PID control (2025 exam): velocity transfer functions and steady-state error (a)

Antonio Sala, UPV

Difficulty: ** ,       Relevance: ,      Duration: 14:54

Summary:

In this video, we begin solving the PID control exercise from the December 2025 exam for our SAU-GITI course at ETSII-UPV. The full solution will comprise four videos, plus two additional ones regarding MATLAB coding and simulations (which were not required in the written examination).

In this first video, we discuss the block diagram of a velocity control loop subject to disturbances, and carry out its resolution in order to obtain the two transfer functions from setpoint and disturbance inputs to loop error output.

Then, we apply the final value theorem with generic proportional and proportional-integral regulators to derive the formula for the steady-state position error when subject to constant setpoint and disturbance signals. If the controller gains are wisely chosen so the closed loop is stable (we’ll carry out such a design problem in the next video), then proportional control has a nonzero steady-state error (process was type zero, non-integrating), but proportional-integral control has zero steady-state error when subject to step inputs.

Next video in the series is [p2252bEN], discussing the PI controller tuning to achieve given specifications in the velocity control loop we are analyzing.

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