Identification, estimation, and control of temperature dynamics are ubiquitous and challenging control engineering problems. The main challenges originate from the fact that the temperature dynamics is usually infinite dimensional, nonlinear, and coupled with other physical processes. Furthermore, the dominant system time constants are often long, and due to various time constraints that limit the measurement time, we are only able to collect a relatively small number of input-output data samples. Motivated by these challenges, in this paper we present experimental results of identifying the temperature dynamics using subspace and machine learning techniques. We have developed an experimental setup consisting of an aluminum bar whose temperature is controlled by four heat actuators and sensed by seven thermocouples. We address noise reduction, experiment design, model structure selection, and overfitting problems. Our experimental results show that the temperature dynamics of the experimental setup can be relatively accurately represented by low-order models.

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