The primary function of the proportional-integral (PI) compensator is to increase the low frequency gains to reduce steady-state errors and decrease sensitivity to noise and parameter variations.

Transfer function

Bode plots

**To design a PI
compensator**

Because the function of the PI compensator is to increase low frequency gain, the design steps differ from those for the previous two compensators.

1. Determine the frequency (ω*) that defines the region ω < ω* in which the gain is to be increased.

2.
Determine the amount of gain to be added (*K**) using the error coefficient
specifications for the system.

3. Identify the cross-over frequency and phase margin from the uncompensated system Bode plots, and .

4. Select the zero of the PI compensator to satisfy the steady-state error specifications. If, however, a phase margin problem exists (for example, the phase margin is less than 30 degrees), do not allow it to move past .

5.
Initially select *K* = 1 and tune the compensator slightly by modifying the
value of *K* for the desired performance.