for PID Root Locus Generator
I. Input the coefficients of the transfer function.
( Note: throughout the program, when the values in text are being
edited, the font color will change to red. This indicates that the values
have not yet been entered. Press the [TAB] or [ENTER] keys
to accept the new values. After doing so, the font color will change back
Input the order of the polynomials
Input the coefficients in the corresponding text boxes
II. Proceed to obtain root locus by clicking
on the [PLOT ROOT LOCUS] button located at the bottom.
III. Change parameters to observe behavior of root locus
The characteristic roots should appear as star-symbols
in the plot. The values of the roots are given in the rightmost panel.
Example 1: all roots are stable and appear in plot
Example 2: Three stable roots but the root at –2.256 is not
visible in the plot
Example 3: Two unstable roots and one stable root (but not
in the plot)
Select controller mode: P, PI or PID
The transfer functions used for the controllers are:Proportional Control:
Choose whether gain is positive or negative.
A label should appear below the scrollbar to indicate
that the negative domain was chosen.
Enter a different maximum absolute gain if needed by entering
positive values in the textbox above the scrollbar.
Slide the scrollbar to change the gain values within the
Alternatively, key in specific values for gain
( Note again the value of 5.2 in the figure above is not accepted
until the user hits the [TAB] or [ENTER] keys )
Change parameters via up/down buttons or key-in new values
(Using the up/down buttons, the increments for tI
while the increments
for tD is
and the increments
for a is 0.01.)
Zoom to desired levels if needed using the drop-down choice
list located above the plot.
Roots are color coded: Black=roots are stable and appear
in the plot. Gray=roots are stable but do not appear in plot (e.g. after
zooming in). Red=roots are unstable.
IV. Edit transfer function if needed by clicking
on [EDIT TRANSFER FUNCTION] button located at the bottom of the right panel.
This page is maintained by Tomas B. Co (
firstname.lastname@example.org ). Last revised 11/30/1999.
Tomas B. Co
Department of Chemical Engineering
Michigan Technological University
1400 Townsend Avenue
Houghton, MI 49931-1295
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