What is the primary function of integral and derivative functions in control systems?

The primary function of integral and derivative functions in control systems is to help maintain a process variable on set-point. In a control system, the set-point is the desired target value for a particular variable, such as temperature, pressure, flow rate, etc.

Integral functions accumulate the error over time, allowing the system to eliminate steady-state errors by adjusting the control output in response to the cumulative error. This ensures that the process variable reaches and stays at the set-point.

Derivative functions, on the other hand, predict future error based on the rate of change of the process variable. By responding to the rate of change, the derivative action can dampen oscillations and improve the system's stability and responsiveness.

Together, these functions form the cornerstone of PID (Proportional-Integral-Derivative) control systems, where the integral and derivative components significantly enhance performance compared to simple on-off control or other less sophisticated methods. This integration is crucial in maintaining the desired performance of a process over time, ensuring that fluctuations are minimized and control is precise.