Proportional-Integral control for stable 1st order plant: academic PI, trial-and-error

Antonio Sala, UPV

Difficulty: ** ,       Relevance: ,      Duration: 18:39

*Enlace a Spanish version

Summary:

This video develops trial-and-error PI controller tuning for a 1st-order process. Well, actually the underlying simulated process is second order $G(s)=1.8∕(2s+1)∕(0.2s+1)$, in order to illustrate that 1st-order heuristics (dominant pole) do apply fairly well, unless we wish to accelerate our closed-loop system ‘too much’: open-loop settling time is 6 seconds; then, if we aim for closed-loop settling time of around 1.5 seconds, there is nothing that the fast time constant at 0.2 does so we can operate ‘as if’ we were in a plain 1st-order process.

Hence, we start by tuning a proportional controller as we did in video [PintuEN]. As there is steady-state position error (and we cannot increase the gain because oscillations appear), such error will be corrected by adding integral action, thus proposing a PI controller.

Integral action improves both setpoint tracking and input disturbance rejection, until we reach a value of integral gain that keeps improving disturbance rejection performance but starts worsening (overshooting) the setpoint step response. Thus, there is a tradeoff between how fast disturbances are rejected and the overshoot in the step response. Saturation also has a deleterious effect on system response.

Some tweaks to overcome such issues (two-degree-of-freedom and antiwindup) will be discussed in the continuation video [PIintu2EN].

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