Merge pull request #485 from ledvinap/doc-pid-internals

Doc pid internals

docs/development/PID Internals.md

@@ -0,0 +1,46 @@
+### 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)
+
+`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 +- 5 * D8[PIDLEVEL])
+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), over 3 samples) * 3 * dynD8 / 32
+```