Step 1:Fig. 2a shows the result of slowly increasing only the proportional term. The system begins to oscillate at approximately .5 Hz (fo = .5Hz) with Ko of approximately 5E-5 Nm/ rad.
Step 2:Using these values, the optimum P.I .D. gains according to Ziegler-Nichols (Z-N) are then (using equation (6)): Kp = 3.0E-4 Nm/ rad Ki = 3.0E-4 Nm/ (radgsec) Kd = 7.4E-5 Nm/ (rad/sec)
Fig. 2b shows the result of using the Ziegler Nichols gains. The response is somewhat better than just a
straight proportional gain. As a comparison, other gains were obtained by trial and error. One set of additional gains is listed in Fig. 2b. Although the trial and error gains gave a faster, less oscillatory response, there is no way of telling if a better solution exits without further exhaustive testing. a) Determining Ko of Z-N Method b) Comparing Z-N to Trial and Error Method Figure 2. Step Response curves for both Ziegler Nichols and Trial and Error Method. One characteristic that is very apparent in Fig.2 is the length of the settling time. The system using
Ziegler Nichols takes about 6 seconds to finally settle making it very difficult to incorporate into any highperformance motion control application. In contrast, the trial and error settings gives a quicker settling
time, however no solution was found to completely remove the overshoot.