Integraalisäätimen

Integraalisäädin, often referred to as an I-controller, is a component of a PID controller used in control systems. Its primary function is to eliminate steady-state error, which is the difference between the desired setpoint and the actual output of a system when it has settled. The integral action achieves this by accumulating the error over time. If there is a persistent error, even a small one, the integral term will continue to grow, generating an increasing control signal until the error is driven to zero.

The output of an integral controller is proportional to the integral of the error signal with respect to time. Mathematically, if e(t) is the error signal at time t and K_i is the integral gain, the output of the integral controller, u_i(t), is given by u_i(t) = K_i * integral(e(tau) d(tau)) from 0 to t. A higher integral gain (K_i) will cause the integral term to grow more quickly, leading to faster elimination of steady-state error but also potentially introducing overshoot and instability.

While integral control is effective at removing steady-state error, it can also slow down the response of the system and make it more prone to oscillations if not properly tuned. It is often used in conjunction with a proportional controller (P-controller) to form a PI-controller, which balances the fast response of the proportional term with the steady-state error elimination of the integral term. In a full PID controller, a derivative term (D-controller) is also included to anticipate future errors and dampen oscillations.