I understand that, at least for remote-controlled model planes, the control surfaces can point to a range of angles, say, from $-30^\circ$ degrees to $30^\circ$. My questions are:
Would the same airplane work if the control surfaces can only point to, say, $-30^\circ$, $0^\circ$, $30^\circ$.
If I rapidly switch the surface on ($0^\circ$) and off ($30^\circ$) like in pulse-width modulation (PWM). Is that equivalent to having the control surface pointing at $15^\circ$?
Theoretically it could work that way. A maneuver that needs a certain control surface deflection for a certain amount of time could be done with full 30 degree deflection in a shorter time.
Fine control and trimming would be more difficult. Small adjustments would require a very short time at full deflection. Control laws would have to take into account the step response of the system to determine how quickly the surface can reach the full deflection. By pulsing a deflection command like with PWM, you could determine a modulation that would keep the surface near some nominal deflection.
For an RC plane's systems this may be fine. With larger aircraft you would need to consider the effect of these large inputs into the control system, and structural effects, including whether 30 degree deflection is possible in the current flight conditions.
I once had a very cheap electric ducted fan styrofoam RC plane that I found for sale at Woolworths sometime in the 90s that had "bang bang" flight control surfaces and throttle. In lieu of servos, it had a very light, weak solenoid with the control rod as its core.
I was a novice, but was able to get it to 'fly' a maximum distance of 20ft, bank either left or right as commanded, descend steeply or slightly less steeply by blipping the elevator, but never climb without instantly rolling into a knife edge dive. More of a slightly delayed crash than flight. But someone believed in the design enough to market and sell it.
Depends what you're talking about. Do you mean for the flight controls to actually slam all the way to stop, then center, then slam to stop, etc., violently slamming the aircraft around? (Terrible for fuel economy by the way, and hard on everything else).
Or do you mean to use PWM to select an intermediate position? E.g. 50% duty cycle gives you stable 15 degree rudder?
The trick is to put damping in the operating mechanism, and PWM at a frequency fast enough for the damping to do its job: before the surface physically gets a chance to move, the PWM reverses. The PWM is too fast to wobble the surfaces.
Then also either add some spring resistance so deflection will be predictable for a given duty cycle, or have an analog position sensor educating the PWM as to its effects. Air resistance varies with speed, and without something to equalize it, surfaces at a given duty cycle will deflect different amounts for different speeds. Of course, that could be made a "feature": as DJ319 points out, you actually want less deflection at higher speeds.
As many people have mentioned examples of where it has been used. I would just like to mention that on full scale aircraft the stresses involved in deflecting control surfaces to maximum deflection at cruise speeds (even for a fraction of a second) would probably result in structural failure. In addition to this those kinds of deflections would result in huge g-forces for the crew and any passengers possibly resulting in black outs or red outs.
I would then suggest that something like this could only be used for unmanned craft. Unless the max min values scaled with the aircraft velocity. For example at cruise instead of +-30 degrees of deflection you would have +- 10 to 15 degrees.
This has been done in WWII glide-bomb systems. However, since the idea isn't widely used, it presumably has practical disadvantages.
Yes, it could. The first guided bomb, the German Fritz X developed during WW2, used such a setup. They refined it a bit by oscillating the control surface from neutral to deflection rapidly, so that it wasn't a pure on/off control input.
This was a clever way to get around the limitations of tech of that day, that they weren't able to develop a porportionally adjustable control surface. They could, however, change the oscillation rate with the analog electronics they had available, which in effect gave some proportional control. The faster the surface oscillated, the greater the control input.
The Fritz X was very successful, sinking the Italian battleship Roma, and damaging several allied ships. It fell into disuse when the allies got full control of the air - the Fritz X was visually guided, and required a bomber to remain near the target while the bomb pilot guided it in.
