Che 185 process control and dynamics
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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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Block diagram algebra
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


System algebra and block diagram
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


System algebra and block diagram1
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


System algebra and block diagram2
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


System algebra and block diagram3
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


Example of block diagram development
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.


Example of block diagram development1
EXAMPLE OF BLOCK DIAGRAM DEVELOPMENT

  • TRANSFER FUNCTIONS RELATING FLOWS IN AND OUT OF EACH UNIT:

    • LINEAR COMPONENT MATERIAL BALANCES:


Example of block diagram development2
EXAMPLE OF BLOCK DIAGRAM DEVELOPMENT

  • LaPLACE TRANSFORMS FOR MATERIAL bALANCES:


Example of block diagram development3
EXAMPLE OF BLOCK DIAGRAM DEVELOPMENT

  • FROM THE FIRST OF THESE mass balance EQUATIONS:

  • AND FROM THE SECOND EQUATION:


Example of block diagram development4
EXAMPLE OF BLOCK DIAGRAM DEVELOPMENT

  • DEFINING TRANSFER FUNCTIONS FOR THE CONCENTRATIONS IN/OUT OF EACH REACTOR:

    :


Example of block diagram development5
EXAMPLE OF BLOCK DIAGRAM DEVELOPMENT

  • THE BLOCK DIAGRAM FOR THE PROCESS IS:

    :


Example of block diagram development6
EXAMPLE OF BLOCK DIAGRAM DEVELOPMENT

  • BLOCK DIAGRAM MATH::

  • ALTERNATE DIAGRAM CAN BE DEVELOPED TO REPRESENT THE SAME OVERALL TRANSFER FUNCTION


Example of block diagram development7
EXAMPLE OF BLOCK DIAGRAM DEVELOPMENT

  • ALTERNATE DIAGRAM CAN BE DEVELOPED TO REPRESENT THE SAME OVERALL TRANSFER FUNCTION


Example of block diagram development8
EXAMPLE OF BLOCK DIAGRAM DEVELOPMENT

  • FORMAT FOR BLOCK DIAGRAMS

  • Use of transfer function:


Other block diagram math structures
OTHER BLOCK DIAGRAM math structures



General signal relationships1
GENERAL SIGNAL RELATIONSHIPS

  • (EX. 5-9), RIGGS

  • Overall transfer function

  • Which compares with the same function derived with laplace transforms in ex. 5-4


Block diagram algebra example
Block Diagram Algebra example

  • Consider following block diagram:


Block diagram algebra example1
Block Diagram Algebra example


In class exercise block diagram algebra
In-Class Exercise: Block Diagram Algebra

  • Develop overall transfer function for


In class exercise block diagram algebra1
In-Class Exercise: Block Diagram Algebra

  • Develop overall transfer function for


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