Question

Problem #2: For experimental test data, you have a system with the following unit step responses. 1.0 0.8 0.6 0.4 0.2 0123456789 10 Time (sec) a) b) Determine the response's time delay and tangential slope along the transient response. Find the PID Control gains using Zeigler-Nichols tuning method.

Answer 1

Referring figure above, L=0.8 and T=1.2.

a)

Inflection point is observed at t=0.8 seconds(approximately).

Time delay is the time taken by the response to reach 50% of final value. i.e., 50% 0f 1 = 0.5. Hence, from figure, delay time can be approximated to seconds.(Orange line intersection with time axis)

td 2.8

Tangent drawn is shown by red line. Tangential Slope =
2-0,8
=

Slope Angle = degrees

arctan 0.833 39.81

b)

With L=0.8 and T=1.2, PID Control Gains are

7 1.2 Kp 1.2- -1.2-1.44

Кр 1.44 Кр KJ 0.9 T12L2 0.8 2L 2

Kn = Kp * T) = Kp * 0.5L = 1.44 * 0.5 * 0.8 = 0.576