Starting PID internals documentation

docs/development/PID Internals.md

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+### IO variables
+
+gyroData/8192*2000 = deg/s
+gyroData/4 ~ deg/s
+
+rcCommand - -500-500 nominal, but is scaled with rcRate/100, max +-1250
+
+inclination - in 0.1 degree, default 50 degrees (500 units)
+
+axisPID - output to mixer, will be added to throttle(1000-2000), output range is <minthrottle, maxthrottle> (default <1150 - 1850>)
+
+### PID controller 0, "MultiWii" (default)
+
+
+
+## Leveling term
+
+error = constrain(2*rcCommand[axis], limit +- max_angle_inclination) - inclination[axis]
+P = constrain(P8[PIDLEVEL]/100 * error, limit +- D8[PIDLEVEL] * 5)
+I = intergrate(error, limit +-10000) * I8[PIDLEVEL] / 4096
+
+## Gyro term
+
+P = rcCommand[axis];
+error = rcCommand[axis] * 10 * 8 / pidProfile->P8[axis] - gyroData[axis] / 4; (conversion so that error is in deg/s ?)
+I = integrate(error, limit +-16000) / 10 / 8  * I8[axis] / 100 (conversion back to mixer units ?)
+reset I term if
+      - axis rotation rate > +-64deg/s
+      - axis is YAW and rcCommand>+-100
+
+## Mode dependent mix(yaw is always from gyro)
+
+HORIZON - proportionally according to max deflection
+Gyro - gyro term
+Angle - leveling term
+
+## Gyro stabilization
+P = -gyroData[axis] / 4 * dynP8 / 10 / 8
+D = -mean(diff(gyroData[axis] / 4), 3) * 3 * dynP8 / 32