How can I know when the TRIAC turns off?
When the triac is on, the voltage across the triac is clamped to a voltage near zero. (The data sheet for your triac might say something like worst-case V_A1_A2_on is +- 1.5 V).
Many circuits detect when the voltage (positive or negative) across the triac is above roughly +10 V or below roughly -10 V, to indicate that the triac is definitely off. See Figure 4 of AN307.
Have you considered possibly sensing the voltage across the triac, like all zero-crossing solid-state relays do, rather than sensing the line voltage, which no solid-state relay does?
When should I fire the TRIAC's gate to obtain an arbitrary motor speed (let's say half the normal speed)?
For a few loads, the speed is roughly proportional to the triac on-time.
For these loads, turn on the triac 1/2 the time (turn the triac off 1/2 the time) to get a speed close to half the maximum speed.
More often the load increases as the square of the speed
(for example, when pushing a vehicle through the air).
For these loads, turn on the triac 1/4 the time (turn the triac off 3/4 the time) to get a speed close to half the maximum speed.
Nearly always there is some minimum on-time (maximum off-time) just to get things moving; anything less than that and some electric power goes in, but nothing moves.
As Olin Lathrop mentions, it is often adequate to experimentally measure the output speed vs. triac on-time a few times (perhaps for 1/5, 2/5, 3/5, 4/5, of the full on-time or full off-time), figure out which setting gives close to half-speed, and hope it stays approximately the same when you run open-loop.
If precisely maintaining some particular speed is important, you may want to run closed-loop -- in other words, add some sort of tachometer to measure the actual speed at all times, and close the loop by adding something to automatically increase the on-time (decrease the off-time) when the measured speed is too low, etc.
When should I fire the TRIAC's gate when controlling an inductive load?
Please consider doing things in the way recommended by the data sheets and app notes provided by the manufacturer, in this case ST application note AN307: "Use of triacs on inductive loads".
Perhaps the simplest approach is
- watch the voltage across the triac (between pins A1 and A2). When that voltage goes above +10 V or below -10 V, the triac is definitely off.
- After we sense the triac is definitely off, delay some time from 0 (full-speed) to nearly 10 ms (nearly motionless), then pull the gate LOW.
- Keep pulling the gate low for some time, until the triac appears to turn on (until the voltage across the triac is small). Then pull the gate HIGH (set the gate voltage the same as the triac A1 pin voltage).
- Repeat.
If the existing heater is a fire hazard, you must select a different heater! It is far too easy for some part of your "regulator" circuit to fail in such a way that full power is applied to the heater.
One simple solution would be to wire two heaters in series — each heater would operate at 1/4 power, producing lower temperatures, and the total power would be half that of the original heater alone.
Best Answer
See formula from Jony130 here: https://www.physicsforums.com/threads/how-to-calculate-rms-voltage-from-triac-phase-angle.572668/
On the other hand, if your load is not a lamp, but a slow resistive thing with huge current draw like heaters, you may better go for a standard zero crossing SSR.
The solution is just like PWM (or phase control), except that it is slower. Assume you have a time period of 0.8 seconds (800ms), and you only turn on/off the load at zero crossing. Zero crossing triac triggering takes care of turning on, and the triac itself will turn off after a zero cross. Now, if you turn on the SSR for one half-cycle (8 ms) and keep it off for 99 following half cycles, you have an 1% power. If you keep it on for 22 half cycles, and off for 78, you have 22% power, and so on.
This however assumes that the load reacts slowly, i.e. this trick will cause serious flickering if you're using a light bulb, or humming in case of some load. On the other hand this trick is quite friendly for slow loads, makes no transients and no unwanted harmoics on the power lines.