NUR 502 PID Controller Work And Tuning Methods

Q1: How a PID controller works

Quadcopter PID is a form of art which helps in understanding the ways varied aspects of the characteristics of a flight that are useful in ensuring that the craft is able to perfectly respond to a certain style of flying. PID is an abbreviation for Proportional, Integral Derivative and is one of the components of the controller software for flight that is used in reading data from sensors as well as making calculations of how swift the moors should spin to maintain the desired speed of rotation of the aircraft¹. The PID controller aims at correcting the error that is normally the different between the desired set point (the desired rotation speed) and the measured value (gyro sensor measurement). This error can be reduced by making the necessary adjustments in every loop, which are responsible for controlling the speed of the motors.

The PID controller has three values namely the P term, I term and the D term. The P term takes into consideration the present error such that the further it looks away from the set point, the hard it would push while the D term is used in predicting future errors. It determined how fast the set-point is being approached and thereby counteracting P should it be getting closer so as minimized overshoot. The I term refers to the accumulated past errors and examines forces that take place over time. Alteration of any of the PID values brings about an effect on the behavior of the quadcopter in in various ways:

An increase in the values of the P term increase the control while lowered P gains results into softer controls. The quadcopter gains very high sensitivity levels and thus over-correct in the cases of very high P. this results in overshoots and thus high frequency oscillations. On the other hand, lowering of P lowers the oscillations and the reduction can be too much to the extent of making the quadcopter have a sloppy feel. D gain operates as a damper and aims at lowering the overshoots and over-corrections caused by P term. Very low D makes the quad to have bad bounce backs at end roll or flip ends thereby creating the worst propwash oscillations in the vertical descents. An excessive increased in the D values results into vibrations in the quadcopter as it amplifies the noise in the system and may in the end lead to quad oscillation and overheating of the motor. The quadcopter feels unresponsive and stiff with very high values of the I term which translates to a decrease in P gain and slower reaction.

Q2: How to experimentally tune the roll angle stabilization controllers using closed loop tuning

The roll angle stabilization controllers can be tuned by tuning one axis at a time: first tune the roll, then pitch and finally the yaw. Adjustments are done each of the values at a time beginning with the P, then D and finally the I values². In order to achieve a fine tune, it might be important to move in a back and forth manner when changes are made on each of the values as a change in one value affects the other values⁴. The Ziegler-Nichols rule assumes that the system has a transfer function in the form

References

Aström, Karl Johan. Feedback Systems: An Introduction for Scientists and Engineers. Chicago: Princeton University Press, 2010.

Rojas, Raul. Neural Networks: A Systematic Introduction. New York: Springer Science & Business Media, 2013.