Polynomial Transfer Function 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.

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.

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.

Theory and design of narrowband band-stop filters using slotted ground resonators

This paper reports the demonstration of design and implementation of narrow band band-stop filters using slotted ground resonators. Using coupled-mode resonator theory, the systematic implementation of BSFs are performed to achieve narrow stopband (<25% FBW) with desired stopband isolation. By exchanging the band-pass transfer function polynomials, the BSF design has become straight-forward with these band-stop resonators. Designed and optimized BSFs are fabricated, characterized and analysed as a detailed report. Slotted ground resonators yield compact and scalable BSFs which are potential alternatives for the development of future microwave systems.

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.

Age, Sex, and Pathology Effects on Stability of Electroencephalographic Biometric Features Based on Measures of Interaction

Electroencephalographic (EEG) biometric features have attracted considerable interest, but they have also drawn major criticism as having low stability. Moreover, most published studies ignore the potential effect of individual factors interacting with stability on the performance of the examined system. We examined the effects of age, sex, and neurological conditions in 60 subjects: 1) using a single EEG recording; 2) when pooling two EEG sessions; and 3) when performing cross-session cross-validation in a biometric system based on multivariate autoregressive measures, in order to extend previous work on autoregressive coefficients. Feature-level fusion and wrapped feature subset-selection in multivariate autoregressive coefficients (MVAR), power spectral density, and 14 additional measures derived from the MVAR model resulted in a maximum area under the curve of receiver operating characteristics (AUC of ROC)/top equal error rate of 98.85/5.34 for a single EEG, 95.51/9.70 for EEG-pooling, and 85.34/22 for cross-session cross-validation. This best result was obtained by the transfer function polynomial, which outperformed the MVAR coefficients, based on the example data set used in this paper. Age, sex, and pathology significantly interacted with the stability of features ( $p ). We suggest further investigation of frequency-dependent measures derived from the MVAR model. We emphasize the serious problem of ignoring stability in most previously published research and recommend accurate reporting of individual factors when studying EEG biometric features in multiple sessions for enrolment and authentication on separate days.

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.

Influence of Transfer Function Zeros on Controller Parameters

The paper is devoted to the influence of transfer function zeros on state feedback controller parameters. Nowadays, during the modal control system design process, the most attention is paid to the analysis of transfer function poles. If transfer function zeros are located closely to the poles, the control object tends to singularity, when the influence of the input control signals to the output signals becomes weaker. This fact leads to the designing of state-space controllers with extremely high values of control coefficients. Available methods for selecting the desired poles of closed loop systems are represented by the following variants: quantitative evaluation of the controllability and observability of object models and object model reduction. These methods have some disadvantages: dependence on the state-space representation of the control object model, ignoring some parts and characteristics of the control object model. In this paper, to analyze the state feedback controller parameters the invariant of the state-space representation characteristic is used – catalecticant (Hankel) matrix. As a result, it was found that control coefficients of the state feedback controller are inversely proportional to the determinant of the catalecticant matrix of the control object, and the determinant of the catalecticant matrix is equal to the resultant of transfer function polynomials. A method of converting the block diagram of the control object model using the residues of the transfer function was suggested. As a result of the conversion, poles, which cause high values of control coefficients, are isolated as a multiplicative uncertainty in the object model structure. The robust control theory can be used for control system designing with such organization of the control object.

PROGRAM COMPLEX FOR THE CALCULATION AND DESIGN OF ACTIVE FILTERS BASED ON THE E-LAYER MODEL

Objectives. The article is devoted to the development of a method for designing analogue filters, including active, which differs from known methods due to the fundamentally different approach taken to the selection of optimisation criteria. Methods. Most contemporary methods, as a rule, calculate the parameters of filter forming electronic components based solely on the required values of the transfer function polynomial coefficients. At the same time, the maintenance of the required stability and reproducibility of filter characteristics is achieved primarily by technological methods; for example, by using precision elements. Nevertheless, it is possible to achieve a similar effect in a different way, namely, by appropriate choice of the circuit component parameter values. This approach is possible by selecting the individual circuit component values in an arbitrary manner, while the necessary transfer function polynomial coefficients are obtained by selecting the values of the remaining elements. Thus, having solved the optimisation task, it is possible to achieve optimal design results in accordance with the chosen quality criterion. Results. In this paper, the e-layer model is proposed as the basis for this criterion, according to which either the deviations of the transfer function or the signal passed through the filter should be minimally different from the given type and be located within the given layer, either in the entire domain of the function or signal definition, or in the most significant defined range. Conclusion . The software package for the calculation of active filters is developed according to the proposed approach. The productivity of its application is confirmed by experimental studies and the calculations performed using this application.

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.

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.

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.

Characterization of nonlinearity using polynomial transfer function of all‐optical sampling

AbstractA novel method for full characterizing nonlinear distortion of all‐optical sampling is proposed based on polynomial transfer function.The method only requires fitting transfer curve with a polynomial function and enables a uniform expression of nonlinear distortion in terms of polynomial coefficients and input parameters. Simulation and experiment are designed and performed to check the accuracy. The results with our method are in good agreement with the measurement. Our method avoids both Fourier expansion and spectrum measurement, which is suitable for fast evaluating and optimizing distortion of all‐optical sampling. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:216–219, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25655