Modeling and Simulation with Compose and Activate by Stephen L. Campbell & Ramine Nikoukhah

Author:Stephen L. Campbell & Ramine Nikoukhah
Language: eng
Format: epub
ISBN: 9783030048853
Publisher: Springer International Publishing

(9.2a)

(9.2b)

9.2 Thermostat

The model of a heating control unit using an observer-based thermostat is considered in this section. This example is inspired by Example 3.1 in [48]. The Luenberger observer introduced on page 167 is used to estimate the temperature based on noisy observations. The model concerns the heating unit of a two room house:

The temperature sensor is placed inside the wall separating the rooms. The measured temperature is denoted . The temperature inside the wall is . The outside temperature is also measured. The temperatures in the two rooms are denoted and . Each room is assumed to have well mixed air. The interior wall is treated as a homogeneous material.

Each room is equipped with a heater and each heater can be on or off independently of the other. The states of the heaters are denoted by and , which can take values 1 (heater is on) and 0 (heater is off). The on/off states are controlled by Hysteresis blocks with identical on/off temperature thresholds for the two rooms. The blocks’ inputs are the estimated room temperatures provided by the Luenberger estimator. The model is given in Figure 9.8. The green part of the model is the physical plant and the yellow part is part of the observer.

A mathematical model of the evolution of the temperatures in the house can be expressed as follows (basic laws of Thermodynamics)

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