Project: PI heater controller

This week showed P, PI, D, tuning and cascades in small pieces. Now you build a controller that really holds a room: the lab with a wall heater, a dial for the setpoint and two displays for the trend.

The plant#

The wall heater gives off 1000 J per tick and only runs above 6.3 kPa. It knows only On – no Setting, no half power.

PI controller with pulse width#

The PI controller computes an output u between 0 and 1. Because the heater can only be on or off, you turn that into pulse width modulation (PWM): in a window of 10 ticks the heater is on for as many ticks as u says. u = 0.3 means 3 ticks on, 7 off.

add tick tick 1
mod tick tick WINDOW      # 0 to 9, then start over
mul tmp u WINDOW
slt on tick tmp           # on while tick < u * 10

A room is sluggish enough not to notice switching on and off within a 5-second window. It only feels the average power.

The controller itself is the one from day 156, only in kelvin and with u from 0 to 1:

sub e target t
mul tmp e KI
add i i tmp
clamp i i 0 1             # anti-windup: never more than full power
mul u e KP
add u u i
clamp u u 0 1

Setpoint and failures#

• The dial delivers °C. add target target CELSIUSOFFSET turns it into kelvin. If the dial is missing, target is NaN – then TARGET_STD (20 °C) applies.
• If the sensor is missing, t is NaN. Then: heater off, “Leistung” shows −1, “Abweichung” 0, and i is not touched. Otherwise the controller is poisoned after the repair.

Milestones#

1. Cold room: heater on, “Leistung” 100, “Abweichung” in K
2. Close to the setpoint the I term pushes on and holds the output once the setpoint is reached
3. PWM: at u = 0.5 the heater is on in the first half of the window and off in the second
4. Anti-windup: after a long cold spell the heater switches off as soon as the room is above the setpoint
5. Setpoint from the dial, 20 °C without the dial
6. Sensor gone: heater off, “Leistung” −1, i stays put