Transfer Function Identification Research Articles

压电倾斜镜传递函数辨识方法

压电倾斜镜传递函数辨识方法

A Multifrequency Model of Electric Locomotive for High-Frequency Instability Assessment

The high-frequency instability (HFI) issue results in serious harmonic overvoltage phenomena in the electrification railway system. This issue is rooted in the range that is not only below, but also above half the switching frequency. The commonly used small-signal averaging model is a single-frequency model in which the corresponding frequency component with perturbation frequency is considered merely. The inherent sampling nature has been neglected by the moving average operator. Therefore, it cannot reveal the effect of sideband components and may not be valid for predicting the high-frequency input admittance of a locomotive. To investigate the HFI issue, the sideband components generated by analog/data (A/D) sampling process and pulse width modulation (PWM) are taken into consideration. Then the multifrequency model of a locomotive is developed for evaluating the influences of sideband components. Meanwhile, the proposed model is validated by means of the frequency scan method, including the identification of PWM transfer functions and crossed-frequency transfer functions. Several HFI cases are summarized for comparing the accuracy between the traditional single-frequency model and the proposed multifrequency model. It denotes that the multifrequency model is more accurate to assess the high-frequency input admittance of a locomotive, especially the regions around the sampling frequency. Hardware-in-loop (HIL) results validate the theoretical analysis.

Modeling, system identification and design of fuzzy PID controller for discharge dynamics of metal hydride hydrogen storage bed

This paper presents the mathematical modeling of metal hydride based hydrogen storage bed. The novelty of this research work is the identification of transfer function for the dynamic discharge process of hydrogen storage bed is carried out using system identification tool box. A Fuzzy PID controller is modeled to regulate the pressure rate of hydrogen storage bed using MATLAB Simulink toolbox. The proposed controller reduces the complexity in controlling the pressure rate of hydrogen storage bed during desorption process for an adequate use in fuel cell and in other applications. To validate the reliability of the hydrogen storage bed model, the obtained results are verified with the results of other literature. The exact system transfer function model chosen is Box-Jenkin model, based on the simulated results of different black box model structures for the parameters such as percentage of fitness, final prediction error and the cost function. Usually, for the safer discharge of hydrogen gas, the classical PID controller is employed to control the pressure by manipulating the heating temperature of the storage bed. In order to have a better control, a Fuzzy-PID controller is proposed in this study. The proposed controller produces improved time domain response and better performance compared to the conventional PID controller.

Structural optimization and algorithm design for temperature control system of mid-infrared diode laser

Mid-infrared tunable diode laser absorption spectroscopy (TDLAS) has been extensively applied in high-sensitivity gas detection. Diode laser temperature control systems exert considerable influence on the comprehensive performance of gas detection systems. The overall design of temperature control systems for mid-infrared diode lasers is established in this research on the basis of the system’s structural optimization, thermoelectric cooler (TEC) selection, transfer function identification and control algorithm optimization, and the first-stage fuzzy PID combined with a second-stage PID control algorithm is applied to the actual system finally. The system can be quickly stabilized at any setting temperature between 10 °C–50 °C with a precision of ±10 m °C, and the energy consumption efficiency is high. The results lay the foundation for the optimization of the TDLAS systems’ overall performance.

A 12.5-MHz Bandwidth 77-dB SNDR SAR-Assisted Noise Shaping Pipeline ADC

This article presents a successive approximation register (SAR)-assisted noise-shaping (NS) pipeline architecture which breaks the speed bottleneck of the existing SAR or SAR-assisted-type NS analog-to-digital converters (ADCs). Rather than only for residue amplification and pipeline operation, the multiplying digital-to-analog converter (MDAC) is also reused as unity buffer and analog adder to realize the NS with error feedback (EF) structure in this design. While incorporating the proposed alternative loading capacitor (ALC) technique, an ideal first-order noise transfer function (NTF) is realized without additional feedback phase and only with a small analog circuit overhead. Unlike other NS SAR ADCs that involved amplification, the inter-stage gain attenuates the noise from the second-stage comparator, thus leading to both high speed and resolution. Fabricated in a 65-nm CMOS process, the prototype achieves a signal-to-noise-and-distortion ratio (SNDR) of 77.1 dB over 12.5-MHz bandwidth (BW) with only over-sampling ratio (OSR) of 8. Under a 1.2-V supply voltage, the ADC consumes 4.5 mW and exhibits a Scherier figure of merit (FoM) of 171.5 dB.

Strategy for the determination of unsteady aerodynamic forces on elongated bodies in grid-generated turbulent flow

In this study, we developed a general method for estimating the unsteady aerodynamic forces on elongated bodies in grid-generated turbulent flow. The key to this method is the identification of the one-wavenumber aerodynamic transfer function (ATF) of bluff sections. Based on our previous studies, the accuracy of the strip theory in estimating the unsteady aerodynamic forces on bluff sections in isotropic homogeneous turbulence is higher than that of a thin airfoil. The thin airfoil section is therefore intended to serve as a standard configuration to calibrate the experimental parameters to satisfy the accuracy of the strip theory. This can provide a road map for the experimental determination of the unsteady aerodynamic forces on elongated bodies with different configurations in turbulent flow. To explore the deviations between the ATFs of airfoil and bluff sections, buffeting force measurement wind tunnel tests were performed on NACA 0015 airfoils and 5:1 rectangular (REC) cylinders with different length-width ratios at a 0° attack angle in grid-generated turbulence. The measured one-wavenumber ATFs of the airfoil sections correspond strongly to the theoretical predictions. In addition, it was found that the one-wavenumber ATF of the REC model is larger than Sears’ function at low reduced streamwise wavenumbers, which is explained by the difference between the lift generation mechanisms of the bluff and airfoil sections in grid-generated turbulence.

Partial Discharge Localization on Power Cables Using On-Line Transfer Function

An on-line method is proposed for cable transfer function (TF) identification. For a cable's TF identification with this method, no knowledge about the cable geometry and material specification is needed. Moreover, it does not require that the cable system go out of service. An identification signal is injected through a high-frequency current transformer (HFCT) to the shield of the cable. By measuring the injected signal via HFCTs clamped on the shield at two distinct locations along the cable, the TF of the cable can be identified. A novel partial discharge (PD) localization method is also introduced, which is based on asynchronous PD measurements. In this method, travel distance of the signal is estimated by the reconstruction of a reference signal from the measured signals, using the obtained cable TF. Reference signal refers to the typical waveform of PD signal at its source location. Both the cable identification and PD localization methods are validated using two experimental setups to simulate a diverse range of PD source distance. The test cables are a 666-m long, single-core, low-voltage (2 kV) signal cable with PE insulation, and a 51-km long, single-core, medium-voltage (24 kV) power cable with XLPE insulation.

Stabilization of a double inverted rotary pendulum through fractional order integral control scheme

Rotary double inverted pendulum is a highly nonlinear complex system and requires a high performance controller for its control. Using gain matrix which is obtained through state feedback technique may create complexity while removing the steady-state error for all states. Incorporating an integral action can be an alternative for these errors. Therefore, a state space–based fractional order controller with fractional integral action is designed and tested on a rotary double inverted pendulum in this article. The fractional integral controller is designed based on Bode’s ideal transfer function. Two degree of freedom is considered for tuning purpose as well. The integer order controller based on the state space approach is also shown for comparison. Simulation and experimental results are presented for both controllers of this rotary double inverted pendulum system.

Asymptotic magnitude Bode plots of fractional-order transfer functions

Development of asymptotic magnitude Bode plots for integer-order transfer functions is a well-established topic in the control theory. However, construction of such plots for the fractional-order transfer functions has not received much attention in the existing literature. In the present paper, we investigate in this direction and derive the procedures for sketching asymptotic magnitude Bode plots for some of the popular fractional-order controllers. In addition, we deduce these plots for general fractional commensurate-order transfer functions as well. As applications of this work, we illustrate the analysis of the designed fractional-control loop, and the identification of fractional-order transfer function from a given plot.

Analytical fractional PID controller design based on Bode’s ideal transfer function plus time delay

In this paper, a fractional order PID controller cascaded with a fractional filter is proposed for higher order processes. In this analytical design methodology, one or two reduced fractional orders plus time delay models are used to represent higher order system transfer functions. The controller parameters are determined so as to meet certain frequency domain specifications. A unity feedback reference model is employed where Bode’s ideal loop transfer function plus time delay of the fractional order model is placed in the forward path. The addition of this time delay provides the exact determination of frequency domain specifications if the system either intrinsically owns a time delay or a time delay is injected by its reduced order model. The proposed methodology is compared with two other related methodologies and it has been observed that the proposed controller performs much better than the others. Moreover, some empirical formulas for time domain characteristics of the reference model are numerically derived in terms of certain frequency domain specifications and time delay of the fractional reduced order model. The accuracy of these formulas is tested by simulations. The iso-damping, noise attenuation and load disturbance suppression performances of the proposed controller are also considered and compared with those of other related controllers.

Heating-up control with delay-free output prediction for industrial jacketed reactors based on step response identification

To improve the heating-up control performance for industrial jacketed reactors typically involved with long input delay, a predictor-based two-degree-of-freedom (2DOF) control scheme is proposed for the heating-up process operation, based on model identification from a practical step response test. By performing a simple step test (i.e., turning on the electrical heater with certain power (e.g., 50% or 100% of the heating power) to observe the heating-up temperature response), a transfer function identification method is developed to establish an integrating type process model with time delay for describing fundamental dynamics of the heating-up response. Based on the identified model, a predictor-based 2DOF control structure is established, where the delay-free output prediction is obtained by constructing two filters. The 2DOF controllers are analytically derived by proposing the desired transfer functions for the set-point tracking and load disturbance rejection, respectively. There is a single adjustable parameter in each controller (or filter), which may be monotonically tuned to obtain the desired control (or prediction) performance. Illustrative examples from the existing references and a practical application to a 4-liter jacketed reactor for pharmaceutical crystallization are given to demonstrate the effectiveness and advantage of the proposed identification and control methods in comparison with the existing methods.

Transfer function identification through total least squares

When transient diffusion and/or advection occur in a physical system modelled by linear equations whose coefficients are time-invariant, the relationships between a source (a temperature or a thermal power) and its consequences (local temperatures) are convolution products. This study deals with identification of a transfer function when an additive noise not only corrupts the output (response) but also the input (excitation) in a calibration experiment. Regularization is implemented either through Truncated Singular Value Decomposition or by Total Least Squares.

Simultaneous identification of transfer functions and combustion noise of a turbulent flame

The Large Eddy Simulation/System Identification (LES/SI) approach allows to deduce a flame transfer function (FTF) from LES of turbulent reacting flow: Time series of fluctuations of reference velocity and global heat release rate resulting from broad-band excitation of a simulated turbulent flame are post-processed via SI techniques to derive a low order model of the flame dynamics, from which the FTF is readily deduced. The current work investigates an extension of the established LES/SI approach: In addition to estimation of the FTF, a low order model for the combustion noise source is deduced from the same time series data. By incorporating such a noise model into a linear thermoacoustic model, it is possible to predict the overall level as well as the spectral distribution of sound pressure in confined combustion systems that do not exhibit self-excited thermoacoustic instability. A variety of model structures for estimation of a noise model are tested in the present study. The suitability and quality of these model structures are compared against each other, their sensitivity regarding certain time series properties is studied. The influence of time series length, signal-to-noise ratio as well as acoustic reflection coefficient of the boundary conditions on the identification are examined. It is shown that the Box-Jenkins model structure is superior to simpler approaches for the simultaneous identification of models that describe the FTF as well as the combustion noise source. Subsequent to the question of the most adequate model structure, the choice of optimal model order is addressed, as in particular the optimal parametrization of the noise model is not obvious. Akaike's Information Criterion and a model residual analysis are applied to draw qualitative and quantitative conclusions on the most suitable model order. All investigations are based on a surrogate data model, which allows a Monte Carlo study across a large parameter space with modest computationally effort. The conducted study constitutes a solid basis for the application of advanced SI techniques to actual LES data.

Identification of flame transfer functions in the presence of intrinsic thermoacoustic feedback and noise

The Large Eddy Simulation/System Identification (LES/SI) approach is a general and efficient numerical method for deducing a Flame Transfer Function (FTF) from the LES of turbulent reacting flow. The method may be summarised as follows: a simulated flame is forced with a broadband excitation signal. The resulting fluctuations of the reference velocity and of the global heat release rate are post-processed via SI techniques in order to estimate a low-order model of the flame dynamics. The FTF is readily deduced from the low-order model. The SI method most frequently applied in aero- and thermo-acoustics has been Wiener–Hopf Inversion (WHI). This method is known to yield biased estimates in situations with feedback, thus it was assumed that non-reflective boundary conditions are required to generate accurate results with the LES/SI approach. Recent research has shown that the FTF is part of the so-called Intrinsic ThermoAcoustic (ITA) feedback loop. Hence, identifying an FTF from a compressible LES is always a closed-loop problem, and consequently one should expect that the WHI would yield biased results. However, several studies proved that WHI results compare favourably with validation data. To resolve this apparent contradiction, a variety of identification methods are compared against each other, including models designed for closed-loop identification. In agreement with theory, we show that the estimate given by WHI does not converge to the actual FTF. Fortunately, the error made is small if excitation amplitudes can be set such that the signal-to-noise ratio is large, but not large enough to trigger nonlinear flame dynamics. Furthermore, we conclude that non-reflective boundary conditions are not essentially necessary to apply the LES/SI approach.

A recursive algorithm for estimating multiple models continuous transfer function with non-uniform sampling

ABSTRACTA multiple model recursive least squares algorithm combined with a first-order low-pass filter transformation method, named λ-transform, is proposed for the simultaneous identification of multiple model orders continuous transfer functions from non-uniformly sampled input–output data. The λ-transformation is shown to be equivalent to a canonical transformation between discrete z-domain and δ-domain using the negative value of the λ-transform filter time-constant instead of the sampling interval parameter. The proposed algorithm deals with oversampling, sampling jitter or non-uniform sample intervals without the need for extra digital anti-aliasing pre-filtering, downsampling or interpolation algorithms, producing multiple models with a cost function that facilitates automatic selection of best-fitted models. Besides, measurement noise is noted as beneficial, bringing up an inherent bias toward low-order models. Simulated examples and a drum-boiler level experimental result exhibiting non-minimum phase behaviour illustrate the application of the proposed method.

Model-free tuning strategy of fractional-order PI controller for speed regulation of permanent magnet synchronous motor

This paper investigates a model-free tuning method of a fractional-order proportional–integral (FOPI) controller and its application for the speed regulation of a permanent magnet synchronous motor (PMSM). Firstly, the presented practical FOPI tuning method formulates the FOPI controller parameter identification problem via virtual reference feedback tuning (VRFT). Under the lack of accurate models, the proposed model-free method depends only on the measured input–output data of the closed-loop PMSM servo system. Secondly, Bode’s ideal transfer function is incorporated into the VRFT with consideration of the systematic fractional dynamics. Thus, the properties of the resulting system may be approximated to the desired fractional-order reference model. Thirdly, the proposed method fully considers optimal performance constraints on the stability requirements, sensitivity criteria, frequency-domain and time-domain characteristics. Then, the comprehensive optimization problem is derived and solved. Using suitably tuned parameters, the robustness and disturbance rejection ability of the VRFT-based FOPI control system are enhanced to achieve optimal performance. The convergence of the proposed method is proved by theoretical analysis. Finally, experimental results are presented to illustrate the effectiveness of the proposed model-free FOPI control method for the PMSM servo system.

Antlion optimizer tuned PID controller based on Bode ideal transfer function for automobile cruise control system

Abstract Automobile cruise control reduces driver fatigue and ensures traffic safety by heavily relying on ICT and control engineering. A number of cruise control schemes are expected to be designed for proper safety management of vehicles in automobile design sector. Due to boosting road crowds, there is a new demand in developing automation of cruise control. The successfulness of automation of cruise control is heavily dependent on the efficient design of feedback control system. The use of evolutionary algorithms in designing feedback control of automobile cruise control system has reported in recent literature. It involves the communication of traffic data captured by sensor with actuator of the vehicle. The literature still lacks use of recently developed evolutionary algorithms for cruise control that could leverage road safety by tuning the control parameters. This paper presents the design of robust PID controller for an automobile cruise control system (ACCS). A linearized version of the cruise control system has been studies as per the dominant characteristics in closed loop system. The PID controller is designed as per Bode ideal transfer function to ensure robustness and formulated as an optimization problem. The gain parameters of the designed PID controller are tuned by ant lion optimizer (ALO) algorithm such that the proposed compensated system depicts the Bode ideal reference model. A comparison of this approach, a state space method, classical PID, fuzzy logic, genetic algorithm is presented. Numerical simulations shows that the ALO tuned PID controller based on bodes ideal model has better performance in terms of settling time, rise time, maximum overshot, peak time and steady state error. The performance analysis has performed by time domain analysis and frequency domain analysis. The robustness of the system is evaluated by considering sensitivity, complimentary sensitivity and controller sensitivity function. Further, the disturbance rejection behavior is studied for the proposed system. The analysis result reveals that the proposed ALO based PID controller with Bode ideal model for ACCS performs better than other recently published methods. All the simulations are carried out in Simulink/Matlab environment.

PI-PD Controllers Design Using Bode’s Ideal Transfer Function

In this paper, a method is presented to design PIPD controllers for control system with time delay. The presented method takes Bode’s ideal transfer function as reference model and thus PI-PD controller parameters can be obtained by optimization. Bode's ideal transfer function gives the desired unit step response by setting two parameters. PI-PD parameters corresponding to the minimum value of the error which is the difference between the reference model and system to be controlled are obtained by using integral performance criteria which are frequently used in evaluating the performance of control systems. Matsuda's 4th order integer approximation is used in the Bode’s ideal transfer function. The reason of using Bode’s ideal transfer function instead of a standard second order system is that a fractional order plant represents a real system better than an integer order plant. Finally, the success of the method is demonstrated in the given example.

A practical method for the consistent identification of a module in a dynamical network

We present a new and simple method for the identification of a single transfer function that is embedded in a dynamical network. In existing methods the consistent identification of the desired transfer function relies on the positive definiteness of the spectral density matrix of the vector of node signals, and it typically requires knowledge of information about the topology and the excitation of the whole network. The positivity condition is on the internal signals and therefore can not be guaranteed a priori; in addition it is not necessary. The new method of this paper provides simple conditions on which nodes to excite and which nodes to measure in order to produce a consistent estimate of the desired transfer function. Just as importantly, it requires knowledge of the local topology and excitation only.

Design of experiments application, concepts, examples: State of the art

Design of Experiments (DOE) is statistical tool deployed in various types of system, process and product design, development and optimization. It is multipurpose tool that can be used in various situations such as design for comparisons, variable screening, transfer function identification, optimization and robust design. This paper explores historical aspects of DOE and provides state of the art of its application, guides researchers how to conceptualize, plan and conduct experiments, and how to analyze and interpret data including examples. Also this paper reveals that in past 20 years application of DOE have been growing rapidly in manufacturing as well as non-manufacturing industries. It was most popular tool in scientific areas of medicine, engineering, biochemistry, physics, computer science and counts about 50% of its applications compared to all other scientific areas.