Hi again Eric,
Let me try to clarify the questions being brought up by some of the other members, and also talk about what you have said so far and where we are at this point.
First, the questions being brought up are related to what exactly you are doing with this "load". See, it is rare (although not without precedent) that someone connects a resistor up to a triac just for the sake of connecting a resistor to a triac, unless maybe for the educational value. In real life that load usually does something ie performs some function for the user such as heat a room (heater) make toast (filament heater) produce light (filament bulb or LED or other). The reason they are pointing these things out is because the type of control you would need may vary based on what your load actually does. Using an average voltage feedback signal will make sure the output maintains a relatively constant average voltage, but that average voltage may not be what your load really needs. It may need to regular RMS voltage or even the actual Power, or even the heat output or the light output. The output is therefore best regulated when the correct quantity is measured at the output.
Why any question at all about the average voltage you might ask...
When you say you want to regulate the "average voltage" that's just fine with me, and there are relatively simple ways to do this if you dont need super fast response. But then later you said that you want to keep the "power" constant. Well, keeping the power constant and keeping the average voltage constant are not the same thing for some loads. That's why it is good to know what the load actually is and what it has to do before we decide what quantity to regulate.
Average voltage, RMS voltage, or average power are the usual choices. You said two of these so i am guessing you want to keep the power in the load constant, but i'll wait for your further clarification on this as to what the load actually does in real life (if anything).
Now this isnt to say that you cant use average voltage and get some approximate results that work good enough either. It may just so happen that once you adjust the circuit for the required output while measuring average voltage you get reasonable results with line variations that are quite acceptable even though we're not measuring actual output power. Whether or not you want to try it this way first is up to you of course. Measuring the average voltage is the simplest of all measurements so it makes sense to think about this. I will outline this method first so you get some idea what you have to do.
First, the output voltage needs to be averaged. The average of a DC signal that varies about some nominal value is easy to obtain. Just connect a resistor to a capacitor and measure the voltage across the capacitor. The time constant needs to be large enough to smooth over any of the slowest frequency changes in the variations.
The average of an AC signal is a little different, but almost the same. The difference is the output must be full wave rectified first, then using the same idea with the resistor and capacitor you can then measure the average voltage. The RC goes at the output of the rectifier and the voltage is again measured across the cap. Sometimes you can even get away with half wave rectification.
Once you have that average measurement, it is then used as feedback to vary the firing phase angle of the triac. This requires a circuit that is basically open loop and the feedback signal closes the loop making it a closed loop control system.
So next it would be a good idea if you clarify what your load actually is and what it has to do in real life. You might also mention how fast you really need it to respond. That means how fast it has to correct for a change in input line voltage. Can it be as long as a full second, or does it really have to respond very very fast? The simplest circuits require a slow response time, but that is usually quite good enough for many AC type applications so dont think that it must be fast unless there is some REALLY good reason for this because the *need for speed* will cost you a much more complex circuit.
Actually now that i think about it i think we talked about this kind of circuit a while back right here on this forum. Someone would have to do a search i guess to find it as i dont remember when it was now...not too long ago though.