Fractional-Order System Identification of a Sub-Scaled Multi-Room Building Test-Bed

Graduate #109
Discipline: Technology and Engineering
Subcategory: Civil/Mechanical/Manufacturing Engineering

Kin Li - California State University, Los Angeles

In this study, we design a system identification model of fractional order using global regression analysis. The model linear fractional differential equation (linear FDE) is introduced with the following parameters: the order of the equation q, the linear factor p, and the derivative of the initial condition. The model finds the best values of parameters that minimize the error cost function. We perform tests to a number of problems from literature, including: analytical solution to heat transfer, one-dimensional heat equation, heat exchanger data, and finally the experimental data from a sub-scaled building test bed. The testbed is created in CSULA to imitate heat transfer behavior in commercial buildings. The testbed has two floors and eight rooms, with a sensor reading off the temperature in each room over time. The rooms are allowed to cool after being heated through the use of a 25 W light bulb. In effort to capture the physics of the problem, the search for the order of model is set in the range between 0 and 2, reflecting the heat equation. The derivative of the initial condition is set in the range of -2 to 2, since the literature suggests that a negative value is possible for similar processes. The resulting model represents experimental data accurately with only three parameters. As opposed to a second order model with three parameters, the fractional order model provides better accuracy using the same numbers of parameters.

Not Submitted

Funder Acknowledgement(s): Kin Li is the recipient of a CEaS-CSULA fellowship (NSF HRD-1547723), for which we are grateful. This work is supported by the National Science Foundation under Award No. HRD-1547723.

Faculty Advisor: Dr. Arturo Pacheco-Vega, apacheco@calstatela.edu

Role: I write the MATLAB algorithm and generate the plots for the results. I am also responsible for the analysis and comparison to existing literature. The experimental data is provided by another team of students working on the building test-bed.