Answer to Question #239158 in Chemical Engineering for Lucky

Question

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?

Answer 1

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$t = θ.$