Proportional control for 1st-order stable plant: setpoint tracking, theory

Antonio Sala, UPV

Difficulty: ** ,       Relevance: ,      Duration: 18:46

*Enlace a Spanish version

Summary:

This video discusses the theory behind the closed-loop behaviour of 1st-order systems under proportional control (P). The study is divided into two videos: this one (problem statement and setpoint response), and a second one [Pteo2EN], dealing with input disturbance rejection and measurement noise high-frequency amplification.

In this first video, we present the block diagram and the closed-loop transfer functions of controlled variable, manipulated variable, and error as outputs with respect to reference, input disturbance, and measurement noise input variables.

Then, the setpoint-to-output response $y(s)=GK∕(1+GK)\cdot r(s)$ is computed for a particular example with $G(s)=2∕(2s+1)$, and its stability, settling time and final value (position error) are analysed.

The example is the same one we used in ‘trial and error’ controller tuning in video [PintuEN], so we can confront the intuition-based rules of thumb in said video with the theoretical backup provided here.

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