PID control design/tuning

[stenbergd]

• Create linearized model of quadcopter with transfer functions
• Enter control signals for thrust, roll, pitch, yaw as output from PID
• Try to tune the parameters, check step responses and Bode diagrams
• Also check step response for disturbance rejection transfer function
• Try to apply pole placement so we get a scientific approach to PID tuning

[stenbergd]

Tuning according to litterature found here: http://lup.lub.lu.se/luur/download?func=downloadFile&recordOId=4610294&fileOId=4610295

Restructuring PID algorithm on parallell form

[stenbergd]

Hopefully a decent starting controller for now using PD for roll/pitch and P for yaw rate.

PD essential to stabilize absolute angle, else it would be unstable/oscillating. Since it is a double-integrator system there are two poles needing both P and D parts to even be theoretically possible.

P used for yaw rate since its system is only a single integral.

Looking forward, integral action can be involved but let's keep it simple for now.

Here's an example of the roll/pitch tuning step response from Scilab: http://postimg.org/image/gwotvfknl/

[stenbergd]

We will eventually need a yaw ANGLE controller when UAV is run in autopilot/autonomous mode. When implementing this, care must be taken at the +180 / -180 degree wrap-around so that this doesn't cause large incorrect control errors.

[stenbergd]

Implement dynamic sample time calculated based on last control update time. Take care to init the last update time each time PID flight mode starts.

[stenbergd]

Fix: Increase N value for controllers significantly to allow correct D-part control (up to maybe 1000 from 15)

TODO: Document control of second order system with P, PD, PID using pole placement for optimal response (critical damping)

[stenbergd]

Control still suffers from some oscillations and gets out of control when larger control actions are applied.

Fixing instability:

• Increase control sampling rate (up from 100 to maybe 200 or 400 Hz). This includes the sampling rate of the Kalman filter, so sensors need to be sampled more often (increase ODR) and prediciton called at 200-400 Hz.
• Perhaps tweak the Kalman filter to provide even smoother output
• Use the Kalman angular rate states instead of calculating derivative?
• Output ctrlSignals (protomessage should include the flight state variable), refSignals and sensorValues over CLI for debug and visualisation purposes (create separate issue?)
• Decrease N to maybe 200

Other

• Use of integral action could be beneficial in wind or if unbalanced aircraft (may be an issue/task on its own)
• Thrust calculation dead-zone bottom 5% of throttle to provide safer startup and easier shut down (should set all motor action to minimum, including moment/angle contorl action)
• Reset ctrlSignals and refSignals when leaving pid_control state

Yaw Control Update (create separate issue?)

Yaw control should perhaps no longer control the yaw rate, but the yaw angle. RC controller input should integrate the yaw stick action to generate reference yaw angle. This will need some logic, e.g. the reference starting in the start up direction, keeping track of +/- 180 deg transition as well as making sure the quadcopter yaw-rotates the correct direction (e.g. along stick movement direction, otherwise a large step could rotate to the nearest yaw location rather than taking the desired direction). Also, the calculation of control error aroung the +/-180 needs to be taken care of.

Yaw will likely need integral control action

See Brescianis quadrotor Helicopter work for reference: http://www.control.lth.se/documents/2008/5823.pdf

Documentation

Document the PID control algorithm and tuning principles. Include discretization, discussion on second-order system damping, pole-placement, some diagrams/plots. Closed-loop response: P / (s² + D*s + P)