CHE 185 – PROCESS CONTROL AND DYNAMICS

# CHE 185 – PROCESS CONTROL AND DYNAMICS

Télécharger la présentation

## CHE 185 – PROCESS CONTROL AND DYNAMICS

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
##### Presentation Transcript

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