proporcionálisintegrális

The term *proporcionális integrális* (proportional integral) refers to a fundamental concept in control theory, specifically within the design of proportional-integral-derivative (PID) controllers. In this context, the integral component is responsible for eliminating steady-state errors by continuously accumulating past errors over time and applying a correction proportional to this accumulated value.

The integral action is mathematically represented as the integral of the error signal, where the error is the difference between the desired setpoint and the actual process variable. This ensures that even small, persistent deviations from the setpoint are corrected, as the integral term gradually increases until the error is eliminated. The proportional term alone cannot address steady-state errors, as it only reacts to the current error magnitude. The integral term, however, "remembers" past errors, making it essential for achieving precise control in many systems.

In a PID controller, the integral term is typically scaled by an integral gain (often denoted as *Ki*), which determines the strength of the correction. A higher *Ki* value results in faster error elimination but may lead to overshoot or instability if not properly tuned. Conversely, a low *Ki* may leave residual steady-state errors. The integral term is particularly useful in systems where disturbances or load changes occur, as it helps counteract their effects over time.

The proportional-integral (PI) controller combines the proportional and integral actions, omitting the derivative term, which focuses on future error trends rather than past behavior. This simpler configuration is widely used in industrial applications, such as temperature control, motor speed regulation, and chemical process automation, where steady-state accuracy is critical. Proper tuning of the integral gain is crucial to balance responsiveness and stability in these systems.