Model Reduction of Transfer Functions Using a Dominant Root Method

1990 ◽  
Vol 112 (3) ◽  
pp. 547-554 ◽  
Author(s):  
J. E. Seem ◽  
S. A. Klein ◽  
W. A. Beckman ◽  
J. W. Mitchell
Keyword(s):  
Heat Transfer ◽  
Transfer Function ◽  
Model Reduction ◽  
Transfer Functions ◽  
Linear Time ◽  
Padé Approximation ◽  
Computational Effort ◽  
Pade Approximation ◽  
Bilinear Transformation ◽  
Transfer Problems

Transfer function methods are more efficient for solving long-time transient heat transfer problems than Euler, Crank-Nicolson, or other classical techniques. Transfer functions relate the output of a linear, time-invariant system to a time series of current and past inputs, and past outputs. Inputs are modeled by a continuous, piecewise linear curve. The computational effort required to perform a simulation with transfer functions can be significantly decreased by using the Pade´ approximation and bilinear transformation to determine transfer functions with fewer coefficients. This paper presents a new model reduction method for reducing the number of coefficients in transfer functions that are used to solve heat transfer problems. There are two advantages of this method over the Pade´ approximation and bilinear transformation. First, if the original transfer function is stable, then the reduced transfer function will also be stable. Second, reduced multiple-input single-output transfer functions can be determined by this method.

Suboptimal Model Reduction by Multi-Point Padé Approximation

1994 ◽  
Vol 208 (2) ◽  
pp. 131-134 ◽  
Author(s):  
T N Lucas
Keyword(s):  
Transfer Function ◽  
Model Reduction ◽  
Approximation Method ◽  
Padé Approximation ◽  
Order Reduction ◽  
Pade Approximation ◽  
Reduced Order ◽  
Numerical Example ◽  
Integral Square Error ◽  
Reduction Methods

A novel Padé approximation method is used to obtain a reduced-order transfer function, with a predetermined denominator, such that the integral square error between the time responses of the full and reduced models is minimized. The method is seen to be easy to apply compared with existing suboptimal order reduction methods. A numerical example is given to illustrate its application.

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.

Dynamic Observer Method Based on Modified Green’s Functions for Robust and More Stable Inverse Algorithms

2008 ◽  
Author(s):  
Priscila F. B. Sousa ◽  
Ana P. Fernandes ◽  
Vale´rio Luiz Borges ◽  
George S. Dulikravich ◽  
Gilmar Guimara˜es
Keyword(s):  
Heat Transfer ◽  
Transfer Function ◽  
Green's Functions ◽  
Transfer Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Original Method ◽  
Identification Algorithm ◽  
Transfer Function Model ◽  
Function Model

This work presents a modified procedure to use the concept of dynamic observers based on Green’s functions to solve inverse problems. The original method can be divided in two distinct steps: i) obtaining a transfer function model GH and; ii) obtaining heat transfer functions GQ and GN and building an identification algorithm. The transfer function model, GH, is obtained from the equivalent dynamic systems theory using Green’s functions. The modification presented here proposes two different improvements in the original technique: i) A different method of obtaining the transfer function model, GH, using analytical functions instead of numerical procedures, and ii) Definition of a new concept of GH to allow the use of more than one response temperature. Obtaining the heat transfer functions represents an important role in the observer method and is crucial to allow the technique to be directly applied to two or three-dimensional heat conduction problems. The idea of defining the new GH function is to improve the robustness and stability of the algorithm. A new dynamic equivalent system for the thermal model is then defined in order to allow the use of two or more temperature measurements. Heat transfer function, GH can be obtained numerically or analytically using Green’s function method. The great advantage of deriving GH analytically is to simplify the procedure and minimize the estimative errors.

EFFICIENT COMPUTATION OF MULTI-FREQUENCY FAR-FIELD SOLUTIONS OF THE HELMHOLTZ EQUATION USING PADÉ APPROXIMATION

2000 ◽  
Vol 08 (01) ◽  
pp. 223-240 ◽  
Author(s):  
MANISH MALHOTRA ◽  
PETER M. PINSKY
Keyword(s):  
Transfer Function ◽  
Near Field ◽  
Padé Approximation ◽  
Linear Operators ◽  
Far Field ◽  
Efficient Computation ◽  
Pade Approximation ◽  
Wide Range ◽  
Multiple Frequencies ◽  
Element Matrix

For many problems in exterior structural acoustics, the solution is required to be computed over multiple frequencies. For some classes of these problems, however, it may be sufficient to evaluate the multiple frequency solutions over restricted regions of the spatial domain. Examples include optimization and inverse problems based on the minimization of a functional defined over a specified surface or sub-region. For such problems, which include both near-field and far-field computations, we recently proposed an efficient algorithm to compute the partial-field solutions at multiple frequencies simultaneously. In this paper, we consider the particular case of far-field computations and simplify the recently proposed algorithm by exploiting the symmetry of linear operators. The approach involves a reformulation of the Dirichlet-to-Neumann (DtN) map based finite-element matrix problem into a transfer-function form that can efficiently describe the far-field solution. A multi-frequency approximation of the transfer function is developed by constructing matrix-valued Padé approximation of the transfer function via a symmetric, banded Lanczos process. Numerical tests illustrate the accuracy of the approach for a wide range of frequencies and cost reductions of an order of magnitude when compared to commonly used factorization based methods.

Application of Transfer Functions to Canned Tuna Fish Thermal Processing

2010 ◽  
Vol 16 (1) ◽  
pp. 43-51 ◽  
Author(s):  
M.R. Ansorena ◽  
C. del Valle ◽  
V.O. Salvadori
Keyword(s):  
Transfer Function ◽  
Thermal Processing ◽  
Dynamic Models ◽  
Transfer Functions ◽  
Control Strategies ◽  
Sampling Interval ◽  
Computational Effort ◽  
Operating Conditions ◽  
Tuna Fish ◽  
External Conditions

Design and optimization of thermal processing of foods need accurate dynamic models to ensure safe and high quality food products. Transfer functions had been demonstrated to be a useful tool to predict thermal histories, especially under variable operating conditions. This work presents the development and experimental validation of a dynamic model (discrete transfer function) for the thermal processing of tuna fish in steam retorts. Transfer function coefficients were obtained numerically, using commercial software of finite elements (COMSOL Multiphysics) to solve the heat transfer balance. Dependence of transfer function coefficients on the characteristic dimensions of cylindrical containers (diameter and height) and on the sampling interval is reported. A simple equation, with two empirical parameters that depends on the container dimensions, represented the behavior of transfer function coefficients with very high accuracy. Experimental runs with different size containers and different external conditions (constant and variable retort temperature) were carried out to validate the developed methodology. Performance of the thermal process simulation was tested for predicting internal product temperature of the cold point and lethality and very satisfactory results were found. The developed methodology can play an important role in reducing the computational effort while guaranteeing accuracy by simplifying the calculus involved in the solution of heat balances with variable external conditions and emerges as a potential approach to the implementation of new food control strategies leading not only to more efficient processes but also to product quality and safety.

scholarly journals Liquid-Based Battery Temperature Control of Electric Buses

Energies ◽  
2020 ◽  
Vol 13 (19) ◽  
pp. 4990
Author(s):  
Sebastian Angermeier ◽  
Jonas Ketterer ◽  
Christian Karcher
Keyword(s):  
Heat Transfer ◽  
Temperature Control ◽  
Control Strategy ◽  
Transfer Functions ◽  
Computational Effort ◽  
Coolant Temperature ◽  
Cell Temperature ◽  
Heat Transfer Behavior ◽  
Transfer Behavior ◽  
And Control

Previous research identified that battery temperature control is critical to the safety, lifetime, and performance of electric vehicles. In this paper, the liquid-based battery temperature control of electric buses is investigated subject to heat transfer behavior and control strategy. Therefore, a new transient calculation method is proposed to simulate the thermal behavior of a coolant-cooled battery system. The method is based on the system identification technique and combines the advantage of low computational effort and high accuracy. In detail, four transfer functions are extracted by a thermo-hydraulic 3D simulation model comprising 12 prismatic lithium nickel manganese cobalt oxide (NMC) cells, housing, arrestors, and a cooling plate. The transfer functions describe the relationship between heat generation, cell temperature, and coolant temperature. A vehicle model calculates the power consumption of an electric bus and thus provides the input for the transient calculation. Furthermore, a cell temperature control strategy is developed with respect to the constraints of a refrigerant-based battery cooling unit. The data obtained from the simulation demonstrate the high thermal inertia of the system and suggest sufficient control of the battery temperature using a quasi-stationary cooling strategy. Thereby, the study reveals a crucial design input for battery cooling systems in terms of heat transfer behavior and control strategy.

Sign in / Sign up

Export Citation Format

Share Document