Answer to Question #239158 in Chemical Engineering for Lucky

Question #239158

feedback control loop with a proportional controller has an open loop transfer function GOL = Kc/S(5S+1)²where time is in minutes. Tune for PID controller using Zeigler Nicholas settings.

Explain step by step?

Expert's answer

Desired Closed-Loop Transfer Function

For processes without time delays, the first-order model in Eq. 12-4 is a reasonable choice,

• The model has a settling time of ~ 4τc,

• Because the steady-state gain is one, no offset occurs for set- point changes.

• By substituting and solving for Gc, the controller design equation becomes final.

• The 1/ τc s term provides integral control action and thus

eliminates offset.

• Design parameter τc provides a convenient controller tuning parameter that can be used to make the controller more aggressive (small τc ) or less aggressive (large τc).

The time-delay term in (12-6) is essential because it is physically impossible for the controlled variable to respond to a set-point change at"t = 0" , before"t = \u03b8."

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