8.3 PI controller design via the root locus
Proportional-integral (PI) controlWe will now address how to design a controller that compensates for steady-state error. The technique is a straightforward extension of the proportional control technique developed previously with the root locus. However, it requires a bit of motivation, which we will find by studying the steady-state error.
8.3.1 The steady-state error
Steady state error In Section 8.1, we introduced the steady-state error, the difference between the command and the steady-state output of the closed-loop system. Let us study this further by examining the error from the unity feedback1 block diagram of Figure 8.6. The error is
Applying the final value theorem to [@eq:errortf] gives us the steady-state error in the time domain:
[@Eq:errorss1] is as far as we can …