1 / 13

Interpreting the RGA

Interpreting the RGA. Andrew Kim Stephanie Cleto. What is the RGA?. R elative G ain A rray is an analytical tool used to determine the optimal input-output variable pairings for a multi-input-multi-output (MIMO) system. Significance of the RGA. Below is a general relative gain array.

halen
Download Presentation

Interpreting the RGA

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. Interpreting the RGA Andrew Kim Stephanie Cleto

  2. What is the RGA? • Relative Gain Array is an analytical tool used to determine the optimal input-output variable pairings for a multi-input-multi-output (MIMO) system.

  3. Significance of the RGA • Below is a general relative gain array

  4. Significance of the RGA • Below is a general relative gain array • Different columns represent the different manipulated (input) variables

  5. Significance of the RGA • Below is a general relative gain array • Different columns represent the different manipulated (input) variables • Different rows represent the different controlled (output) variables

  6. Significance of the RGA • The values in the array describe the relationship between the input and output variables • Negative values indicate an unstable relationship • A value of 0 indicates no relationship • A value of 1 indicates that specific input variable is the only influence on that output variable

  7. Example 1 • Assume a mixing tank with constant mass and two inputs as shown below: • wA and wB are manipulated flowrates entering the tank • w is the flowrate leaving the tank and xA is the concentration of A in the tank Example from http://eweb.chemeng.ed.ac.uk/courses/control/restricted/course/advanced/casestudy/exercise2.html

  8. Example 1 (cont.) • This process can be modeled by the following equations: w = wA + wB xA = wA/(wA + wB) • The RGA can be solved for this system:

  9. Example 1Solution • What does the RGA tell us? • If a concentration of xA=0.5 is desired, either wA or wB can be used • If a concentration of xA>0.5 is desired, then the concentration loop should be paired with wA • If a concentration of xA<0.5 is desired, then the concentration loop should be paired with wB

  10. Example 2 Adapted from http://eweb.chemeng.ed.ac.uk/courses/control/restricted/course/advanced/casestudy/exercise2.html

  11. Example 2 Solution • RGA Matrix • Pairing of variables: RGA matrix value should be 1)positive, then 2)close to 1. • Because each combination has only one positive value, that is the combination to be paired (R,xD and P,xB)

  12. Example 3 • Suppose you calculate the following RGA matrix. How should pairing of the variables occur?

  13. Example 3Solution • In the first row, only x3 gives a positive result, and then we go with the closest values to 1 for the others. • y1,x3y2,x2y3,x1

More Related