1 CBE 491 / Oct 12 Deadtime in a Process

2 Dead Time in a Process Show how dead time might show up How it affects block diagrams How it affects response LT LC

Closed loop response: (no setpoint change) Level Loop (melt tank) If: 0 t A

Closed loop response: (setpoint change) Level Loop (melt tank) If: 0 t A

5 Dead Time in a Process Suppose change manipulated variable LT LC FC FT

Level Loop (melt tank) D(s) not a polynomial; can’t do P.F. expansion, so different procedure needed. Dead time effect is to reduce the ultimate loop gain (will oscillate at lower Kc values)

Tuning: adjust controller parameters to obtain specified closed loop response. Feedback Controller Tuning Values of parameters depend upon: Desired response Dynamic characteristics of other elements in the control loop. We’ll come back to general tuning approaches, but lets first explore the solid feeder example that has some dead time…. 7

8 Tuning Introduction Feeder with some dead time (t o ) WC WY WT aT =aV =aP =aC =aT =aV =aP =aC =

9 Tuning Example (w/ P-only Controller)

¼ Decay Ratio or Quarter Amplitude Damping: QAD or ¼ Decay Ratio Convenient Relatively quick response Relatively high overshoot on setpoint changes Non-unique (theoretically infinite no. tuning parameters) If dead time in loop: Makes closed loop closer to unstable Reduce Kc … but then more sluggish response Instead of pure feed back control … could implement Dead- Time Compensation (Smith Predictor) 10

Ziegler Nichols Tuning Method (I) For our simple example with WC WY WT To achieve QAD we set Ziegler Nichols Tuning Method I P-only control Find Set We’ll see another Ziegler Nichols: ZN II related to FOPDT fit Empirical formula to get closed loop response close to QAD 11

Feedback Controller Tuning: (General Approaches) 1)Simple criteria; i.e QAD via ZN I, t r, etc easy, simple, do on existing process multiple solutions 2)Time integral performance criteria ISEintegral square error IAEintegral absolute value error ITAEintegral time weighted average error 3)Semi-empirical rules FOPDT (ZN II) Cohen-Coon 4)ATV, or Autotuning 5)Trial and error 6)Rules of thumb 12

13 Questions ??