Great question. I'll describe each type. Hopefully, you and others can understand what I'm trying to say, though it can be difficult without a diagram. Anyway, here goes:
First some definitions:
Process temperature: The actual temperature of the thing or area you are trying to control. For example, the cage floor when heated with heat tape.
Setpoint temperature: The process temperature you desire, or the setting on the dial/display of the controller that is what you want the process temp to be.
Load: The heating device(s).
ON/OFF control: Temp control where the output to the load goes full OFF (no voltage, no current) when the process temp meets the setpoint temp, and goes full ON (full voltage, full current) when the process temp falls below the setpoint temp. In practice, there is a built-in hysteresis (see below.)
Hysteresis: The number of degrees between the process temp when the ON/OFF controller goes OFF and the process temp when the controller goes back ON. In practice, this can be about 4 deg F for the cheapo thermostats.
Proportional control: Temperature control whereby the output to the load is pulsed so as to deliver a range of average power to the load over a range of temps near the setpoint. This eliminates hysteresis and allows for the process temperature to stay very close to the setpoint temperature at all times, even when the room temp changes or the size of the load (aka number of heaters) changes.
Manual control: Also known as using a dimmer. With this control, there is no probe, hence no feedback. The dimmer doesn't know what the temp of the load is. You are setting a percent of full output to the load.
Discussion:
In a nutshell, proportional control keeps a much tighter tolerance on the difference between the process temp and the setpoint temp. ON/OFF controllers can only provide a tolerance equal or greater than the built-in hysteresis, which is usually about 4 deg F with some of the cheaper thermostats out there. So with an ON/OFF controller, the process temp actually varies by 4 degrees each cycle of an ON and an OFF of the controller.
Proportional controllers also use solid-state relays to switch the power. These are semiconductors and not mechanical relays. That is why you don't hear the "click" that you hear with your ON/OFF controller. Solid-state relays cost more than mechanical relays. Most ON/OFF thermostats use mechanical relays to cut costs and for space-savings because higher-power solid state relays require a large heat sink. Mechanical relays can wear out far faster than solid-state. But, solid-state relays can fail full ON if you short circuit the heater through them.
Rancos have an adjustable hysteresis down to 2 deg F I think and a mechanical relay that is rated for 13 or 15 Amps. They are good for space heaters along with the usual general purpose uses (Flexwatt, heat lamps, etc).
In general, proportional control is the best for tight control of heat tape, pads, heat rope, CHEs, and heat panels. ON/OFF control is best for lamps and for high-load devices that have fans or motors (like space heaters and air conditioners.) Helix controllers are proportional, and the pulses are fast enough so-to-speak so that lamps will "dim" instead of flashing ON and OFF annoyingly. So you can use a Helix with a heat lamp. Some of the older proportional controllers will flash the light ON and OFF slower than 50Hz, so you see it clearly. For that reason, they should be used only on non-light-emitting heaters.
And lastly, dimmers are fine when the air temp in the room doesn't change much from morning to afternoon to evening. Otherwise, dimmers can suck. Why? Because it is easier to overheat with a dimmer. Say you set the dimmer when your room is 72 deg so that the heat pad stays around 85 deg. Then you go to work, and during the day your room temp goes up to 80 deg. That same dimmer setting will now result in the heater being much warmer than you anticipated.
For any heating application, insulating the room or even the cage helps alot. You can often get away with using the cheap thermostats for any application just fine if the room/cage is insulated well.
I hope this helps some.
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Mark G