PI Controller Integral Role Explained
A Proportional-Integral (PI) controller combines proportional (P) and integral (I) control actions. Its transfer function is given by $G_c(s) = K_c \left(1 + \frac{1}{\tau_I s}\right)$. The integral component is represented by the term $\frac{K_c}{\tau_I s}$.
The primary function of the integral component is to address the steady-state error, often called offset. It achieves this by continuously summing or integrating the control error over time.
The control error, denoted as $e(t)$, is the difference between the desired value (set point, SP) and the actual value measured from the process (measured variable, PV). Mathematically, this is expressed as:
$e(t) = SP - PV$The integral action calculates the integral of this error signal $e(t)$. As long as an error exists, the integral term will continue to increase or decrease, driving the controller's output further until the error is eliminated ($e(t) = 0$).
Therefore, the role of the integral component is specifically to integrate the difference between the set point and the measured variable, which is the error signal, aiming to remove steady-state offset.
Important Questions from Proportional Derivative and Integral Control
- A proportional controller is used to control the temperature of an autoclave from $60\degree C$ to $130\degree C$. If the proportional band setting of the controller is 25%, the proportional gain value is ________
Which of the following statements are CORRECT for a controller?
P. In a proportional controller, a control action is proportional to the error
Q. In an integral controller, a control action is proportional to the derivative of the error
R. There is no “offset” in the response of the closed-loop first-order process with a proportional controller
S. There is no "offset" in the response of the closed-loop first-order process with a proportional-integral controller
- Which one of the following statements is CORRECT about proportional controllers?
