Proportional control of stable 1st order system: trial-and error tuning of PID controllers

Antonio Sala, UPV

Difficulty: ** ,       Relevance: ,      Duration: 22:56

*Enlace a Spanish version

Summary:

This video discusses proportional control in a first-order system and its relationship with on-off (bi-level) control. The specific process will be $3∕(2s+1)$.

First, we recall what the behavior of a stable 1st order system is (i.e., exponential transient between two equilibrium points, instantaneous effect between manipulated variable and output velocity)... level, pressure, concentration are, as a first approximation, examples of this class of dynamics.

Next, we recall the block diagram of a typical closed loop; however, in trial-and-error tuning, closed-loop equations are not actually necessary. In the loop to be simulated, measurement noise, saturation, and disturbances are added to the input (process noise), and they are represented in the said block diagram.

Next, the video presents the structure and interface of a controller simulation application that will be used in this video and in subsequent ones.

We begin by testing proportional regulators with increasing gain. It is observed that there is a residual error (position error) in steady state that decreases as the gain increases; The transients are also increasingly faster as controller gain grows larger.

The simulation presents the speed limitation caused by saturation and measurement noise amplification. Then, we discuss that when the gain is very high, it converges to a kind of ’ON-OFF’ control. The relationship between proportional control and ON-OFF (bi-level in a generic case) is discussed.

The final part of the video discusses correcting the error at setpoint changes by correctly calculating the ‘input operating point’ (called ‘manipulated variable offset’ in some documentation). This is also called proportional control with ‘2 degrees of freedom’... But it does NOT help when cancelling the effect of error due to non-measurable external disturbances, because if the reference is not increased, no calculation or correction can be made. To cancel the error in the event of non-measurable disturbances, it is necessary to use integral action, but that is not the objective of this video.

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