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CHE 185 – PROCESS CONTROL AND DYNAMICS

CHE 185 – PROCESS CONTROL AND DYNAMICS. State Space Models. Block Diagram Algebra. THE SEQUENCE OF SIGNAL PROCESSING IN A CONTROL LOOP CAN BE EXPRESSED IN BLOCK DIAGRAMS. BLOCK DIAGRAM ADVANTAGES EACH STEP IN THE PROCESS IS RETAINED AND CAN BE ADJUSTED INDEPENDENTLY

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CHE 185 – PROCESS CONTROL AND DYNAMICS

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  1. CHE 185 – PROCESS CONTROL AND DYNAMICS State Space Models

  2. Block Diagram Algebra • THE SEQUENCE OF SIGNAL PROCESSING IN A CONTROL LOOP CAN BE EXPRESSED IN BLOCK DIAGRAMS. • BLOCK DIAGRAM ADVANTAGES • EACH STEP IN THE PROCESS IS RETAINED AND CAN BE ADJUSTED INDEPENDENTLY • CAUSE AND EFFECT RELATIONSHIPS FOR THE OVERALL SYSTEM ARE EASY TO ANALYZE • THE IMPACT OF EACH COMPONENT IN tHE SYSTEM CAN BE CHECKED WHILE RETAINING A COMPREHENSIVE MODEL

  3. System Algebra and Block Diagram • Laplace transform – PARALLEL SYSTEM • time-domain • h(t) is the overall impulse response http://fourier.eng.hmc.edu/e102/lectures/Laplace_Transform/node15.html

  4. System Algebra and Block Diagram • Laplace transform – Series combination • time-domain • h(t) is the overall impulse response http://fourier.eng.hmc.edu/e102/lectures/Laplace_Transform/node15.html

  5. System Algebra and Block Diagram • Laplace transform – Feedback system • time-domain • h1(t) is the FORWARD PATH AND h2(t) IS FEEDBACK • S-DOMAIN • transfer function http://fourier.eng.hmc.edu/e102/lectures/Laplace_Transform/node15.html

  6. System Algebra and Block Diagram • Laplace transform – Feedback system • feedback could be either positive or negative • FOR NEGATIVE • TRANSFER FUNCTION http://fourier.eng.hmc.edu/e102/lectures/Laplace_Transform/node15.html

  7. EXAMPLE OF BLOCK DIAGRAM DEVELOPMENT • DEVELOP THE RELATIONSHIPS BETWEEN CA2 AND CA0 FOR TWO STAGE CSTR SYSTEM WITH CONSTANT FLOWS, SAME VOLUME, AND REACTION RATE CONSTANT, k.

  8. EXAMPLE OF BLOCK DIAGRAM DEVELOPMENT • TRANSFER FUNCTIONS RELATING FLOWS IN AND OUT OF EACH UNIT: • LINEAR COMPONENT MATERIAL BALANCES:

  9. EXAMPLE OF BLOCK DIAGRAM DEVELOPMENT • LaPLACE TRANSFORMS FOR MATERIAL bALANCES:

  10. EXAMPLE OF BLOCK DIAGRAM DEVELOPMENT • FROM THE FIRST OF THESE mass balance EQUATIONS: • AND FROM THE SECOND EQUATION:

  11. EXAMPLE OF BLOCK DIAGRAM DEVELOPMENT • DEFINING TRANSFER FUNCTIONS FOR THE CONCENTRATIONS IN/OUT OF EACH REACTOR: :

  12. EXAMPLE OF BLOCK DIAGRAM DEVELOPMENT • THE BLOCK DIAGRAM FOR THE PROCESS IS: :

  13. EXAMPLE OF BLOCK DIAGRAM DEVELOPMENT • BLOCK DIAGRAM MATH:: • ALTERNATE DIAGRAM CAN BE DEVELOPED TO REPRESENT THE SAME OVERALL TRANSFER FUNCTION

  14. EXAMPLE OF BLOCK DIAGRAM DEVELOPMENT • ALTERNATE DIAGRAM CAN BE DEVELOPED TO REPRESENT THE SAME OVERALL TRANSFER FUNCTION

  15. EXAMPLE OF BLOCK DIAGRAM DEVELOPMENT • FORMAT FOR BLOCK DIAGRAMS • Use of transfer function:

  16. OTHER BLOCK DIAGRAM math structures

  17. GENERAL SIGNAL RELATIONSHIPS • (EX. 5-9), RIGGS

  18. GENERAL SIGNAL RELATIONSHIPS • (EX. 5-9), RIGGS • Overall transfer function • Which compares with the same function derived with laplace transforms in ex. 5-4

  19. Block Diagram Algebra example • Consider following block diagram:

  20. Block Diagram Algebra example

  21. In-Class Exercise: Block Diagram Algebra • Develop overall transfer function for

  22. In-Class Exercise: Block Diagram Algebra • Develop overall transfer function for

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