Laboratory Waterbath with Proportional Control
A laboratory waterbath consists of a heater, a nearby sensor, the thermostated object further downstream, a cooling coil covering the bottom of the container, and a stirrer that circulates and mixes. It is modeled here by a set of differential equations describing the heat flow in each of 11 radial sectors of the waterbath when the object temperature is initially dropped to 19 °C from the temperature setting of 20 °C.
The best configuration is for the sensor to be very near the heater, and for the object to be farther downstream. To simulate an off-on control, reduce the spread between the variables and , which represent the upper and lower limits of the proportioning range.