double-integrator PD design via pole placement

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 23:38

Summary:

This video designs a PD controller for the double-integrator plant $G(s)=2∕s^2$ to meet certain static (zero position error with reference step change, limited steady-state drift when subject to input disturbances) and dynamic (settling time less than or equal to 2 seconds, damping coefficient $\chi$ greater than or equal to 0.7) specifications.

The design is based on the final value considerations from the video [dintteoerrEN] and on equating the characteristic equation $0=s^2+2K_{d}s+2K_p$ to that from a certain polynomial $0=s^2+2\chi {\omega }_{n}s+{\omega }_n^2$ that meets the specifications.

The final part of the video simulates the calculated controller, with the correct result being verified when there is no saturation or measurement noise, which are the prior assumptions under which the theoretical calculations operated.

When saturation and measurement noise are switched on, the results are very different: derivative action noise needs to be filtered quite intensely and the transient needs to be slowed down so that the differences between ’theoretical calculations’ and ’simulations closer to practice’ are smaller (smaller gains both amplify noise less and saturate less, obviously). This idea is simply stated as a guideline; a redesign following it is not carried out, for brevity.

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.