Question

The value of ultimate period of oscillation \(P_u\) is 3 minutes, and that of the ultimate controller gain \(K_{cu}\) is 2. What is the correct set of tuning parameters (controller gain \(K_C\), the derivative time constant \(\tau_D\) in minutes, and the integral time constant \(\tau_I\) in minutes) for a PID controller using Zielger-Nichols controller settings?

• A. \( K_C = 1.1; \tau_I = 2.1; \tau_D = 1.31 \)
• B. \( K_C = 1.5; \tau_I = 1.8; \tau_D = 0.51 \)
• C. \( K_C = 15; \tau_I = 1.8; \tau_D = 0.51 \)
• D. \( K_C = 1.2; \tau_I = 1.5; \tau_D = 0.38 \)

Hint:

Ziegler-Nichols tuning provides initial estimates for controller gains based on the ultimate gain and period of oscillation.

Answer 1

The Correct Option is B

Using the Ziegler-Nichols tuning formula for PID controller: \[ K_C = 0.6 K_{cu}, \quad \tau_I = 0.5 P_u, \quad \tau_D = 0.125 P_u \] Substituting \( K_{cu} = 2 \) and \( P_u = 3 \) minutes: \[ K_C = 1.5, \quad \tau_I = 1.8 { minutes}, \quad \tau_D = 0.375 { minutes} \] Thus, the closest match is option (B).