P, PI and PID controllers are types of feedback controllers used in various automated systems to regulate a process variable (like temperature, pressure, or speed) to a desired setpoint.

Here's a breakdown of their functionalities and key differences:

Proportional (P) Controller:

• The simplest form of feedback controller.
• Continuously adjusts the output based on the proportional difference (error) between the current process variable and the desired setpoint.
• Larger error results in a larger output adjustment to reduce the error.
• Faster response to changes in the setpoint or disturbances.
• Can lead to steady-state error (the process variable may not perfectly reach the setpoint).

Proportional-Integral (PI) Controller:

• Combines proportional (P) action with integral (I) action.
• P action addresses current error, while I action eliminates the steady-state error observed in P controllers.
• The integral term essentially "remembers" the historical error and continuously adjusts the output to drive the process variable towards the setpoint.
• Slower response compared to P controllers due to the averaging effect of the integral term.
• Better at maintaining setpoint accuracy in processes with varying loads or disturbances.

PID Controller:

• The most comprehensive form, combining proportional (P), integral (I), and derivative (D) actions.
• P and I actions function similarly to a PI controller.
• The derivative (D) term anticipates future changes in the error based on the rate of change of the error signal.
• D action helps minimize overshoot (process variable exceeding the setpoint) and reduces settling time (time taken to reach and stabilize around the setpoint).
• Generally offers the most precise control and minimizes both steady-state error and transient errors (overshoot and undershoot).
• Tuning the P, I, and D gains (adjustable coefficients) of a PID controller requires more expertise compared to PI controllers.

Here's a table summarizing the key differences: