Approximate Frequency Response Research Articles

An investigation of active enclosed-space noise control with a nonlinear loudspeaker

Active control algorithms are widely used in enclosed-space noise control with the nonlinearities of secondary-source loudspeakers ignored. Inspired by nonlinear energy transfer resulting from nonlinear stiffness, this work concerns using a nonlinear loudspeaker to improve enclosed-space noise control. An enclosed-space active noise control system with a nonlinear loudspeaker is modeled. Based on the model, an approximate frequency response function of the noise control system is derived analytically via the harmonic balance method and verified using numerical methods. A globally consistent and bounded Lyapunov function is derived. The effects of the mass, nonlinear stiffness, volume, and area ratio on the noise reduction are also explored. Both analytical and numerical results demonstrate that the improved nonlinear loudspeaker is effective in improving the low-power characteristics of the loudspeaker, increasing noise reduction and improving fault-tolerant and robustness of the active noise control system.

Time response optimal rational approximation: Improvement of time responses of MSBL based approximate fractional order derivative operators by using gradient descent optimization

Fractional calculus has become a popular topic in recent years. Its applications have been seen frequently in the analysis and solution of many engineering problems. Since, the exact realization of fractional order (FO) operators is not computationally feasible, several integer order approximations methods such as Oustaloup, Matsuda, Curve Fitting, modified stability boundary locus (MSBL) are utilized for frequency domain approximation of FO operators. These methods present advantages in frequency response approximation. However, real-world engineering applications require more accurate time responses to implement FO operators. Thus, any improvement in the approximate transfer function of FO systems will positively contribute to realization performance of FO system models in real-world applications. In this work, time responses of MSBL based approximate FO derivative models are improved by using gradient descent optimization (GDO) technique. Frequency domain approximation methods do not guarantee optimal approximation performance for the step response of FO elements. To deal with this weakness, author proposes a new GDO based rational approximation scheme that can considerably enhance the step response performance of MSBL method without deteriorating frequency response approximation performance. Results for the improved approximate FO model obtained by GDO (GDO-MSBL) are compared with the results of approximate FO models for popular FO approximation methods. The analog circuit realization is performed for the derivative operator, and the performance improvements for the proposed method are shown on the FO-PID controller and FO filter.

Minimax Design of M-D Sparse FIR Filters With Arbitrary Frequency Response Using SOCP

The number of coefficients of multi-dimensional (M-D) finite-extent impulse response (FIR) filters increases exponentially with the number of dimensions leading to significantly high computational complexities. In this brief, we propose a minimax design method for M-D FIR filters having sparse coefficients, therefore, having low computational complexities. We consider the design of M-D FIR filters with arbitrary frequency responses and low group delays of which the coefficients are complex valued. We formulate the minimax design as a second-order cone programming problem. Design examples confirm that M-D sparse FIR filters designed using the proposed method provide more than 60% reduction in the computational complexity for a similar error in the frequency response approximation compared to M-D FIR nonsparse filters designed using previously proposed minimax methods.

An Approximate Model of Load Frequency Control Systems with Time Delay

In this paper we present an approximate model for load frequency control system with time delay. The load frequency control is one of the conventional power system control problems. In order to secure the stability of the grid the frequency must remain within its limited range which is achieved through the load frequency control. The load frequency control signals experience time delay that could destabilize the power systems. The presence of the time delay complicates the analysis of the load frequency control system. In this paper we present a stability method based on the Direct Frequency Response approximation for the time delay. This approximation transforms the transcendental time delay equation into linear equation. This results in a simple stability criterion for the loadfrequency control system with time delay. A one-area load frequency control system is chosen as a case study. The effectiveness of the proposed approximation has been tested through simulation and comparison with the published research work. By tracking the eigenvalues or using Routh's criterion the maximum delay margin can be estimated. The proposed stability criterion has been compared with the most recent methods and showed it is merit. The range of the PI controller parameters for a given time delay can be determined which is very important in practice.

Photovoltaic System Power Reserve Determination Using Parabolic Approximation of Frequency Response

The most commonly used method for including photovoltaic system in the control of system frequency is to operate a PV power plant at reduced power while maintaining a specific amount of available power reserve. Such operating regime, often referred to as de-loaded, can cause additional costs and, consequently, determining a required power reduction becomes vitally important. This paper introduces a method for determining the required minimum de-loaded reserve of a photovoltaic system. To achieve the desired result a parabolic approximation of the system frequency response is developed to derive an explicit function of the frequency nadir. Taking this approximation into consideration, a method for determining the required minimum de-loaded margin was developed and tested in a case-study which observed a small power system consisting of several power plants. To demonstrate the accuracy of the proposed parabolic approximation, the calculated approximate values of the frequency nadir were compared to the values of the frequency nadir obtained from the frequency response simulations performed on the power system model developed in MATLAB/Simulink.

Application of Butterworth high pass filter as an approximation of Wood Anderson seismometer frequency response to earthquake signal recording

The method for generating maximum amplitude and signal to noise ratio values by using second order high pass Butterworth filter on local seismic magnitude scale calculations is proposed. The test data are signals from local earthquake that have been occurred in Sunda Strait on April 8th 2012. Based on the experimental results, a 8 Hz cutoff frequency and a gain of 2200 of second order Butterworth high pass filter as an approach to simulating the frequency response of Wood Anderson seismometer can provide maximum amplitude value, SNR, and the magnitude better than simulated Wood Anderson frequency response.

Centralized PI controller design method for MIMO processes based on frequency response approximation

A simple method of controller design for multi-input multi-output (MIMO) processes have been proposed in frequency domain. The intensive calculation for the inverse of the process transfer function matrix is simplified to a great extent by evaluating the process transfer function matrix at a low frequency point. The desired closed loop transfer functions are derived for the process using a single tuning parameter for each diagonal element of the process transfer function matrix which represents the desired closed loop time constant. Centralized PI controllers are then designed using a model matching technique by evaluating the transfer functions at a low frequency point. The PI controllers provide acceptable performances for lag dominated as well as time-delay dominated processes and is also applicable to high-dimensional processes. The proposed method is extended for the non-square MIMO processes using two approaches one of which squares up the process transfer function matrix to apply the proposed technique while the other is based on pseudo-inverse evaluation of the process transfer function matrix at a low frequency point.

Some Features of Geometric Nonlinear Damping on Isolation Performance

The addition of nonlinear characteristics to improve the dynamic performance of isolation systems and vibration absorbers has been extensively investigated in the past decades. Both nonlinear stiffness and nonlinear damping have been largely analysed. A common way in which this can be achieved in practice, is by arranging linear elements (springs and viscous dampers) in a specific geometrical configuration. This paper focuses on the fundamental effect of geometrical nonlinear damping in a vibration isolation system, and briefly revises two of the classical implementation mechanisms. They can achieve a better performance than linear systems, by assuring lower damping force at lower displacements, and higher damping force at higher displacements. However, strong nonlinear effects can manifest around resonances, causing non-negligible higher-order harmonics to appear, and making the approximate frequency response obtained by the harmonic balance, unuseful. This paper proposes a new strategy to limit such undesired dynamic effects. For this aim, a coupling is introduced on purpose in the damping mechanism, which allows tailoring the damping force for the specific need.

Tuning of Fractional Order PID Controllers based on the Frequency Response Approximation Method

Abstract Fractional Order PID (FOPID) controllers have been heavily studied in recent years, but most of the methods developed for its optimal design rely on the idea of including several robustness and performance specifications in the objective function. Thus they suffer from the same problem, namely the difficulty in finding the optimal controller parameters due to the impossibility of meeting all the specifications, and the high sensitivity to the initial parameter values. In this work, a new optimization-based tuning method for FOPID controllers is proposed. The method presents fast convergence and consists of specifying a desired closed-loop transfer function and finding the FOPID controller which gives the closed-loop behavior closest to the specified. The parameterization of the controller is shown, and the optimization procedure used is detailed. Then the proposed method is applied to design a FOPID to control an underdamped third order system with time delay, obtaining good robustness and performance.

Novel realization of GIC based wave digital filters using Al-Alaoui transform

By using the concepts of wave characterization, Al-Alaoui transform and generalized immittance converter (GIC), a new digital GIC structure is proposed which is capable of realizing all the standard second-order digital filter sections. The Al-Alaoui transform is utilized for reference circuit discretization, leading to development of second-order digital filter sections which possess better noise properties than the conventional GIC and GIC discretized using the fractional bilinear transform. The proposed second-order digital filter sections are used as building blocks in cascade synthesis of filter. Two design examples are considered to analyze the effectiveness of the proposed filter sections and their comparison with the other filter sections is performed in terms of quantization noise and approximation to analog filter response. The proposed synthesis yields lowpass and highpass filters that have a better signal to noise ratio and better approximation of the analog filter frequency response than the conventional GIC digital filters and fractional GIC digital filters.

Damage detection by a FE model updating method using power spectral density: Numerical and experimental investigation

Abstract This paper investigates the viability of damage detection using power spectral density (PSD) of structural response both numerically and experimentally. The paper establishes a sensitivity based damage detection method to use PSD. The advantages of PSD as a model updating metric are explained and its challenges are addressed. An approximate frequency response function of damaged model is used to redeem the method for the effect of incomplete measurement. The robust solution of the developed sensitivity equation is achieved through a least-squares error minimization scheme, and the challenging issues are discussed. The ability of the method in localizing and quantifying the damage and its robustness against measurement and modeling errors is investigated by a numerical example. Experimental vibration test data of a laboratory concrete beam with various level of distributed damage is used to probe the method in practical conditions. The results show that PSD of response can be used to detect damages in lower frequency ranges with acceptable accuracy.

Evidence-Theory-Based Analysis for Structural-Acoustic Field with Epistemic Uncertainties

Evidence theory has a strong capacity to deal with epistemic uncertainty, in view of the overestimation in interval analysis, the responses of structural-acoustic problem with epistemic uncertainty could be untreated. In this paper, a numerical method is proposed for structural-acoustic system response analysis under epistemic uncertainties based on evidence theory. To improve the calculation accuracy and reduce the computational cost, the interval analysis technique and radial point interpolation method are adopted to obtain the approximate frequency response characteristics for each focal element, and the corresponding formulations of structural-acoustic system for interval response analysis are deduced. Numerical examples are introduced to illustrate the efficiency of the proposed method.

A novel evolutionary method of structure-diversified digital filter design and its experimental study

Digital filters are now key components in many modern digital systems. This paper proposed a novel evolutionary method to design structure-diversified digital filters. On the investigation of the existing evolution-based digital filter design methods, most state-of-the-art works concentrate on the evolution of appropriate transfer functions for digital filters. However, a transfer function is not equivalent to a practical digital filter that has proper structure and can be implemented by a hardware directly. Some researchers proposed a synthesis method to generate the structure of digital filter from a specified transfer function. However, this method needs an existing transfer function as the prior knowledge. Compared with existing works on the evolution of digital filters, the proposed method is novel at the following aspect: the proposed method can directly evolve the structure and parameters of digital filter without the pre-definition of the transfer function. The only prior knowledge we need is the specification of the design target, such as the frequency range of the passband and stop-band. In the experimental study, a significant characteristic is revealed that the proposed method is able to evolve structure-diversified filters with approximate frequency response. The proposed method is a prototype, and it is demonstrated to be a promising way of digital filter design.

Poles Extraction of Radar Target Based on Narrowband Frequency Response Approximation

Pole is the most important feature of radar target in resonance region, and it is attitude insensitive. The poles extraction requires UWB (ultra-wideband) late-time response signal or frequency response data, which is difficult to achieve through general equipment. This paper proposed a method for extracting poles from narrowband data. At first, the frequency response equation of the resonance region was derived. Then, the equation parameters were solved by the interior point method through the narrowband data. At last, the zeros of the transfer function denominator were calculated. FEKO simulation data test verifies that the method has extrapolation ability.

Theoretical and experimental study of the dynamic response of absorber-based, micro-scale, oscillatory probes for contact sensing applications.

This paper presents two models for predicting the frequency response of micro-scale oscillatory probes. These probes are manufactured by attaching a thin fiber to the free end of one tine of a quartz tuning fork oscillator. In these studies, the attached fibers were either 75 μm diameter tungsten or 7 μm diameter carbon with lengths ranging from around 1 to 15 mm. The oscillators used in these studies were commercial 32.7 kHz quartz tuning forks. The first theoretical model considers lateral vibration of two beams serially connected and provides a characteristic equation from which the roots (eigenvalues) are extracted to determine the natural frequencies of the probe. A second, lumped model approximation is used to derive an approximate frequency response function for prediction of tine displacements as a function of a modal force excitation corresponding to the first mode of the tine in the absence of a fiber. These models are used to evaluate the effect of changes in both length and diameter of the attached fibers. Theoretical values of the natural frequencies of different modes show an asymptotic relationship with the length and a linear relationship with the diameter of the attached fiber. Similar results are observed from experiment, one with a tungsten probe having an initial fiber length of 14.11 mm incrementally etched down to 0.83 mm, and another tungsten probe of length 8.16 mm incrementally etched in diameter, in both cases using chronocoulometry to determine incremental volumetric material removal. The lumped model is used to provide a frequency response again reveals poles and zeros that are consistent with experimental measurements. Finite element analysis shows mode shapes similar to experimental microscope observations of the resonating carbon probes. This model provides a means of interpreting measured responses in terms of the relative motion of the tine and attached fibers. Of particular relevance is that, when a "zero" is observed in the response of the tine, one mode of the fiber is matched to the tine frequency and is acting as an absorber. This represents an optimal condition for contact sensing and for transferring energy to the fiber for fluid mixing, touch sensing, and surface modification applications.

Internal resonance for nonlinear vibration energy harvesting

The transformation of waste vibration energy into low-power electricity has been heavily researched over the last decade to enable self-sustained wireless electronic components. Monostable and bistable nonlinear oscillators have been explored by several research groups in an effort to enhance the frequency bandwidth of operation. Linear two-degree-of-freedom (2-DOF) configurations as well as the combination of a nonlinear single-DOF harvester with a linear oscillator to constitute a nonlinear 2-DOF harvester have also been explored to develop broadband energy harvesters. In the present work, the concept of nonlinear internal resonance in a continuous frame structure is explored for broadband energy harvesting. The L-shaped beam-mass structure with quadratic nonlinearity was formerly studied in the nonlinear dynamics literature to demonstrate modal energy exchange and the saturation phenomenon when carefully tuned for two-to-one internal resonance. In the current effort, piezoelectric coupling and an electrical load are introduced, and electromechanical equations of the L-shaped energy harvester are employed to explore primary resonance behaviors around the first and the second linear natural frequencies for bandwidth enhancement. Simulations using approximate analytical frequency response equations as well as numerical solutions reveal significant bandwidth enhancement as compared to a typical linear 2-DOF counterpart. Vibration and voltage responses are explored, and the effects of various system parameters on the overall dynamics of the internal resonance-based energy harvesting system are reported.

A New Method for Getting Rational Approximation for Fractional Order Differintegrals

AbstractIn this paper a new algorithm is presented to calculate the poles and zeros to approximate a fractional order (FO) differintegral (s±α,α∈(0,1)) by a rational function on a finite frequency band ω∈(ωl,ωh). The constant phase property of the FO differintegral is the basis for development of the algorithm. Interlacing of real poles and zeros is used to achieve the constant phase. The calculations are done using the asymptotic Bode phase plot. A brief investigation is made to get a good approximation for the Bode phase plot. Two design parameters are introduced to keep the average phase close to the desired phase angle and to keep the error within the allowed bounds. A study is done to empirically understand the relationship between the error and the design parameters. The results thus obtained help in the further calculations. The algorithm is computationally simple and inexpensive, and gives a fairly good approximation of fractance frequency response on the specified frequency band.

Evidence-theory-based analysis for the prediction of exterior acoustic field with epistemic uncertainties

Evidence theory has a strong ability to handle the epistemic uncertainty, based on which the uncertain parameters with limited information can be conveniently treated. In this paper, a numerical method is developed to predict the exterior acoustic field with epistemic uncertainties based on evidence theory. In order to alleviate the computational cost, the interval analysis technique is adopted to acquire the approximate frequency response amplitude bounds for each focal element, and the corresponding formulations of interval perturbation analysis for exterior acoustic field prediction are deduced. Inspired by the probability theory, the mean value, standard deviation and cumulative distribution are used to describe the distribution characteristics of evidence variables. Two numerical examples are given to illustrate the feasibility and effectiveness of the present method.

무곱셈 구현을 위한 FIR 필터 계수의 압축 센싱

In case the coefficient set of an FIR filter is represented in the canonic signed digit (CSD) format with a few nonzero digits, it is possible to implement high data rate digital filters with low hardware cost. Designing an FIR filter with CSD format coefficients, whose number of nonzero signed digits is minimal, is equivalent to finding sparse nonzero signed digits in the coefficient set of the filter which satisfies the target frequency response with minimal maximum error. In this paper, a compressive sensing based CSD coefficient FIR filter design algorithm is proposed for multiplierless and high speed implementation. Design examples show that multiplierless FIR filters can be designed using less than two additions per tap on average with approximate frequency response to the target, which are suitable for high speed filtering applications.

A frequency domain design of PID controller for an AVR system

We propose a new proportional-integral-derivative (PID) controller design method for an automatic voltage regulation (AVR) system based on approximate model matching in the frequency domain. The parameters of the PID controller are obtained by approximate frequency response matching between the closed-loop control system and a reference model with the desired specifications. Two low frequency points are required for matching the frequency response, and the design method yields linear algebraic equations, solution of which gives the controller parameters. The effectiveness of the proposed method is demonstrated through examples taken from the literature and comparison with some popular methods.