Approximation and Identification of Fractional Systems

2005 ◽  
Author(s):  
Amel Benchellal ◽  
Thierry Poinot ◽  
Jean-Claude Trigeassou
Keyword(s):  
Heat Transfer ◽  
Spectral Band ◽  
State Space Model ◽  
Thermal System ◽  
Fractional Systems ◽  
Space Model ◽  
Proposed Model ◽  
Fractional Integrator ◽  
Fractional System ◽  
Transfer Problems

Heat transfer problems obey to diffusion phenomenon. They can be modelled with the help of fractional systems. The simulation of these particular systems is based on a fractional integrator where the non integer behaviour acts only on a limited spectral band. Starting from frequential considerations, a more general approximation of the fractional system is proposed in this communication. It makes it possible to define a state-space model for simulation of transients, and to carry out an output-error technique in order to estimate the parameters of the model. A real application on a thermal system is presented to illustrate the advantages of the proposed model.

Identification for Control of Low Pressure Die Casting

2010 ◽  
Author(s):  
XinMei Shi ◽  
Daan M. Maijer ◽  
Guy Dumont
Keyword(s):  
Heat Transfer ◽  
State Space ◽  
Die Casting ◽  
State Space Model ◽  
Heat Transfer Model ◽  
Transfer Model ◽  
Process Data ◽  
Space Model ◽  
Model Based ◽  
Virtual Process

Controlling and eliminating defects, such as macro-porosity, in die casting processes is an on-going challenge for manufacturers. Current strategies for eliminating defects focus on the execution of a pre-set casting cycle, die structure design or the combination of both. To respond to process variability and mitigate its negative effects, advanced process control methodologies may be employed to dynamically adjust the operational parameters of the process. In this work, a finite element heat transfer model, validated by comparison with experimental data, has been developed to predict the evolution of temperatures and the volume of liquid encapsulation in an experimental casting process. A virtual process, made up of the heat transfer model and a wrapper script for communication, has been employed to simulate the continuous operation of the real process. A stochastic state-space model, based on data from measurements and the virtual process, has been developed to provide a reliable representation of this virtual process. The parameters of the deterministic portion result from system identification of the virtual process, whereas the parameters of the stochastic portion arise from the analysis and comparison of measurement data with virtual process data. The resulting state-space model, which can be extended to a multi-input multi-output model, will facilitate the design of a model-based controller for this process.

Predicting Thermal System Performance and Estimating Parameters for Systems Burdened With Uncertainties and Noise Using Hierarchical Bayesian Inference

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
A. F. Emery ◽  
D. Bardot
Keyword(s):  
Heat Transfer ◽  
System Performance ◽  
Taylor Series Expansion ◽  
Heat Losses ◽  
Thermal System ◽  
Computing Power ◽  
Bayesian Hierarchical ◽  
Hierarchical Bayesian Inference ◽  
Transfer Problems ◽  
The Bayesian Approach

The precision of estimates of system performance and of parameters that affect the performance is often based upon the standard deviation obtained from the usual equation for the propagation of variances derived from a Taylor series expansion. With ever increasing computing power it is now possible to utilize the Bayesian hierarchical approach to yield improved estimates of the precision. Although quite popular in the statistical community, the Bayesian approach has not been widely used in the heat transfer and fluid mechanics communities because of its complexity and subjectivity. The paper develops the necessary equations and applies them to two typical heat transfer problems, measurement of conductivity with heat losses and heat transfer from a fin. Because of the heat loss the probability distribution of the conductivity is far from Gaussian. Using this conductivity distribution for the fin gives a very long tailed distribution for the heat transfer from the fin.

A New Dynamic State Space Model for the Cylindrical Grinding Process

2005 ◽  
Author(s):  
Cheol W. Lee
Keyword(s):  
Surface Roughness ◽  
State Space ◽  
State Space Model ◽  
Dynamic State ◽  
Grinding Process ◽  
Cylindrical Grinding ◽  
Space Model ◽  
Proposed Model ◽  
Grinding Power ◽  
Actual Part

A new dynamic state space model is proposed for the in-process estimation and prediction of part qualities in the plunge cylindrical grinding process. A through review on various grinding models in literature reveals a hidden dynamic relationship among the grinding conditions, the grinding power, the surface roughness, and the part size due to the machine dynamics and the wheel wear, based on which a nonlinear state space equation is derived. After the model parameters are determined according to the reported values in literature, several simulations are run to verify that the model makes good physical sense. Since some of the output variables, such as the actual part size, may or may not be measured in industry applications, the observability is tested for different sets of outputs in order to see how each set of on-line sensors affects the observability of the model. The proposed model opens a new way of estimating the part qualities such as the surface roughness and the actual part size based on application of the state estimation algorithm to the measured outputs such as the grinding power. In addition, a long term prediction of the part qualities in batch grinding processes would be realized by simulation of the proposed model. Possible applications to monitoring and control of grinding processes are discussed along with several technical challenges lying ahead.

scholarly journals A non integer order, state space model for one dimensional heat transfer process

2016 ◽  
Vol 26 (2) ◽  
pp. 261-275 ◽  
Author(s):  
Krzysztof Oprzedkiewicz ◽  
Edyta Gawin
Keyword(s):  
Heat Transfer ◽  
State Space ◽  
Transfer Process ◽  
State Space Model ◽  
State Equation ◽  
Heat Transfer Process ◽  
Order Model ◽  
One Dimensional ◽  
Integer Order ◽  
Proposed Model

Abstract In the paper a new, state space, non integer order model for one dimensional heat transfer process is presented. The model is based on known semigroup model. The derivative with respect to time is described by the non integer order Caputo operator, the spatial derivative is described by integer order operator. The elementary properties of the state operator are proven. The solution of state equation is calculated with the use of Laplace transform. Results of experiments show, that the proposed model is more accurate than analogical integer order model in the sense of square cost function.

Initial Conditions and Initialization of Fractional Systems

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Massinissa Tari ◽  
Nezha Maamri ◽  
Jean-Claude Trigeassou
Keyword(s):  
Initial Conditions ◽  
Fractional Order Systems ◽  
Fractional Systems ◽  
Infinite Dimensional ◽  
State Variable ◽  
Future Behavior ◽  
Fractional Integrator ◽  
True State ◽  
Fractional System ◽  
Dimensional Variable

In this paper, the initialization of fractional order systems is analyzed. The objective is to prove that the usual pseudostate variable x(t) is unable to predict the future behavior of the system, whereas the infinite dimensional variable z(ω, t) fulfills the requirements of a true state variable. Two fractional systems, a fractional integrator and a one-derivative fractional system, are analyzed with the help of elementary tests and numerical simulations. It is proved that the dynamic behaviors of these two fractional systems differ completely from that of their integer order counterparts. More specifically, initialization of these systems requires knowledge of z(ω,t0) initial condition.

Flatness Control: Application to a Fractional Thermal System

2005 ◽  
Author(s):  
Pierre Melchior ◽  
Mikae¨l Cugnet ◽  
Jocelyn Sabatier ◽  
Alain Oustaloup
Keyword(s):  
Control Strategy ◽  
Path Tracking ◽  
Dynamic Inversion ◽  
Thermal System ◽  
Differential Systems ◽  
Fractional Systems ◽  
Crone Control ◽  
Flatness Control ◽  
Fractional System ◽  
Control Application

This paper concerns the application of flatness principle to fractional systems. As soon as the path has been obtained by flatness, a new robust path tracking based on CRONE control is presented. The flatness concept in path planning is used when the trajectory is fixed (in space and in time), to determine the controls to apply without having to integrate any differential equations. A lot of developments have been made but, in the case of non integer differential systems (or fractional systems), few developments are still to be made. So, the aim of this paper is to apply flatness principle to a fractional system and to define a robust path tracking by CRONE control strategy. Firstly, we remind flatness principle definitions used in control’s theory. We study the fractional systems dynamic inversion. A robust path tracking based on CRONE control is presented. Finally, simulations with two different controllers (PID and CRONE) illustrate the path tracking robustness.

Identification of Metal Temperature Distribution in Steam Turbine During Start-Up Operation Using Particle Filter and Model Order Reduction

2019 ◽  
Author(s):  
Hiroshi Ito
Keyword(s):  
Heat Transfer ◽  
Model Order Reduction ◽  
State Space Model ◽  
Order Reduction ◽  
Metal Temperature ◽  
Heat Transfer Analysis ◽  
Bulk Temperature ◽  
Model Order ◽  
Space Model ◽  
Start Up

Abstract In steam turbines (STs), evaluation technology of thermal deformations during transient operations is increasingly important, because of a demand for improvement of operability such as shortening startup time. However, it is still difficult to predict temperatures of metal parts with sufficient accuracy due to complexity of heat transfer phenomena. The present study puts its focus on developing a method to identify metal temperatures of STs during start-up operations using particle filter (PF), a kind of sequential Bayesian filter utilizing ensemble approximation, and model order reduction (MOR) technique. In this method, a self-organizing state-space model is used to calculate time evaluations of metal temperatures, and heat transfer coefficient (HTC) parameters and steam bulk temperature parameters. And an optimal estimate of these is obtained through iterations of a short-time prediction and a correction of variables using measured temperatures. In this state-space model, state variables including HTC and bulk temperature parameters are treated as random variables, and the time evolution of each variable is modeled as follows; (1) Metal temperature is modeled using a reduced order model (ROM) in order to reduce computational time of PF. The ROM is constructed from a finite element model for unsteady heat transfer analysis using MOR technique. (2) HTC is modeled as a random walk model where its changes during one time step is randomly determined using Gaussian noise. Here, the magnitude of this noise is adjusted automatically. (3) Bulk temperature is modeled using prediction formulas with Gaussian noise added. As a validation problem, a cold start-up operation of a ST unit of a gas turbine combined cycle (GTCC) is considered. The proposed method is applied to the problem, and boundary conditions (BCs) are identified using measured temperatures at 68 measurement points. Then, the heat transfer analysis based on finite element analysis (FEA) is performed using the identified BCs. As a result of this FEA, it is confirmed that the calculated metal temperature tends to agree better with measurements compared with that of initial FEA, and that the errors of the calculated temperature at measurement points reduce by 41% on average compared with initial FEA. From this result, it is concluded that this proposed method is effective for metal temperature identification during start-up operations.

Sign in / Sign up

Export Citation Format

Share Document