Explain the purpose of a PID controller in feedback control systems.

Here's a breakdown of the components of a PID controller and their roles:

Proportional (P) Term:

The proportional term is responsible for producing a control output that is proportional to the error between the setpoint and the actual process variable. The error is calculated as the difference between the setpoint (SP) and the PV at any given time. The larger the error, the larger the output from the proportional term. This means that as the error reduces, the controller's response decreases proportionally. The P-term contributes to achieving a faster response to disturbances and reducing steady-state errors.

Integral (I) Term:

The integral term considers the accumulated error over time and aims to eliminate any steady-state errors that persist even when the proportional term has reduced the error to zero. Steady-state errors can occur due to factors like system bias or disturbances that are not corrected by the P-term alone. The I-term continuously sums up the error over time and applies a corrective action proportional to the integral of the error. This helps in driving the system to its desired state and maintaining accuracy over the long term.

Derivative (D) Term:

The derivative term anticipates the future trend of the error by calculating its rate of change. It provides a control signal based on how fast the error is changing with time. The D-term helps in damping the system's response, reducing overshoot and oscillations, and improving system stability. It acts as a predictive element to avoid sudden changes in the control output.

In summary, a PID controller combines the three terms to generate a control signal that effectively regulates the system and minimizes the error between the desired setpoint and the actual process variable. The P-term handles the current error, the I-term addresses accumulated past errors, and the D-term anticipates future errors. By striking the right balance between these three terms through appropriate tuning, a PID controller can stabilize a wide range of control systems and maintain the system at the desired operating point despite disturbances or changes in the system.