation. The method relies on the use of Laplacian polynomial transfer function models by means of using AM-FM bi-modulated signals as reference inputs to achieve system identification. The proposed simulation scheme is implemented and assessed using optical tracking methods by testing a real 2-DOF pitch-roll parallel robot, although the method is not intrinsically restricted to this type of device. The performance of the proposed solution is also assessed with the classical washout algorithm. Results show that the accuracy of the method is satisfactory and the performance of the proposed simulation scheme is very high, being suitable to test and tune washout algorithms.

Robust stabilization of discrete generalized systems

The robust stabilization problem for generalized discrete-time systems described by polynomial or improper transfer function matrices, subject to perturbations acting on the normalized coprime factors, is solved. The maximum achievable stability margin and the robust stabilizing controller are given in terms of realizations and solutions to appropriate Riccati equations.

Optimized Synthesis of Self-Equalized Microwave Filters

In this paper, a new methodology for synthesizing self-equalized filters is introduced. The methodology consists of optimizing the polynomial transfer and reflection functions considering amplitude and phase constraints simultaneously. The algorithm gives access to a more general class of functions than generalized Chebyshev (also called quasi-elliptic) functions. Two self-equalized filters are designed using this new methodology, and their performances are compared to general Chebyshev filters in order to put into evidence the interest of the proposed optimization algorithm. The first design leads to reduced group-delay variations, and the second one leads to a simplification of the hardware, reducing the number of resonators.

A Linearizing Digitizer for Differential Sensors With Polynomial Characteristics

This paper presents a new linearizing digital converter (LDC) that accepts output from differential type sensors with third-order polynomial transfer characteristics and provides a linear digital output proportional to the measurand. The LDC is realized using a modified dual-slope converter. Detailed operation of the proposed LDC, design procedure, and analysis of the effect of various circuit parameters on performance of the LDC are presented in this paper. The proposed methodology of LDC is also extended for sensors with second-order polynomial characteristics. The functionality of the LDC has been verified with the help of simulation studies. A prototype LDC has been developed and interfaced with a novel reluctance-Hall effect-based angle sensor (having a third-order characteristic) and tested. Test results show that the output of the overall transducer is linear across a wide range of angles, and thus underline the efficacy of the proposed scheme for differential type sensors with third-order transfer characteristics.

On the design transitional Legendre–Butterworth filters

This paper presents a new method of the polynomial transfer function approximation both in the analog and the digital domain for the recursive digital filter design. The transfer function of these filters, referred as the transitional Legendre–Butterworth (TLB) filters, has properties that lie between Legendre and Butterworth filters. The so-designed TLB filters exhibit non-equiripple passband and monotonic transition and stopband responses. There are three types of TLB IIR filters which can be approximated in the digital domain. The closed form expressions for the magnitude squared functions coefficient of all types of transfer functions are provided, and a straightforward design technique for each approximation in the digital domain is described. Resulting digital filters are always stable.

Safety monitoring of exothermic reactions using time derivatives of temperature sensors

We propose a new method of safety monitoring for overheating in exothermic reactions that is applicable to detection of thermal runaway in Li-ion batteries. The proposed method is based on the solutions of a one-dimensional heat conduction problem across the wall thickness of a cylinder. The problem is known as an Inverse Heat Conduction Problem (IHCP) since heat is conducted outwards while monitoring sensors only have access to the outside surface. We first obtain the transfer functions relating the inner and outer boundaries through Laplace transform. We then use Hadamard factorization theorem to express the transfer functions in terms of infinite product of polynomials. Truncations of the polynomial transfer functions represent time domain relationships between physically accessible measurements and the heating inside a cylindrical wall. These relationships lead us to propose time derivatives of temperature as better indicators for safety monitoring in exothermic processes.

Complex Performance Modeling of Parallel Algorithms

Parallel principles are the most effective way how to increase parallel computer performance and parallel algorithms (PA) too. In this sense the paper is devoted to a complex performance evaluation of chosen PA. At first the paper describes very shortly PA and then it summarized basic concepts for performance evaluation of PA. To illustrate the analyzed evaluation concepts the paper considers in its experimental part the results for real analyzed examples of discrete fast Fourier transform (DFFT). These illustration examples we have chosen first due to its wide application in scientific and engineering fields and second from its representation of similar group of PA. The basic form of parallel DFFT is the one-dimensional (1-D), unordered, radix–2 algorithm which uses divide and conquer strategy for its parallel computation. Effective PA of DFFT tends to computing one – dimensional FFT with radix greater than two and computing multidimensional FFT by using the polynomial transfer methods. In general radix - q DFFT is computed by splitting the input sequence of size s into q sequences each of them in size n/q, computing faster their q smaller DFFT’s, and then combining the results. So we do it for actually dominant asynchronous parallel computers based on Network of workstations (NOW) and Grid systems.

Optimisation of wavelengths selection used for the multi-spectral temperature measurement by ordinary least squares method of surfaces exhibiting non-uniform emissivity

In this paper, a method based on the ordinary least squares method for optimising the wavelength selection used for the multi-spectral temperature measurement of surfaces exhibiting non-uniform temperature-depending emissivity is presented. The goal consists of minimising the standard deviation of the estimated temperature (optimal design experiment). Two methods for wavelengths selection are presented – sequential and global with or without constraints – on the spectral range. Then, the estimated temperature results obtained by two different models taking into account a second-order polynomial transfer function including the emissivity and for different number of parameters and wavelengths are compared. The first model is based on Wien’s approximation and fluxes ratio (as done in the bicolour temperature technique) and the other is based on the fluxes (Planck’s law but without fluxes ratio). Different selection criteria are presented. These points are treated from theoretical, numerical and experimental points of view.

Experimental implementation and verification of multi‐degrees‐of‐freedom effective force testing

SUMMARYThis paper presents an experimental implementation and verification of multi‐degrees‐of‐freedom effective force testing (MDOF‐EFT). An experimental setup that consists of a two‐degrees‐of‐freedom structural system and two hydraulic actuators at the Johns Hopkins University was utilized in this study. First, experimental system identification was performed to develop compatible analytical models for the multi‐input and multi‐output systems. Dynamics of the control plant, that is, the valve‐to‐force relations, were modeled with a rational polynomial transfer function matrix and delay components. By using the analytical model, a centralized decoupling loop‐shaping force feedback controller was designed such that the forces are uncoupled and the loop transfer functions have desirable dynamic characteristics in the frequency domain. Then, a series of harmonic force and earthquake simulation tests were performed to assess capabilities and limitations of MDOF‐EFT. Experimental results showed that the dynamic forces in the two actuators were accurately controlled to provide tracking while the system was stable and robust for the entire period of the experiment. Furthermore, earthquake simulation tests with increased levels of the reference forces demonstrated the feasibility of MDOF‐EFT with highly nonlinear test structures. Copyright © 2013 John Wiley &amp; Sons, Ltd.