Energy Balance Parameter Estimation

The objective of this activity is to fit the physics-based predictions to the data as well as fit a first-order plus dead-time (FOPDT) model to the data. In both cases, select parameters are adjusted to minimize an objective function such as a sum of squared errors between the model predicted values and the measured values. Test the temperature response of the Arduino device by introducing a step in the heater.


Fit FOPDT Model with Optimization

Determine the parameters of an FOPDT model that best match the dynamic temperature data including KpKp, τpτp, and θpθp. A second order (SOPDT) can also be fit to investigate whether a higher order model is more accurate.


Fit Physics-Based Model with Optimization

The full energy balance includes convection and radiation terms.

mcpdTdt=UA(TT)+ϵσA(T4T4)+αQmcpdTdt=UA(TT)+ϵσA(T4T4)+αQ

where mm is the mass, cpcp is the heat capacity, TT is the temperature, UU is the heat transfer coefficient, AA is the area, TT is the ambient temperature, ε=0.9ε=0.9 is the emissivity, σ=σ= 5.67x10-8 Wm2K4Wm2K4 is the Stefan-Boltzmann constant, and QQ is the percentage heater output. The parameter αα is a factor that relates heater output (0-100%) to power dissipated by the transistor in Watts.

Adjust the uncertain parameters such as UU and αα from the modeling exercise to best match the dynamic data from the impulse response.


Compare FOPDT and Linearized Model


Moving Horizon Estimation


Return to Temperature Control Lab Overview

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