Accuracy analysis of the fractional order, positive, state space model of heat transfer process

2021 ◽  
Author(s):  
Krzysztof Oprzedkiewicz ◽  
Klaudia Dziedzic ◽  
Wojciech Mitkowski
Keyword(s):  
Heat Transfer ◽  
State Space ◽  
Fractional Order ◽  
Transfer Process ◽  
State Space Model ◽  
Heat Transfer Process ◽  
Accuracy Analysis ◽  
Space Model ◽  
Positive State

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.

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.

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