Question

Ex. 1780. A closed-loop system has sustained oscillations (i.e. constant

amplitude) with a period of 88 seconds when the gains are:
proportional=22, integral=0, and derivative=0. Determine the ideal-
PID gains Kp, Ki (minutes^-1), Kd (minutes) using the Ziegler-Nichols
method. Also determine the standard-PID values which are commonly used
in industry, such as LabVIEW: Kc, Ti (min), Td (min). ans:6

Answer 1

To determine the ideal PID gains using the Ziegler-Nichols method, find the critical gain and period. Then use the critical gain to calculate Kp, Ti, and Td.

Step-by-step explanation:

To determine the ideal PID gains using the Ziegler-Nichols method, we first need to find the critical gain and critical period. In this case, the critical gain is the proportional (Kp) gain that causes sustained oscillations with a period of the least 88 seconds. The critical period is the corresponding period of these sustained oscillations.

For a closed-loop system, the critical gain (Kc) is usually around 1.2 to 2 times the critical gain. The integral time constant (Ti) can be determined using the critical period, and the derivative time constant (Td) is a fraction of the critical period. In industry, standard PID values like those used in LabVIEW are commonly used, where Kp is typically set to Kc/2, Ti is set to 4 times the critical period, and Td is set to half the critical period.