scholarly journals Estimation of Transfer Function Coefficients for Second-Order Systems via Metaheuristic Algorithms

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4529
Author(s):  
Omar Rodríguez-Abreo ◽  
Juvenal Rodríguez-Reséndiz ◽  
Francisco Antonio Castillo Velásquez ◽  
Alondra Anahi Ortiz Verdin ◽  
Juan Manuel Garcia-Guendulain ◽  
...  
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Standard Form ◽  
Estimation Method ◽  
Second Order ◽  
Parametric Estimation ◽  
Metaheuristic Algorithms ◽  
Step Response ◽  
Gray Wolf ◽  
Final Value

The present research develops the parametric estimation of a second-order transfer function in its standard form, employing metaheuristic algorithms. For the estimation, the step response with a known amplitude is used. The main contribution of this research is a general method for obtaining a second-order transfer function for any order stable systems via metaheuristic algorithms. Additionally, the Final Value Theorem is used as a restriction to improve the velocity search. The tests show three advantages in using the method proposed in this work concerning similar research and the exact estimation method. The first advantage is that using the Final Value Theorem accelerates the convergence of the metaheuristic algorithms, reducing the error by up to 10 times in the first iterations. The second advantage is that, unlike the analytical method, it is unnecessary to estimate the type of damping that the system has. Finally, the proposed method is adapted to systems of different orders, managing to calculate second-order transfer functions equivalent to higher and lower orders. Response signals to the step of systems of an electrical, mechanical and electromechanical nature were used. In addition, tests were carried out with simulated signals and real signals to observe the behavior of the proposed method. In all cases, transfer functions were obtained to estimate the behavior of the system in a precise way before changes in the input. In all tests, it was shown that the use of the Final Value Theorem presents advantages compared to the use of algorithms without restrictions. Finally, it was revealed that the Gray Wolf Algorithm has a better performance for parametric estimation compared to the Jaya algorithm with an error up to 50% lower.

scholarly journals Research on Heat Transfer Dynamic Characteristics of Composite Layer Based on Laplace Transform

2019 ◽  
Author(s):  
Chunyu Xu ◽  
Junhua Lin ◽  
Wenhao Liu ◽  
Yuanbiao Zhang
Keyword(s):  
Heat Transfer ◽  
Composite Materials ◽  
Temperature Distribution ◽  
Transfer Function ◽  
Dynamic Characteristics ◽  
Transfer Functions ◽  
Composite Layer ◽  
Engineering Application ◽  
Second Order ◽  
Inverse Transformation

This paper predict and effectively control the temperature distribution of the steady-state and transient states of anisotropic four-layer composite materials online, knowing the density, specific heat, heat conductivity and thickness of the composite materials. Based on the transfer function, a mathematical model was established to study the dynamic characteristics of heat transfer of the composite materials. First of all, the Fourier heat transfer law was used to establish a one-dimensional Fourier heat conduction differential equation for each composite layer, and the Laplace transformation was carried out to obtain the system function. Then the approximate second-order transfer function of the system was obtained by Taylor expansion, and the Laplace inverse transformation was carried out to obtain the transfer function of the whole system in the time domain. Finally, the accuracy of the simplified analytical solutions of the first, second and third order approximate transfer functions was compared with computer simulation. The results showed that the second order approximate transfer functions can describe the dynamic process of heat transfer better than others. The research on the dynamic characteristics of heat transfer in the composite layer and the dynamic model of heat transfer in composite layer proposed in this paper have a reference value for practical engineering application. It can effectively predict the temperature distribution of composite layer material and reduce the cost of experimental measurement of heat transfer performance of materials.

Placing Minimum Phase Zeros to Shape Transient Response: Generalization From Control of Hybrid Power Systems

2017 ◽  
Author(s):  
Bilal S. Salih ◽  
Tuhin K. Das
Keyword(s):  
Power Systems ◽  
Transient Response ◽  
Transfer Functions ◽  
Higher Order ◽  
Second Order ◽  
Step Response ◽  
Minimum Phase ◽  
Hybrid Power Systems ◽  
Hybrid Power ◽  
Second Order Systems

Conservation of energy can be applied in designing control of hybrid power systems to manage power demand and supply. In practice, it can be used for designing decentralized controllers. In this paper, this idea is analyzed in a generalized theoretical framework. The problem is transformed to that of using minimum phase zeros to generate a specific type of transient response admitted by dynamical systems. Here, the transient step response is shaped using an underlying conservation principle. In this paper, emphasis is placed on second order systems. However, the analysis can be extended to higher order transfer functions. Analytical results relating zero location to the matched/ mismatched areas of the transient response are established for a class of second order systems. A combination of feedback and feedforward actions are shown to achieve the desired zero placement/addition and the desired transient response. The proposed analysis promises extension to nonlinear systems. Optimization studies also seem appropriate, especially for higher order transfer functions.

scholarly journals Validation of Fractional-Order Lowpass Elliptic Responses of (1 + α)-Order Analog Filters

2018 ◽  
Vol 8 (12) ◽  
pp. 2603 ◽  
Author(s):  
David Kubanek ◽  
Todd Freeborn ◽  
Jaroslav Koton ◽  
Jan Dvorak
Keyword(s):  
Transfer Function ◽  
Least Squares ◽  
Fractional Order ◽  
Frequency Band ◽  
Operational Amplifier ◽  
Transfer Functions ◽  
Second Order ◽  
Experimental Results ◽  
Analog Filters ◽  
Lowpass Filter

In this paper, fractional-order transfer functions to approximate the passband and stopband ripple characteristics of a second-order elliptic lowpass filter are designed and validated. The necessary coefficients for these transfer functions are determined through the application of a least squares fitting process. These fittings are applied to symmetrical and asymmetrical frequency ranges to evaluate how the selected approximated frequency band impacts the determined coefficients using this process and the transfer function magnitude characteristics. MATLAB simulations of ( 1 + α ) order lowpass magnitude responses are given as examples with fractional steps from α = 0.1 to α = 0.9 and compared to the second-order elliptic response. Further, MATLAB simulations of the ( 1 + α ) = 1.25 and 1.75 using all sets of coefficients are given as examples to highlight their differences. Finally, the fractional-order filter responses were validated using both SPICE simulations and experimental results using two operational amplifier topologies realized with approximated fractional-order capacitors for ( 1 + α ) = 1.2 and 1.8 order filters.

A Novel Method of Transfer-Function Identification for Unknown Systems

2013 ◽  
Vol 321-324 ◽  
pp. 1967-1970
Author(s):  
Chung Neng Huang ◽  
Chen Min Cheng
Keyword(s):  
Transfer Function ◽  
Electromechanical Coupling ◽  
High Efficiency ◽  
Transfer Functions ◽  
Second Order ◽  
System A ◽  
Derivative Free ◽  
Efficiency Control ◽  
Novel Method ◽  
Free Search

This study proposes a new modeling method for unknown systems. Through this method, the transfer functions can be identified. First, the input-output data pairs of the unidentified system should be collected. Then, the transfer function’s coefficients can be identified based on the errors via the derivative-free search methods such as GA etc. Here, a second-order transfer function is used in this study. For a second-order transfer function is difficult to approach each system, a plurality of transfer functions may be used depending on the precise requirement. Finally, following the previous steps, the other transfer function can be found in succession. In order to confirm the effectiveness of this proposed method, an electromagnetic flywheel (EF) system is used in this study. Such kinds of systems are always with many uncertainties as nonlinear electromechanical coupling and electromagnetic saturation, etc. They are difficult to modeling via traditional mathematic ways. In this study, the data pairs of EF system is collected by experiments. By assessing the results of the proposal and experimental data shows that this method is feasible to any unknown systems. system, achieve more saving energy and high efficiency control purposes.

Transient Response of Linear Systems Under Integral Constraints

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Bilal Salih ◽  
Tuhin Das
Keyword(s):  
Transfer Function ◽  
Power Systems ◽  
Transfer Functions ◽  
Adaptive Estimation ◽  
Sufficient Conditions ◽  
Parametric Uncertainty ◽  
Step Response ◽  
Integral Constraints ◽  
Second Order Systems ◽  
Necessary And Sufficient

Abstract The requirement of satisfying an integral constraint imposed on a linear system's transient step-response is considered in this paper. The problem is first analyzed to determine the specific structure of a system's transfer function that helps satisfy such constraints. Analytical results are derived for a class of second-order systems with an additional zero. The results are extended to higher order transfer functions. Subsequently, a standard compensation consisting of a combination of feedforward and feedback actions is proposed to transform a given transfer function to the desired structure. Necessary and sufficient conditions to guarantee stability of the resulting closed-loop system are derived. Next, the problem of satisfying integral constraints in the presence of parametric uncertainty is addressed by augmenting adaptive estimation strategies to the feedforward and feedback compensation structure. Simulation results are provided for validation. The theory presented here is an abstraction from power management algorithms for hybrid power systems, such as a fuel cell hybridized with an ultracapacitor. Further work is ongoing to extend the theory to nonlinear systems.

A Numerical Evaluation of the Quadratic Transfer Function for a Floating Structure

2019 ◽  
Author(s):  
Zhitian Xie ◽  
Yujie Liu ◽  
Jeffrey Falzarano
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Transfer Functions ◽  
Second Order ◽  
Wave Frequency ◽  
Wave Forces ◽  
Floating Structure ◽  
Transfer Function Matrix ◽  
Wave Induced ◽  
Function Matrix

Abstract The second order force of a floating structure can be expressed in terms of a time independent quadratic transfer functions along with the incident wave elevation, through which it is possible to evaluate the second order wave exciting forces in the frequency domain. Newman’s approximation has been widely applied in approximating the elements of the quadratic transfer function matrix while numerically evaluating the second order wave induced force. Through Newman’s approximation, the off-diagonal elements can be numerically approximated with the diagonal elements and thus the numerical calculation efficiency can be enhanced. Newman’s approximation assumes that the off-diagonal elements do not change significantly with the wave frequency and that hydrodynamic phenomenon regarding the low difference frequency are usually of interest. However, it is obviously less satisfying when an element that is close to the diagonal line in the quadratic transfer function matrix shows an extremum if the corresponding wave frequency is close to the natural frequency of the certain motion. In this paper, the full derivation and expression of the second order wave forces and moments applied to a floating structure have been presented, through which the numerical results of the quadratic transfer function matrix including the diagonal and the off-diagonal elements will be illustrated. This work will present the basis of numerically evaluating the second order forces in the frequency domain. The comparisons among various approximations regarding the second order forces in deep water will also be presented as a meaningful reference.

Multimode Vibrations Suppression Compensators Design Using Specified Dynamic Performance Reference Models

2012 ◽  
Vol 463-464 ◽  
pp. 1125-1128
Author(s):  
Marius Sebastian Rusu ◽  
Lucian Grama
Keyword(s):  
Transfer Function ◽  
Dynamic Behavior ◽  
Transfer Functions ◽  
Reference Model ◽  
Dynamic Performance ◽  
Second Order ◽  
Model Parameters ◽  
Mechatronic Systems ◽  
Parallel Connection ◽  
Reference Models

This paper presents a method of designing vibration compensators for linear mechatronic systems based on their inverse multimodal representation and a customized second order transfer function embedding the specified dynamic behavior. The linear non-compensated system is modeled by a parallel connection of independent second order transfer functions. There are four flavors of compensators described in this paper, each having a different choice of the reference model parameters. A brief numerical example is also provided.

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