dyquist atability

dyquist atability

Estimating open-loop process trainer parameters

 

Follow the procedure below to estimate the refers to calculate the process parameters , , , and  from a printed copy of your reaction curve (i.e., the open-loop step response)

 

A. Required constructions

1. Draw a horizontal line H1 through the “mean” initial output steady-state level

2. Mark as point A on line H1 the point corresponding to time +1.000E+00 on the horizontal axis

3. Draw a horizontal line H2 through the “mean” final output steady-state level

4. Measure the distance , in mm, between the lines H1 and H2

5. Calculate , and draw a horizontal line H3 at a distance , in mm, from line H1

6. From the point where line H3 intersects the reaction curve, draw a vertical line V1 down to intersect line H1. Mark the intersection as point C.

7. Draw the steepest slope line T1. This line must be the tangent line to the reaction with the highest gradient/slope.

8. Mark as point B the point where line T1 intersects line H1

9. Mark as point E the point where line T1 intersects line H2

10. Draw a vertical line V2 from point E down to intersect line H1. Mark the intersection as point D.

 

B. Required measurements

Measure and record the following distances in mm:

 

=

Distance between values +1.000E+03 and +3.000E+03 on the vertical axis

=

Distance between points A and B on line H1

=

Distance between points B and C on line H1

=

Distance between values +2.000E+00 and +3.000E+00 on the horizontal axis

=

Vertical distance between points E and D

=

Horizontal distance between points B and D

 

C. Required calculations

Using your measurements and the formulas shown in the sample reaction curve above, calculate the process parameters , , , and .

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