Frequency Response Method Research Articles

Nonlinear vibrations of a thin isotropic circular plate subjected to moving point loads

Here, we have studied the linear and nonlinear vibrations of a thin circular plate subjected to circularly, radially, and spirally moving transverse point loads. We follow Kirchoff’s theory and then incorporate von Kármán nonlinearity and employ Hamilton’s principle to obtain the governing equations and the associated boundary conditions. We solve the governing equations for the simply-supported and clamped boundary conditions using the mode summation method. Using the harmonic balance method for frequency response and Runge-Kutta method for time response, we solve the resulting coupled and cubic nonlinear ordinary differential equations. We show that the resonance instability due to a circularly moving load can be avoided by splitting it into multiple loads rotating at the same radius and angular speed. With the increasing magnitude of the rotating load, the frequency response of the transverse displacement shows jumps and modal interaction. The transverse response collected at the centre of the plate shows subharmonics of the axisymmetric frequencies only. The spectrum of the linear response due to spirally moving load contains axisymmetric frequencies, the angular speed of the load, their combination, and superharmonics of axisymmetric frequencies.

Introduction to Chemical Reactor Analysis

Nonlinear frequency response (NFR) method was used to evaluate the forced periodic operations and their potential for improving the system performance compared to steady-state operations. The NFR method was used to evaluate the time-average performances of forced periodically operated systems subjected to simultaneous periodic modulation of two-inputs of general waveforms. As an example, a forced periodically operated adiabatic CSTR with simple nth order reaction A → νPP and square-wave modulation of two pairs of inputs were analyzed in detail. The theory is illustrated analyzing the hydrolysis of acetic acid anhydride performed in a laboratory scale adiabatic CSTR. The results showed that significant improvements could be achieved by simultaneous modulation of both pairs of inputs. Comparison with the results of numerical integration showed that the approximation using only the asymmetrical second order FRFs and the first three harmonics of the inputs provide very reliable predictions of the DC component.

Dynamic AC Line Frequency Response Method for LUT-Based Variable On-Time Control in 360–800 Hz CRM Boost PFC Converter

To improve the input current total harmonic distortion (THD), the look-up table (LUT) method is used in the 360-800 Hz critical conduction mode (CRM) boost power factor correction (PFC) converter. When the ac line frequency changes drastically and suddenly, the zero-crossing detection method needs the half ac line period to follow the sudden frequency jump, causing a mismatching between the LUT and the ac line frequency. This mismatching in the time domain leads to a large current spike in the input current and even destruction in the PFC converter under some severe conditions. In this letter, a dynamic ac line frequency response method is proposed to eliminate this mismatching. The proposed method only needs to sample the input voltage, leading to a good performance in following the sudden frequency jump in a wide input voltage range. The effectiveness of the proposed method is verified with a 160 W GaN-based CRM boost PFC converter.

Evaluation of Electrochemical Process Improvement Using the Computer-Aided Nonlinear Frequency Response Method: Oxygen Reduction Reaction in Alkaline Media.

The intensification of an electrochemical process by forced periodic operation was studied for the first time using the computer-aided Nonlinear Frequency Response method. This method enabled the automatic generation of frequency response functions and the DC components (Faradaic rectification) of the cost (overpotential) and benefit (current density) indicators. The case study, oxygen reduction reaction, was investigated both experimentally and theoretically. The results of the cost–benefit indicator analysis show that forced periodic change of electrode potential can be superior when compared to the steady-state regime for specific operational parameters. When the electrode rotation rate is changed periodically, the process will always deteriorate as the dynamic operation will inevitably lead to the thickening of the diffusion layer. This phenomenon is explained both from a mathematical and a physical point of view.

Rapid Multi-Objective Optimization of Periodically Operated Processes Based on the Computer-Aided Nonlinear Frequency Response Method

The dynamic optimization of promising forced periodic processes has always been limited by time-consuming and expensive numerical calculations. The Nonlinear Frequency Response (NFR) method removes these limitations by providing excellent estimates of any process performance criteria of interest. Recently, the NFR method evolved to the computer-aided NFR method (cNFR) through a user-friendly software application for the automatic derivation of the functions necessary to estimate process improvement. By combining the cNFR method with standard multi-objective optimization (MOO) techniques, we developed a unique cNFR–MOO methodology for the optimization of periodic operations in the frequency domain. Since the objective functions are defined with entirely algebraic expressions, the dynamic optimization of forced periodic operations is extraordinarily fast. All optimization parameters, i.e., the steady-state point and the forcing parameters (frequency, amplitudes, and phase difference), are determined rapidly in one step. This gives the ability to find an optimal periodic operation around a sub-optimal steady-state point. The cNFR–MOO methodology was applied to two examples and is shown as an efficient and powerful tool for finding the best forced periodic operation. In both examples, the cNFR–MOO methodology gave conditions that could greatly enhance a process that is normally operated in a steady state.

Computer-Aided Nonlinear Frequency Response Method for Investigating the Dynamics of Chemical Engineering Systems

The Nonlinear Frequency Response (NFR) method is a useful Process Systems Engineering tool for developing experimental techniques and periodic processes that exploit the system nonlinearity. The basic and most time-consuming step of the NFR method is the derivation of frequency response functions (FRFs). The computer-aided Nonlinear Frequency Response (cNFR) method, presented in this work, uses a software application for automatic derivation of the FRFs, thus making the NFR analysis much simpler, even for systems with complex dynamics. The cNFR application uses an Excel user-friendly interface for defining the model equations and variables, and MATLAB code which performs analytical derivations. As a result, the cNFR application generates MATLAB files containing the derived FRFs in a symbolic and algebraic vector form. In this paper, the software is explained in detail and illustrated through: (1) analysis of periodic operation of an isothermal continuous stirred-tank reactor with a simple reaction mechanism, and (2) experimental identification of electrochemical oxygen reduction reaction.

A novel frequency-labeled adaptive sparse grid collocation method for uncertainty quantification of the frequency response of general viscoelastic damping structures

In this paper, a frequency-labeled adaptive sparse grid collocation (FL-ASGC) method is proposed to study the uncertainty quantification (UQ) of the frequency response of general viscoelastic damping structures. The advantage of the proposed method is that, on the one hand, it has a good approximation ability for both smooth and non-smooth responses so that it can robustly predict the variability of frequency responses under various damping levels. On the other hand, by evaluating the contribution of each interpolation node to the response at all frequencies, it can adaptively select samples and their accompanying analysis frequency domains, thereby minimizing the computational costs of probabilistic surrogate modeling. To obtain the deterministic solution of each sample, the layer-wise finite element method combined with the direct frequency response (DFR) method is employed. Two numerical examples with different damping materials are provided to test the proposed method. Uncertainties that obey normal distribution in material and geometry are considered. The results show the proposed method can accurately, efficiently, and robustly predict the variability of the frequency response of general viscoelastic damping structures.

Nonlinear vibrations of a polar-orthotropic thin circular plate subjected to circularly moving point load

Here, we formulate and study nonlinear vibrations of a thin, polar-orthotropic circular plate subjected to a circularly moving point load at a fixed radius and constant angular velocity. The governing equations and boundary conditions are obtained following Kirchhoff’s plate theory, incorporating von Kármán nonlinearity, and employing extended Hamilton’s principle. The external damping is introduced via Rayleigh dissipation function. The governing equations are solved using mode summation procedure. The mode shapes and the natural frequencies of the polar-orthotropic circular plate are found using Frobenius series method. Mode summation procedure results in coupled nonlinear ordinary differential equations. These equations are solved using the Runge–Kutta method for time response and method of harmonic balance with the arc continuation method for frequency response. The spectrum of the undamped linear vibration response of isotropic and polar-orthotropic plates exhibits natural frequencies of plates and angular velocity of the rotating load. The damped response contains the frequency of the angular velocity of the rotating load only. The nonlinear transverse vibrations of the undamped and damped plate due to rotating point load reveal frequency rich spectrums. The frequency response function shows strong modal interactions.

Feedback control of boundary layer Tollmien-Schlichting waves using a simple model-based controller

The attenuation of spatially evolving instability Tollmien-Schlichting (T-S) waves in the boundary layer of a flat plate with zero pressure gradients using an active feedback control scheme is theoretically and numerically investigated. The boundary layer is excited artificially by various perturbations to create a three-dimensional field of instability waves. Arrays of actuators and sensors are distributed locally at the wall surface and connected together via a feedback controller. The key elements of this feedback control are the determination of the dynamic model of the flat plate boundary layer between the actuators and the sensors, and the design of the model-based feedback controller. The dynamic model is established based on the linear stability calculation which simulates the three-dimensional input-output behaviour of the boundary layer. To simplify the control problem, an uncoupled control mode of the dynamic model is made to capture only those dynamics that have greatest influences on the input-output behaviour. A Proportional-Integral-Derivative (PID) controller, i.e. a lead-lag compensator, combining with a standard Smith predictor is designed based on the system stability criterion and the specifications using frequency-response methods. Good performance of the feedback control with the uncoupled control mode is demonstrated by the large reduction of the three-dimensional disturbances in the boundary layer. This simple feedback control is realistic and competitive in a practical implementation of T-S wave cancellation using a limited number of localised sensors and actuators.

New method of finding exact frequency response for feedback amplifiers

Due to feedback amplifier analysis simplification, Miller theorem, feedback theorem and Gray-Searle theorem are the most used tools on the calculation of the frequency response. However, they are only approximated results and then are invalid for overall closed-loop voltage gain of the frequency response. The traditional feedback theory, Miller theorem and Gray-Searle theorem are troublesome due to the significant difficulty of using the Kirchhoff's voltage/current law and Thevenin equivalent theorem. Especially, the utilisations of the Kirchhoff's voltage/current law and Thevenin equivalent theorem will be impractical for the complicated differential amplifier with the active load that contains four dependent sources and three bridge elements. The study proposes exact and algebraic frequency response analysis of a feedback amplifier by using the authors series research-Chen's Electric Unifying Approach with L'Hospital rule and Cramer's rule to take the place of those traditional approaches. Some experimental and mathematical results have exploited the fact that the proposed approach can yield the more effective and practical DC quiescent analysis with bias values and AC frequency response analysis with two junction charge-storage capacitances for the common-emitter amplifier with emitter resistance. Some experiments are provided to demonstrate the effectiveness of the proposed method.

Forced periodic reactor operation: Analysis of process and forcing parameters exploiting the nonlinear frequency response method

Special Issue: 10. ProcessNet‐Jahrestagung und 34. DECHEMA‐Jahrestagung der Biotechnologen 2020: Processes for Future

Passivity-Based Design of Repetitive Controller for $LCL$-Type Grid-Connected Inverters Suitable for Microgrid Applications

A repetitive controller (RC) is one of the most promising candidates for harmonic compensation when designing the current controller of grid-connected inverters. The discrete-time closed-loop transfer function based frequency response method can be used to shape RC, which is applicable for a single inverter connecting to well-known inductive-impedance grids, but cannot guarantee the stability in the case of capacitive-impedance grids or complex systems, such as microgrids. To address this issue, this article presents a new passivity-based design method for an RC for LCL-type grid-connected inverters with either inverter-side or grid-side current control. With the proposed design guidelines, the output admittance of the RC-controlled inverter is tuned to be passive in all frequencies, so that it can be plug and play connected to a grid regardless of grid impedance. Meanwhile, thanks to infinite gains of an RC at the fundamental frequency and its multiples as the high-quality grid injected current in accordance with IEC 61000-3-4 standard is ensured even in the presence of distorted grid conditions. Finally, experimental results with an established lab prototype are provided to verify the effectiveness of the proposed approach.

Uncertainty propagation of frequency response of viscoelastic damping structures using a modified high-dimensional adaptive sparse grid collocation method

Uncertainty propagation (UP) of the frequency response is essential for the robust design of viscoelastic damping structures. One challenge in solving this problem is enormous computation cost from the UP analysis. This paper aims to develop a novel computational effective method based on the combination of the adaptive sparse grid collocation (ASGC) method and the high dimensional model representation (HDMR) technique to evaluate the variability of the frequency response of viscoelastic damping structures. First, a well-validated layer-wise finite element method is employed to model the viscoelastic damping structures. The direct frequency response (DFR) method is utilized to calculate the response. Then, a modified adaptive strategy using expectation increments as the sampling indicator is proposed for cost-effective sparse grid construction. Lastly, high dimensional model representation (HDMR) technique is introduced to address the difficulty in moderate and high random dimensional situations. Two numerical examples are provided to assess the performances of the proposed method. Variations in constitutive parameters of viscoelastic material and thicknesses of the viscoelastic layer are considered. Numerical results show that, compared to the original high-dimensional ASGC method and Monte Carlo Simulation (MCS), the proposed method accurately predicts the variability of frequency responses and significantly improves the computational efficiency.

Direct imaging method of frequency response of capacitance in dual bias modulation electrostatic force microscopy

We have proposed and demonstrated a direct imaging method in dual bias modulation electrostatic force microscopy (DI-DEFM) to observe the frequency response of the capacitance between a conductive tip and a sample in a single scan. In DI-DEFM, dual ac biases with different frequencies are simultaneously applied between the tip and the sample to generate an electrostatic force; the frequencies are switched between two pairs of frequency conditions, with a switching frequency . Then, the component in the electrostatic force is detected, similar to a heterodyne method, to analyze the frequency response of the capacitance. The validity of DI-DEFM is assessed through the image acquisition on a Cu(In,Ga)Se2 sample.

Nonlinear frequency response analysis of forced periodic operations with simultaneous modulation of two general waveform inputs with applications on adiabatic CSTR with square-wave modulations

Nonlinear frequency response (NFR) method was used to evaluate the forced periodic operations and their potential for improving the system performance compared to steady-state operations. The NFR method was used to evaluate the time-average performances of forced periodically operated systems subjected to simultaneous periodic modulation of two-inputs of general waveforms. As an example, a forced periodically operated adiabatic CSTR with simple nth order reaction A → νPP and square-wave modulation of two pairs of inputs were analyzed in detail. The theory is illustrated analyzing the hydrolysis of acetic acid anhydride performed in a laboratory scale adiabatic CSTR. The results showed that significant improvements could be achieved by simultaneous modulation of both pairs of inputs. Comparison with the results of numerical integration showed that the approximation using only the asymmetrical second order FRFs and the first three harmonics of the inputs provide very reliable predictions of the DC component.

Design of Multifrequency Proportional–Resonant Current Controllers for Voltage-Source Converters

In recent years, the applicability of multifrequency proportional-resonant (PR) current controllers has been extensively explored. The analysis and controller design are typically performed by means of frequency response methods. In this context, the open-loop system's gain crossover frequency and the associated phase margin are most commonly used as design parameters. However, those parameters are not well defined in applications with multifrequency PR controllers, where multiple 0-dB crossings of the open-loop gain emerge. In contrast, it is shown that the system's gain margin can mostly be utilized as a reliable stability measure. Furthermore, since each resonator introduces an unwanted phase lag to its higher neighbored resonator, the desired stability margin might not be achieved by “conventional” controller designs or the system could even be destabilized. Hence, this article reviews common analytic design guidelines for PR current controllers and extends them to controllers that implement multiple resonators in either a stationary frame or a synchronous reference frame. To achieve a good compromise between the stability margin and a small steady-state control error, a recursive adjustment procedure for the controller's integral gains is proposed. The “plug-and-play” controller design is applied to a grid-connected voltage-source converter and the theoretical findings are validated by computer simulations and experiments.

A Modified Linear Integral Resonant Controller for suppressing jump-phenomenon and hysteresis in micro-cantilever beam structures

This paper demonstrates the effectiveness of a Modified Linear Integral Resonant Controller (MIRC) based on its original LTI cousin, known just as the ‘IRC’, for suppressing Jump-Phenomenon and hysteresis found in Micro-Cantilevers. A Method of Multiple Scales frequency response is derived, explored and compared with a Runge-Kutta based numerical integration method in order to understand any shortcomings in approximate analytical methods for the analysis of closed-loop nonlinear systems with the inclusion of a stability analysis. It is found that there exist some mild inconsistencies when comparing closed-loop Method of Multiple Scales to traditional numerical integration. A suitably designed Modified Integral Resonant Controller is implemented in closed-loop. Both analytical and numerical results agree with each other and show significant damping performance. Efficacy of the proposed control scheme is validated via frequency response plots, phase portraits and quiver plots.

Image Quality Assessment of Digital Image Capturing Devices for Melanoma Detection

The fast-growing incidence of skin cancer, especially melanoma, is the guiding principle for intense development of various digital image-capturing devices providing easier recognition of melanoma by dermatologists. Handheld and digital dermoscopy, following of mole changes with smartphones and digital analysing of mole images, is based on evaluation of the colours, shape and deep structures in the skin moles. Incorrect colour information of an image, under- or overexposed images, lack of sharpness and low resolution of the images, can lead to melanoma misdiagnosis. The purpose of our study was to determine the colour error in the image according to the given lighting conditions and different camera settings. We focused on measuring the image quality parameters of smartphones and high-resolution cameras to compare them with the results of state-of-the-art dermoscopy device systems. We applied standardised measuring methods. The spatial frequency response method was applied for measuring the sharpness and resolution of the tested camera systems. Colour images with known reference values were captured from the test target, to evaluate colour error as a CIELAB (Commission Internationale de l’Eclairage) ΔE*ab colour difference as seen by a human observer. The results of our measurements yielded two significant findings. First, all tested cameras produced inaccurate colours when operating in automatic mode, and second, the amount of sharpening was too intensive. These deficiencies can be eliminated through adjusting the camera parameters manually or by image post-production. The presented two-step camera calibration procedure improves the colour accuracy of captured clinical and dermoscopy images significantly.

Small-Signal Modeling and Closed-Loop Control of Bidirectional Buck-Boost Current-Fed Isolated DC–DC Converter

The bidirectional buck-boost current-fed isolated dc–dc converter (B3CFIdc) has the advantages of low current stress, high efficiency, and wide power/voltage conversion range. The linear models of buck mode and boost mode of B3CFIdc are originally derived using state-space averaging method. The dual-closed-loop control configuration with the inductor current and output voltage is designed. In order to ensure the stability of both operation modes at the same time, the parameters of the controllers are designed using the method of Hurwitz criterion plus frequency response. The asymptotic stability of the operating conditions with periodic switching between the two modes caused by the periodic fluctuation of input voltage is verified using the linear switching theory. The detailed experimental results verify the correctness of the built small-signal models and the feasibility of the designed closed-loop control configuration and the design rule of the controller parameters.

Dynamic characteristics and experiment of push–pull high-power ultrasonic consolidation resonance system for metal foil

To realize metal foil consolidation, a push–pull high-power ultrasonic consolidation resonance system is designed. Firstly, the structure of a high-power piezoelectric transducer was designed and calculated, the push–pull ultrasonic consolidation resonance system was designed according to requirements of ultrasonic consolidation. Secondly, the finite element modal analysis of the ultrasonic consolidation resonance system was carried out, the natural frequency and vibration mode were obtained. The dynamic simulation of the ultrasonic consolidation resonance system was carried out based on the four-terminal network method and MATLAB/Simulink, the displacement of piezoelectric transducer and the resonance system was obtained, the output displacement of piezoelectric transducer and the consolidation sonotrode end surface is 6 μm and 20 μm respectively. Thirdly, the dynamic model of the consolidation resonance system was established, according to the transfer function, the root locus method and frequency response method were used to analyze the characteristics of the system. Finally, the sweep frequency and impedance measurement of piezoelectric transducer were carried out, and the sweep frequency and fixed frequency measurement of the ultrasonic consolidation resonance system were also carried out. Experimental results show that the resonant frequency of piezoelectric transducer is 19,875 Hz, and the minimum impedance value is 261.43 $$\Omega$$ when the frequency is near 20 kHz. When applying 120 V and 160 V voltage signal, the resonant frequency is 20,039 Hz and 20,055 Hz, the maximum displacement of the sonotrode which is excited by double piezoelectric transducers is about 16 μm. The ultrasonic consolidation machine is fabricated, which can meet requirements of metal foil consolidation, such as high-power and amplitude.