What is the role of a PID controller in feedback control?

In a simple term, Proportional answer the question; How big is the error in my system and how big is the response/correction of that system going to be

Integral control action otherwise known as a reset action resets offset until it gets to set point. It's answer the question: what direction and magnitude is the error.

Derivative control action answer the question, at what rate is the error occuring. The disadvantage of derivative action is it doesn't perform way in a noisy environment and it has long lag.

PID tuning is extremely dependent on your environment and is as close as you get can to a debate of "art vs. science" in industrial control systems. For example, the Ziegler-Nichols method is a manual approach that can include open and closed loop variations. It's a classic approach. However, the method can lead to potentially "aggressive" parameters with a higher degree of oscillation and overshoot than what may be truly ideal for the assets in question. Similarly, any environment with complex dynamics may benefit from a different method of tuning altogether. Be aware of your system, your assets, and your physical processes when evaluating PID tuning techniques.

PID tunning provides a lot of advantages in manufacturing. Reducing errors in your process reduces waste which in return increase profitability. Additionally, tunning increase the quality of your product by ensuring the amount of inputs produces the desired output. Tunning also improves safety as it minimizes disturbance; disturbance can alter the behavior of a system which can be unsafe for employees.

PID control, represented as P-Proportional (Present), I-Integral (In the past), and D-Derivative (Distant future), transcends mathematical definitions. P reacts to immediate errors, I accumulates historical errors for adjustment, and D predicts future errors by rate changes. A practical understanding can be gained by balancing on one leg, feeling the body's response to maintain stability against disturbances or overcorrections. This intuitive approach, though mathematically inaccurate, demystifies PID's widespread application, making its complex operations accessible and relatable.

El ajuste PID de un control, especialmente si el proceso está relacionado con la seguridad no se debe hacer a ojo. Lo ideal es modelizar la función de transferencia del proceso para obtener unos parámetros de partida. A partir de aquí, un método de ajuste fino es el de Ziegler-Nichols, de modo que se establezcan pruebas de escalones de las variables a controlar para calcular las variaciones necesarias en las 3 componentes del lazo de control.