Nyquist plot with logarithmic amplitudes

Logarithmically scaled Nyquist plot: viewing problems due to near-infinite amplitudes are avoided.

Description

A polar diagram where the amplitude of the open-loop transfer function h0 is on a logarithmic scale, is presented. This gives a one-size-fits-all diagram with less need for zooming in and out, and no need for additional reasoning about infinite-radius encirclements when there are poles on the imaginary axis -- as opposed to what is often necessary with the standard polar (Nyquist-) diagram. All properties needed for stability considerations are upheld, such as encirclements, gain and phase margins. The path for s in the loop transfer function is carefully chosen with regard to possible poles on the imaginary axis. Small excursions into the right half plane in the form of arcs of different-sized logarithmic spirals result in corresponding large but finite arcs for h0 that do not overlap in the logarithmic polar plots.
Encirclements are counted and info about poles in RHP, and open- and closed-loop (in)stability, is given.
New in February 2009: Bugs are fixed related to encirclement counting.
An added functionality is now that the function also counts poles on the im-axis for the closed-loop system, if any. If such poles exist, this corresponds to the graph going through -1. Encirclement counting is then impossible and is disabled.

Note: the program at this stage works only for SISO and continuous-time systems.

• Required Products: Control System Toolbox
• MATLAB release: MATLAB 7.6 (R2008a)

[Tony Zortea]

Great work, very useful for difficult stability problems.

[Ricardo Lage]

 

[Matteo Massaro]

Great! It would be Excellent if also the number of encirclements was computed.

[tushar oza]

 

[Nabil al-hadawy]

******** Thank you ********
This is Function very nice ,and very good
I am plot 20 examples by it , and all this examples are correct and buty

[Yanbo]

Great work!!!