Question

Using Ziegler-Nichols tuning method, a PID controller is designed for a 3^rd order system that has an ultimate gain of K_cr = 120 and an ultimate period of P_cr = 10 seconds.

For the PID controller gains, the Proportional gain will be equal to:

For the PID controller gains, the Integral gain will be equal to:

For the PID controller gains, the Derivative gain will be equal to:

Answer 1

According to Ziegler-Nichols theorem the Integral and Derivative gains of the controller are set to zero and the proportional gain is increased till the systems response for a step input is continuous steady oscillaitons. Then, this value of the proportional gain is called ultimage gain and the period of these oscillations is called ultimate period.

The values of the proportional, integral and derivative gains are then decided as per the following rules:

Proporitonal gain P = 0.6*Kcr = 0.6*120 = 72

Integral gain I = Pcr/2 = 10/2 = 5

Derivative gain D = Pcr/8 = 10/8 = 1.25