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Registered Member #2431
Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639
Ok will do the above, but also, im wondering how to quantify or qualify the measures on the machine. Ihings like mass, inertia, response time, and other vehicle features. These things need to be known regardless of control method. So im thinking of a micro-processor gyro-acc IMU device to record motion.
In any case, would a dihedral on each fan be meaningful? Or just a bogus "pendulum" fallacy?
Probably the most important parameters of a feedback loop are gain and phase. Think of a room heating control. You have a thermometer and a heater. The error signal is the difference between intended temperature and actual temperature. In case of a T too low, power to the heater is increased and the other way around.
If you feed an error signal corresponding to e.g. a 1 degree too low room T to your system and the room temperature will eventually rise by 2 degrees then your loop gain is 2. Note that in this experiment we don't use a thermometer to generate the error signal but set it manually. (Open loop)
Now consider a sinusoidal error signal with a very long period, e.g. days. The room temperature will also vary sinusoidally with a bit of lag behind the error signal. The phase difference due to the lag is phase of the control loop. For very slow error signal frequencies, the phase will be small and the gain, i.e. the ratio of room T amplitude and error signal amplitude will be 2, as above.
For higher frequencies, the gain will drop and the phase will increase. There will probably be a frequency, where the phase is 180 degrees, which turns the negative feedback loop into a positive feedback loop. This becomes a problem, when the gain at this frequency is above 1. Then the system will begin to oscillate.
This can be avoided by decreasing the gain of the loop, e.g. by reducing the heater power change for a given error signal. The drawback is, that the control accuracy drops, i.e. the room will see a bigger rise in temperature, when e.g. the sun shines through the window. The lower the loop gain is, the less the loop will be able to compensate for disturbances. A PID controller helps here.
The I part of a PID controller increases gain at low frequencies. Since the phase is low there, it doesn't hurt. The D part increases gain at higher frequencies, which can be problematic if the phase approaches 180 degrees. The D component will shift the phase back by up to 90 degrees, though, so positive feedback will happen not beginning with 180 degrees phase but somewhat later.
To establish the parameters of a PID controller you need to make an open loop experiment like I've described above, driving the system with sinusoidal error signals at various frequencies. For copters, that is difficult, since you need to keep the thing flying while driving the error signals.
Registered Member #3414
Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245
When I was considering a similar dynamic problem, I concluded that I'd probably want, say, 256 'output states'. If driving an electric motor using PWM 'chopping', this equates to pulse width.
Same with the input sensors, 256 corresponds to ~1./5 degrees, for example.
The algorythm between input and output does everything else. If you can adjust a few variables 'on the fly', you can trim the sensitivity.
These are only my own thoughts, when thinking through a similar problem. Maybe 256 is too many, it is only 8 bits of data, though.
Registered Member #2431
Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639
Uspring, that was excellent, now i see without the math, the working factors.
Eventually, and i mean way down the line, i want to be able to fly a YF-23 Black Widow, and a Grumman X-29, and perhaps a near tail-less or canard-less design. but ill have to hire a mathematician and a physics PhD, im sure.
NASA, Northrop and Lockeed, must use fluid simulations, but even those must be based on previous wind tunnel measurements. then re-verified in a near-final design in another wind tunnel, else test pilots would be getting killed all the time when their machines ball-up at the end of the run-way on fire...
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Control Loops, Nodes, Poles, Phase and Gain.
