PI Controller: Design

In applications like automatic brightness adjustment on smartphones, Proportional Integral controllers effectively mitigate steady-state errors for step-function inputs, unlike PD controllers, which require time-varying errors.

The integral component of a PI controller eliminates residual steady-state errors not tackled by the proportional part.

An op-amp-based PI controller uses resistors and a capacitor to process an error signal, generating a control signal through proportional feedback from a resistor and an integral response from a capacitor.

The two and three op-amp circuits have unique transfer functions, with PI controller parameters linked to their circuit characteristics.

The three op-amp circuits independently link proportional and integral gains to circuit parameters. Both circuits have integral gain inversely proportional to the capacitor, leading to potentially large capacitor values for effective PI-control designs.

By altering the forward-path transfer function by adding a zero and pole, the PI controller boosts system performance and reduces steady-state error by one order.

If the steady-state error to a given input is constant, the PI control reduces it to zero, provided that the compensated system remains stable.