Clean up description of Bode's phase area formula in Ch 12 and elsewhere [loopsyn]

[Richard Murray]

In Section 12.3 (Feedback Design via Loopshaping) of Ch 12 (loopsyn) there is a paragraph on the amount again associated with phase lead (see subsection "Lead and Lag Compensation"). Bode's phase area formula appears here.

A couple of things to do:

• Change d\omega/\omega to d\log\omega in the integral
• If possible, add something to the left of the formula along the lines of "\delta\arg G = ..." to make more clear what the relationship is.
• Double check the formula and how it is written with Bode's book

In addition, Bode's phase area formula appears as a Exercise 12.17 (exercises/loopsyn/phasearea) in Ch 12 (loopsyn). We should make sure the material agrees and figure out whether to keep the exercise or the body text. Depending on the details of the exercise, it might also be something to move to Ch 14 (limits), perhaps with appropriate wording in Ch 12 (loopsyn) making reference to the exercise.

[Richard Murray]

Updates applied and checked against exercises.