Brief Manual 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 to black.)
    1. Input the order of the polynomials

    2. 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.

    1. Select controller mode: P, PI or PID

    2. The transfer functions used for the controllers are:

      Proportional Control: 

      PI Control:   

      PID Control:  

    3. Choose whether gain is positive or negative.


      A label should appear below the scrollbar to indicate that the negative domain was chosen.

    5. Enter a different maximum absolute gain if needed by entering positive values in the textbox above the scrollbar.

    6. Slide the scrollbar to change the gain values within the range chosen.

    7. 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 )

    8. Change parameters via up/down buttons or key-in new values

    9. (Using the up/down buttons, the increments for  tI is 1.0,
      while the increments for  tis 0.1,
      and the increments for  is 0.01.)

    10. Zoom to desired levels if needed using the drop-down choice list located above the plot.

    11. 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.

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)  


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 ( ). Last revised 11/30/1999.

          Tomas B. Co
          Associate Professor
          Department of Chemical Engineering
          Michigan Technological University
          1400 Townsend Avenue
          Houghton, MI 49931-1295

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