Closed-Loop PID Controller
Aggressive tuning as shown in the Figure 9 offers faster response time, but it is not without overshoot and some oscillation. In this section we present the results of a tuning strategy that lies between the moderate and aggressive tunings we saw above. In doing so, we introduce the derivative term, Kd, to our controller design.
A derivative term in PID controllers is known to have sensitivity to noise, but it can also help decrease overshoot and settling time. Figure 10 shows the PID performance with Kp = 0.006, Ki = 0.005 and Kd = 0.004. The settling time of this controller is ~50ms, which is faster than the moderate tuning by about a factor of 2.5, and slower by less than twice the settling time of the aggressive tuning, but is also free of oscillation.
Fig 10 Critically damped loop response. The closed loop response of our application is about 50 ms.