Intuition on linear dynamics: open loop control sequence of steps, 2nd order plant doesn’t work well

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 10:12

*Enlace a Spanish version

Summary:

This video uses the same methodology as the video [linregla3EN] to calculate a two-step input signal that will bring a process up to a certain desired value in a desired time, and then hold it there, in equilibrium. You should watch the referred video before this one.

The only idea needed in both videos is linearity/superposition/time invariance, the model (e.g. transfer function $G(s)$ or similar) is not used at any time to calculate the input profile.

The previous video we were commenting on used a first-order process, in which the technique worked perfectly. Here, it is applied to a “secret” process that is actually of order 2, so that “inertia” means that when the input that maintains the desired equilibrium point is applied in the second step, there is an overshoot. The overshoot decreases if the first step (which accelerated faster) is made shorter, but then the desired place is not reached exactly. Refining this, either with an additional step of “braking”, or in a closed loop (PID control), is obviously not part of the objectives of this video, which only tries to reinforce the concept of “linearity” and “time invariance” of a dynamic system.

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