1 / 26

CHE 185 – PROCESS CONTROL AND DYNAMICS

CHE 185 – PROCESS CONTROL AND DYNAMICS. DYNAMICS OF SPECIFIC TYPES OF PROCESSES. INTEGRATING PROCESSES. A FIRST ORDER PROCESS WITH CAPACITANCE TYPICAL PROCESS IS THE LEVEL IN A TANK. INTEGRATING PROCESSES. THE HOLDUP TIME IN THIS UNIT IS DEFINED AS τ H

xue
Download Presentation

CHE 185 – PROCESS CONTROL AND DYNAMICS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CHE 185 – PROCESS CONTROL AND DYNAMICS DYNAMICS OF SPECIFIC TYPES OF PROCESSES

  2. INTEGRATING PROCESSES • A FIRST ORDER PROCESS WITH CAPACITANCE • TYPICAL PROCESS IS THE LEVEL IN A TANK

  3. INTEGRATING PROCESSES • THE HOLDUP TIME IN THIS UNIT IS DEFINED AS τH • THE GENERAL RELATIONSHIP BETWEEN CHANGES IN L AND F IS • WHERE THERE IS NO RELATIONSHIP BETWEEN F AND L, SUCH AS IN THE GRAVITY DRAINED TANK EXAMPLE.

  4. INTEGRATING PROCESSES • GENERAL FORM FOR THE TRANSFER EQUATION IS THEN: • FOR THE SPECIFIC CASE WHEN FIN IS CONSTANT, THE FORM OF THE EQUATION IS:

  5. INTEGRATING PROCESSES • THE INTEGRATOR FORM FOR THE FIRST ORDER DIFFERENTIAL EQUATION • INCLUDES A DERIVATIVE TERM THAT IS INDEPENDENT OF • HAS A POLE = 0 IN THE TRANSFER FUNCTION

  6. INTEGRATING PROCESSES • ANALYTICAL FORM FOR THE INTEGRATOR IS: AND IT CAN ACCUMULATE VALUE AS LONG AS INPUT IS NOT ZERO

  7. INTEGRATING PROCESSES • FOR A STEP INPUT, THE RESPONSE IS: • FOR AN IMPULSE OF MAGNITUDE A: THE RESPONSE IS:

  8. DEADTIME (TRANSPORT DELAY) • THIS IS THE RESULT OF AN INHERENT DELAY IN THE SYSTEM TO CHANGES • EXAMPLE 1 - CONSIDER THE TIME DELAY WHEN A LARGE TANKER IS BEING MANEUVERED • THE CAPTAIN SENDS A NOTIFICATION TO THE CREW TO CHANGE SPEED AND OR DIRECTION • THE CREW RESPONDS BY MAKING THE CHANGES • THE TANKER STARTS TO RESPOND TO THE CHANGES

  9. DEADTIME (TRANSPORT DELAY) • EXAMPLE 2 - CONSIDER A HEATING SYSTEM WITH THE FOLLOWING CONFIGURATION:

  10. DEADTIME (TRANSPORT DELAY) • THERE IS A TIME DELAY BETWEEN WHEN THE FUEL FLOW CHANGES AND THE HOTTER/COOLER HEAT TRANSFER FLUID ARRIVES AT THE PROCESS HEAT EXCHANGER, θP. • THE BLOCK DIAGRAM FOR THE fopdt SYSTEM MAY BE APPROXIMATED BY:

  11. DEADTIME (TRANSPORT DELAY) • SENSING THE SIGNAL FROM THE PROCESS FLOW AND ADJUSTING THE SIGNIFICANCE IS RELATED TO THE OVERALL PROCESS RESPONSE TIME • GENERAL FORM OF THE EQUATION FOR DEADTIME IS: Y(t)=X(t−θ ) • GENERAL FORM OF THE TRANSFER FUNCTION IS:

  12. DEADTIME (TRANSPORT DELAY) • FIRST ORDER PLUS DEAD TIME (FOPDT) RESULTS FROM COMBINING THE FIRST ORDER TRANSFER FUNCTION WITH THE DEADTIME TRANSFER FUNCTION:

  13. INVERSE ACTING PROCESSES • PROCESSES WHERE THERE ARE TWO COMPETING ACTIONS OCCURRING SIMULTANEOUSLY • TYPICAL PROCESS MIGHT INCLUDE A BYPASS SYSTEM FOR A HEAT EXCHANGE

  14. INVERSE ACTING PROCESSES • THE BLOCK FLOW DIAGRAM FOR THIS PROCESS IS • THE OVERALL EQUATIONS FOR THIS SYSTEM ARE:

  15. INVERSE ACTING PROCESSES • THE OVERALL EQUATIONS FOR THIS SYSTEM CAN BE COMBINED TO YIELD • IF BOTH PROCESSES ARE FIRST ORDER, THEN SUBSTITUTION WILL PRODUCE:

  16. INVERSE ACTING PROCESSES • WHICH CAN BE REARRANGED TO YIELD:

  17. INVERSE ACTING PROCESSES • WHEN THESE PROCESSES ARE OF OPPOSITE SIGN, THEN EQUATION (6.9.1) RESULTS • .THIS EQUATION HAS A ZERO TERM THAT CAN BE POSITIVE, THEN INVERSE ACTION CAN OCCUR • OTHER RESULTS ARE SHOWN IN THE FOLLOWING GRAPH and Figure 6.9.1, WHERE τ3IS VARIED.

  18. INVERSE ACTING PROCESSES • THE GENERAL FORM OF THE EQUATION OBTAINED FROM INVERSE LaPLACE TRANSFORMS IS: • USING VALUES OF 1 FOR KP AND ΔX, τ1= 2, AND τ2= 1:

  19. INVERSE ACTING PROCESSES

  20. Lead-lag compensation • lead compensator can increase the stability or speed of response of a system • a lag compensator can reduce (but not eliminate) the steady-state error • Lead-lag compensators can be used for the same optimization as pid, pi, pd, I, d controllers.

  21. Lead-lag compensation • lead compensators and lag compensators introduce a pole–zero pair into the open loop transfer function: • lead-lag compensator is a lead compensator cascaded with a lag compensator. Transfer function is: • z1 and p1 are the zero and pole of the lead compensator and z2 and p2 are the zero and pole of the lag compensator

  22. Lead-lag compensation For a first order process where there is a consideration of the time derivative of the input: Results in a transfer function: or the general laplace form for lead-lag: And the time version is (eqn. 6.10.1):

  23. RECYCLE (PROCESS INTEGRATION) SYSTEMS • GENERAL FLOWSHEET FOR RECYCLE OF ENERGY IS SHOWN FOR EXAMPLE 6.12

  24. RECYCLE (PROCESS INTEGRATION) SYSTEMS • GENERAL FLOWSHEET FOR RECYCLE OF ENERGY IS SHOWN FOR EXAMPLE 6.12 • THE TRANSFER FUNCTIONS FOR THIS SYSTEM ARE:

  25. RECYCLE (PROCESS INTEGRATION) SYSTEMS • THE BLOCK DIAGRAM FOR THIS SYSTEM IS: • WHERE T2 REPRESENTS ENERGY RECYCLED TO THE REACTOR VIA THE MIXED FEED STREAM

  26. RECYCLE (PROCESS INTEGRATION) SYSTEMS • THE BLOCK DIAGRAM FOR THIS THE OVERALL TRANSFER FUNCTION FOR THIS SYSTEM IS:

More Related