View source for How is the slope of the gain curve related to robustness?

To first approximation, there is a direct relation between the slope of the gain magnitude curve and the amount of phase in a Bode plot:


-2 slope --> -180 deg phase

-1 slope --> -90 deg phse

0 slope --> 0 deg phase

1 slope --> 90 deg phase

2 slope --> 180 deg phase

etc.


An exact relation using a weighting kernel is given in section 9.4 (p. 280) in [http://www.cds.caltech.edu/~murray/books/AM05/pdf/cds101-complete_20Sep07.pdf AM08].


For robustness, you want relatively high phase margin, and that is achieved by minimizing the phase (making it greater than -180 deg). This can be achieved by minimizing the slope of the magnitude plot when it crosses unity.

--[[User:Fuller|Fuller]] 17:17, 4 December 2007 (PST)

[[Category: CDS 101/110 FAQ - Homework 8]]
[[Category: CDS 101/110 FAQ - Homework 8, Fall 2007]]