Describe the ultimate-cycle method for PID tuning and how Kc and Pu are determined.

Describe the ultimate-cycle method for PID tuning and how Kc and Pu are determined.

• A. Decrease Kc until the loop stabilizes
• B. Set Kp to 1.0 and Ki and Kd to zero
• C. Use random tuning coefficients and adjust by trial and error
• D. Increase Kc until sustained oscillations occur; measure Pu (oscillation period); use tuning formulas to derive Kp, Ki, and Kd.

Answer: (D)

The ultimate-cycle method is about using the most aggressive proportional gain that still yields a stable, periodic response to set the PID parameters. You slowly increase the proportional gain until the closed-loop output oscillates with constant amplitude. The gain at this point is the ultimate gain, Ku, and the period of the oscillation is Pu. Once Ku and Pu are known, you apply the standard Ziegler-Nichols tuning rules to get the PID parameters: set the proportional gain to 0.6 times Ku, set the integral time Ti to Pu/2, and set the derivative time Td to Pu/8. Convert these to Ki and Kd with Ki = Kp / Ti and Kd = Kp * Td. In other words, Ki = 1.2 Ku / Pu and Kd = 0.075 Ku Pu. This gives a solid starting set of parameters you then validate and fine-tune as needed.

The ultimate-cycle method is about using the most aggressive proportional gain that still yields a stable, periodic response to set the PID parameters. You slowly increase the proportional gain until the closed-loop output oscillates with constant amplitude. The gain at this point is the ultimate gain, Ku, and the period of the oscillation is Pu. Once Ku and Pu are known, you apply the standard Ziegler-Nichols tuning rules to get the PID parameters: set the proportional gain to 0.6 times Ku, set the integral time Ti to Pu/2, and set the derivative time Td to Pu/8. Convert these to Ki and Kd with Ki = Kp / Ti and Kd = Kp * Td. In other words, Ki = 1.2 Ku / Pu and Kd = 0.075 Ku Pu. This gives a solid starting set of parameters you then validate and fine-tune as needed.