, Duration: 18:37
Materials: [ Cód.: PIDcontrolAPP1.0.zip ]
This video discusses the tuning of a PD controller for a ‘double integrator’ type
process (mass motion with small, negligible friction). The motivation for studying
this process has been addressed in the video [
Here, the PID control problem of this process is starting to be discussed. This
will be done through purely ‘intuitive’ considerations, common sense. The theory
will be discussed in the video [
The basic intuitive consideration is that a proportional control is ‘analogous’ to a spring on the moving mass. Therefore, as can be seen in simulation, without friction, the response will show sustained oscillations: the P control does not succeed in stabilizing.
To stabilize, ‘damping’, friction... is needed and that is the analogue of the derivative action: a ‘braking’ proportional to the speed. Braking can be proportional to speed or proportional to the ‘error speed’, which gives rise to two possible implementations of the derivative action, parameterized by a certain coefficient ‘c’, which are tested in simulation. In the end, the important thing is that the derivative action does stabilize. Note that the ‘ideal’ derivative action is not feasible: the high-frequency noise is infinitely amplified and, therefore, a noise filter is necessary in all practical applications, as shown in simulations here.
A summary of the ideas concludes the video. Final value justification in intuitive terms, disturbance rejection and integral action are left for a sequel video.
*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.