Transfer Function Identification Research Articles

Identification of fractional-order transfer functionsand nonzero initial conditions using exponentiallymodulated signals

Abstract A new methodology that uses exponentially modulated signals with arbitrary excitation waveforms for the identification of fractional order transfer functions is proposed. In contrast to previous approaches where initial conditions were not considered and the system was required to be at rest for the identification procedure, the current contribution extends the formulation to the case where the system has non-zero initial conditions, dispensing with the need to place it at a resting state. This generalization is important in feedback instrumentation and metrology applications where the measurement or control process may not be disrupted to perform identification. Moreover, the procedure has a broader scope of applications because it structurally contemplates the case when the model presents derivatives in the input. Full identification of the system parameters as well as the fractional exponents associated with the model dynamics are achieved through a grid search procedure with resolution adjustable by the user. Two simulation examples are presented to illustrate the effectiveness of the proposed approach. The first example is concerned with the effect of measurement noise at the observed system output, whereas the second involves the identification of the impedance of a three-dimensional RC network model. These types of RC networks
have dynamics capturing complex phenomena with emergent responses and are ideal for emulating the complex dynamics encountered across physical sciences and in particular interdisciplinary subject areas such as biomedical engineering.

Identification of flame transfer functions during transient operation

Predicting thermoacoustic instabilities requires knowledge of the flame response to acoustic perturbations, which is characterized by the Impulse Response Function. Obtaining stability maps across an extensive parameter space is prohibitively costly with existing methods, both experimentally and numerically, as the data records must be obtained independently for each stationary operating condition. To address this problem, a nonparametric identification technique that enables the characterization of instantaneous Flame Transfer Functions (FTFs) under nonstationary operating conditions, based on a series expansion of the time-varying impulse response function (TV-IRF), is proposed. The technique is a direct extension of the Wiener-Hopf equation to nonstationary signals, yielding the linear minimum mean squared error estimator (LMMSEE) of the TV-IRF. This method is applied to data obtained from a model of a premixed, hydrogen-enriched swirl flame. It's hydrogen power fraction is rapidly varied from 12-43% over 100 milliseconds and the flame response to a band-limited, white-noise signal is computed. From the resulting input-output data, the TV-IRF is accurately estimated and the FTF for all hydrogen power fractions is obtained from a single data record. This method paves the way for cost-effective estimation of a map of FTF's from computational or experimental data, significantly reducing expenses in both cases.

Handrim Reaction Force and Moment Assessment Using a Minimal IMU Configuration and Non-Linear Modeling Approach during Manual Wheelchair Propulsion.

Manual wheelchair propulsion represents a repetitive and constraining task, which leads mainly to the development of joint injury in spinal cord-injured people. One of the main reasons is the load sustained by the shoulder joint during the propulsion cycle. Moreover, the load at the shoulder joint is highly correlated with the force and moment acting at the handrim level. The main objective of this study is related to the estimation of handrim reactions forces and moments during wheelchair propulsion using only a single inertial measurement unit per hand. Two approaches are proposed here: Firstly, a method of identification of a non-linear transfer function based on the Hammerstein-Wiener (HW) modeling approach was used. The latter represents a typical multi-input single output in a system engineering modeling approach. Secondly, a specific variant of recurrent neural network called BiLSTM is proposed to predict the time-series data of force and moments at the handrim level. Eleven subjects participated in this study in a linear propulsion protocol, while the forces and moments were measured by a dynamic platform. The two input signals were the linear acceleration as well the angular velocity of the wrist joint. The horizontal, vertical and sagittal moments were estimated by the two approaches. The mean average error (MAE) shows a value of 6.10 N and 4.30 N for the horizontal force for BiLSTM and HW, respectively. The results for the vertical direction show a MAE of 5.91 N and 7.59 N for BiLSTM and HW, respectively. Finally, the MAE for the sagittal moment varies from 0.96 Nm (BiLSTM) to 1.09 Nm for the HW model. The approaches seem similar with respect to the MAE and can be considered accurate knowing that the order of magnitude of the uncertainties of the dynamic platform was reported to be 2.2 N for the horizontal and vertical forces and 2.24 Nm for the sagittal moments. However, it should be noted that HW necessitates the knowledge of the average force and patterns of each subject, whereas the BiLSTM method do not involve the average patterns, which shows its superiority for time-series data prediction. The results provided in this study show the possibility of measuring dynamic forces acting at the handrim level during wheelchair manual propulsion in ecological environments.

Identification of flame transfer function and mechanism analysis of the influence of boundary impedance characteristics on thermoacoustic instability

Thermoacoustic instability is a common problem in the operation of modern gas turbines. The prediction of thermoacoustic instability and the clarification of its mechanism are the research focus and difficulty in the gas turbine industry. As a response function of flame to acoustic disturbance, flame transfer function is a key parameter in the study of thermoacoustic instability. In this paper, based on the scaled adaptive simulation (SAS) model combined with the eddy dissipation concept (EDC) combustion model, the time-domain flow field data are processed by the system identification method, and the results of flame transfer function extraction are in good agreement with the experimental values. Then, the detailed derivation process of the low-order thermoacoustic network model (LOTAN) is given to capture the behavior characteristics of the acoustic wave in the thermoacoustic system. On this basis, the effects of acoustic boundary conditions and hysteresis time on the thermoacoustic instability of the combustion system are analyzed, and the relationship between the mode shape, pressure, vibration velocity phase, and thermoacoustic instability is explored. It is found that the phase relationship between pressure and vibration mode can be used to determine the thermoacoustic instability of the system. This is of great practical significance for determining the thermoacoustic instability of the system and clarifying the internal mechanism of its generation and provides theoretical support for the subsequent thermoacoustic instability control.

Reduced-order helicopter model identification from closed-loop data

This paper presents the development of an algorithm for open-loop transfer functions identification and reduced-order modelling of a dynamical system, from closed-loop data with highly correlated inputs. Suitable for aeronautical applications (particularly for intrinsically unstable vehicles such as helicopters), it allows the identification of aircraft transfer functions from the knowledge of the time histories of arbitrary external inputs and the corresponding actuated controls and responses. After a numerical verification of the proposed approach considering a simple analytical aircraft dynamical system, it is successfully applied to a realistic engineering problem consisting of identifying the transfer functions of the AW-09 helicopter that relate pilot inputs to vehicle attitude and kinematics. It is shown that helicopter responses to arbitrary pilot inputs predicted by the reduced-order model representation of the helicopter dynamics based on the rational approximation of the identified transfer functions are in good agreement with those determined through the high-fidelity nonlinear flight dynamics solver used to evaluate the closed-loop database.

An Improved Active Disturbance Rejection Control for Bode's Ideal Transfer Function

An Improved Active Disturbance Rejection Control for Bode's Ideal Transfer Function

Transfer Function Identification with Few-Shots Learning and a Genetic Algorithm Using Proposed Signal-Signature

Transfer Function Identification with Few-Shots Learning and a Genetic Algorithm Using Proposed Signal-Signature

Nonlocal Metasurfaces‐Enabled Analog Light Localization for Imaging and Lithography

AbstractLocalization of light spots in a given image is a common task in digital processing but is challenging in analog. Herein, a periodic nonlocal metasurface that has an optical transfer function defined in reciprocal space is proposed to resolve this issue. Assuming an ideal optical transfer function that encodes that of a local lens, the selective spot size reduction of incident Gaussian beams and sharpening of a patterned incidence with a Gaussian line shape are demonstrated. A realistic nonlocal metasurface comprising a trilayer structure with air grating on top that operates as a 2D analog light localizer under unpolarized incidence is presented. Nonlocal metasurfaces, combined with conventional optics, are expected to improve the resolution by sharpening the spatial features and find applications in diverse scientific fields such as medical, materials, and life science.

System Identification and Fractional-Order Proportional–Integral–Derivative Control of a Distributed Piping System

The vibration of piping systems is one of the most important causes of accelerated equipment wear and reduced work efficiency and safety. In this study, an active vibration control method based on a fractional-order proportional–integral–derivative (PID) controller was proposed to suppress pipeline vibration and reduce pipeline damage. First, a mathematical model of the distributed piping system was established using the finite element analysis method, and the characteristics of the distributed piping system were studied effectively. Further, the time-frequency domain parameter identification method was used to realise the system identification of the cross-point vibration transfer function between the brake and sensor, and the particle swarm optimisation algorithm was utilised to further optimise the transfer function parameters to improve the system identification accuracy. Therefore, a fractional-order PID controller was designed using the D-decomposition method, and the optimal controller parameters were obtained. The experimental and numerical simulation results show that the improved system identification algorithm can significantly improve modelling accuracy. In addition, the designed fractional-order PID controller can effectively reduce the system’s overshoot, oscillation time, and adjustment time, thereby reducing the vibration response of piping systems.

Optimal fractional-order series cascade controller design: A refined Bode’s ideal transfer function perspective

In process industries, cascade control is comprehensively used for disturbance attenuation. This manuscript presents the control of the non-minimum phase (NMP) system with dead time via a series cascade scheme. An improved fractional-filter-based control scheme encompassing inverse and dead time compensators with analytical tuning is proposed. The design hinges on an enhanced Bode’s ideal transfer function, which incorporates delay and NMP zero to deal with the system’s NMP and dead time. Particle swarm optimization (PSO) is utilized to obtain the optimal assessment of fractional filter-based controller settings by minimizing an objective function. Two benchmark problems are presented to test the efficacy of the recommended controller. The Riemann surface and sensitivity examination are used to realize the stability and robustness of the feedback design. Numerical simulations exhibit the superiority of the suggested controller for closed-loop results.

Comparison of Unsteady Low- and Mid-Fidelity Propeller Aerodynamic Methods for Whirl Flutter Applications

Aircraft configurations with propellers have been drawing more attention in recent times, partly due to new propulsion concepts based on hydrogen fuel cells and electric motors. These configurations are prone to whirl flutter, which is an aeroelastic instability affecting airframes with elastically supported propellers. It commonly needs to be mitigated already during the design phase of such configurations, requiring, among other things, unsteady aerodynamic transfer functions for the propeller. However, no comprehensive assessment of unsteady propeller aerodynamics for aeroelastic analysis is available in the literature. This paper provides a detailed comparison of nine different low- to mid-fidelity aerodynamic methods, demonstrating their impact on linear, unsteady aerodynamics, as well as whirl flutter stability prediction. Quasi-steady and unsteady methods for blade lift with or without coupling to blade element momentum theory are evaluated and compared to mid-fidelity potential flow solvers (UPM and DUST) and classical, derivative-based methods. Time-domain identification of frequency-domain transfer functions for the unsteady propeller hub loads is used to compare the different methods. Predictions of the minimum required pylon stiffness for stability show good agreement among the mid-fidelity methods. The differences in the stability predictions for the low-fidelity methods are higher. Most methods studied yield a more unstable system than classical, derivative-based whirl flutter analysis, indicating that the use of more sophisticated aerodynamic modeling techniques might be required for accurate whirl flutter prediction.

DsPIC Implementation and Performances Evaluation of Adaptive Filters for System Identification

This paper aims to implement and evaluate performances of adaptive filters applied to linear systems identification on a dsPIC platform. To do so, we considered two different applications: the identification of DC motor transfer function and the acoustic echo cancellation. For the DC motor case, real-time identification is not necessarily required. However, for the acoustic echo cancellation case, real-time identification is crucial, making execution time a key parameter in this scenario. We have implemented three adaptive algorithms: LMS, NLMS, and RLS. The first two are known for their computational simplicity, while RLS is recognized for its convergence speed. Performances evaluation is primarily based on accuracy and computation speed. A comparison is carried out in both cases to determine which algorithm is more suitable for each application. The results obtained showed that RLS is better suited for the DC motor case, while NLMS is more suitable for acoustic echo cancellation, particularly when the impulse response of the echo path is long.

VPSA-Based Transfer Function Identification of Single DoF Copter System

In this study, an experimental set of a Single-DoF Copter system is created and transfer functions that could model the dynamics of the physical system with high accuracy were investigated. In order to model the dynamics of the physical system with the highest accuracy, the five different transfer functions have been proposed, in which the zero and pole values are determined by optimizing with the Vibrating Particle System Algorithm. Integral Square Error (ISE), Integral Time Square Error (ITSE), Integral Absolute Error (IAE), Integral Time Absolute Error (ITAE) functions, which are widely used in the literature in determining transfer functions, are determined as fitness functions. In order to verify the transfer functions, the responses of the transfer functions and the experimental system response are presented comparatively, and their suitability was evaluated. It has been observed that the proposed method is successful in defining the transfer function of the experimental system, and the compatibility of the obtained transfer functions with the system response is between 75.407% and 98.612% accuracy.

Frequency domain online secondary path modelling for active noise control without auxiliary noise

The identification of the secondary path transfer function is of vital importance for active noise control (ANC) system. Online secondary path modeling method is preferable to offline modeling due to its tracking capability in time-varying acoustic environments. However, the auxiliary noise of online modeling mixed with the residual error signal diminishes the noise control performance. In this paper, we propose a frequency domain online secondary path modelling algorithm based on our previous work which achieves simultaneous acoustic paths modeling and noise control without auxiliary noise. The uniqueness of the solution is theoretically analyzed, and the computational burden is shown significantly lower than the previously proposed method. Simulations are conducted to verify that the proposed algorithm also has a better convergence behavior.

Research on system of ultra-flat carrying robot based on improved PSO algorithm

Ultra-flat carrying robots (UCR) are used to carry soft targets for functional safety road tests of intelligent driving vehicles and should have superior control performance. For the sake of analyzing and upgrading the motion control performance of the ultra-flat carrying robot, this paper develops the mathematical model of its motion control system on the basis of the test data and the system identification method. Aiming at ameliorating the defects of the standard particle swarm optimization (PSO) algorithm, namely, low accuracy, being susceptible to being caught in a local optimum, and slow convergence when dealing with the parameter identification problems of complex systems, this paper proposes a refined PSO algorithm with inertia weight cosine adjustment and introduction of natural selection principle (IWCNS-PSO), and verifies the superiority of the algorithm by test functions. Based on the IWCNS-PSO algorithm, the identification of transfer functions in the motion control system of the ultra-flat carrying robot was completed. In comparison with the identification results of the standard PSO and linear decreasing inertia weight (LDIW)-PSO algorithms, it indicated that the IWCNS-PSO has the optimal performance, with the number of iterations it takes to reach convergence being only 95 and the fitness value being only 0.117. The interactive simulation model was constructed in MATLAB/Simulink, and the critical proportioning method and the IWCNS-PSO algorithm were employed respectively to complete the tuning and optimization of the Proportional-Integral (PI) controller parameters. The results of simulation indicated that the PI parameters optimized by the IWCNS-PSO algorithm reduce the adjustment time to 7.99 s and the overshoot to 13.41% of the system, and the system is significantly improved with regard to the control performance, which basically meets the performance requirements of speed, stability, and accuracy for the control system. In conclusion, the IWCNS-PSO algorithm presented in this paper represents an efficient system identification method, as well as a system optimization method.

Identification of Transfer Function to Model Brush Temperature of a Small DC Machine at No-Load

Using temperature measurement to provide insight into the health condition of an electrical machine at any operating point could be possible if a baseline temperature of the machine could be modelled in real-time and compared to the actual current temperature. In this study, transfer functions are being identified to be used as a baseline temperature response model for a small DC machine. As a preliminary study, the transfer functions are identified using experimental data of temperature responses at several no-load speed step inputs. The order of transfer function tested was between a range from 0 to 4. The third order transfer function was found to be the best followed by the first order transfer function with a model MSE error of less than 0.41 and 0.65 respectively. The slight variation on the poles of the system indicates that the thermal system of the electrical machine does not obey exactly the LTI hypothesis.

A Novel Data-Driven Self-Tuning SVC Additional Fractional-Order Sliding Mode Controller for Transient Voltage Stability With Wind Generations

This paper proposes a novel data-driven self-tuning additional sliding mode controller for power system transient voltage stability enhancement considering wind integration. We first develop a new additional fractional-order sliding mode controller (FOSMC) for the static var compensator (SVC). The tuning of FOSMC parameter settings is then reformulated as a Markov decision process (MDP) and solved by the deep reinforcement learning (DRL) algorithm. In addition, a data-driven estimation method is proposed for the identification of an equivalent transfer function that is further used to calculate reward during the training process, yielding the model-free training. After that, the well-trained agent allows us to tune the controller parameters considering system uncertainties and achieve robustness against various operating conditions. Comparative results with other state-of-art methods demonstrate that the proposed method can effectively suppress the chattering issue of the sliding mode controller and ensure transient voltage stability under different operating conditions.

Prediction method for bridge buffeting responses based on the integrated transfer function identified via segmental model vibration test

On the basis of the definition and the three-dimensional characteristics of an integrated transfer function, the transfer function identification method based on reasonable technical means considering the three-dimensional effect was proposed. An original method to predict the bridge buffeting responses directly using the integrated transfer function is presented and investigated by means of segmental model vibration tests. Taking a suspension bridge as the background, the integrated transfer function was identified using segmental model vibration tests, and the effect of span-width ratio on it was studied. The buffeting response test of a full-bridge model was carried out in two different wind fields. Further, the identified integrated transfer functions were applied to predict the buffeting responses of the full-bridge model. By comparing the results, it is demonstrated that the method using reasonable segmental model vibration tests to obtain the integrated transfer functions to predict the bridge buffeting responses was highly accurate. The feasibility of the proposed method according to segmental model vibration tests was verified through tests for the first time. The method can effectively improve the deviation of results arise from the inaccurate simulating of turbulent characteristics in the tests, and avoid the many limitations of pressure and force measurement methods.

Fractional Order Transfer Function Identification of Six-Phase Induction Motor Using Dual-Chirp Signal

Fractional Order Transfer Function Identification of Six-Phase Induction Motor Using Dual-Chirp Signal

The buffered optimization methods for online transfer function identification employed on DEAP actuator

The buffered optimization methods for online transfer function identification employed on DEAP actuator