Lecture: Frequency Analysis (Part 3)

[sophiabelvedere]

Posted this on Piazza but remembered you said to post lecture questions in the video comments:


1. In Freq. Analysis part 2, we discussed how the argument of GC must be < -180 deg for oscillatory decay. This appeared to be dervied generically for a closed or open loop transfer function of any order. Then in Part 3, it says that a 1st order system has a min -90 deg phase lag, second has min -180 deg, etc.. Two questions about this:

(i) Does this exerpt from Part 3 refer to the minimum lag for 1st and 2nd order functions for the open-loop (G), or closed-loop (GC/(1+GC)) transfer function?

(ii) If the exerpt from Part 2 is correct, first and second order functions both will always fail to have an arument < -180 deg so they will always have an utimate gain of infinity. Is this a correct assessment?

2. (Referring to Freq Analysis Part 3 Lecture): If we use frequency analysis to solve problems that involve time delay and in lecture it is said that any time delayed system will be non-minimum-phase, why do we look at systems like those in Examples 2 and 3 from the youtube lecture that do not have the e^(-as) component? And why does Example 4 of 1/(S+1)^3 say that it is "without time delay" if the previous two examples also don't have a time delay? Do they have an implicit time delay denoted in a different format than e^(-as)?

3. (Referring to Freq Analysis Part 3 Lecture): Finally, what is the mathematical proof that the ultimate gain Ku = infinity for systems where <G(w)> > -180 deg? I am confused because for the two examples where that happens (Ex 2 & 3), it does not show the calculation of <G(wc) or |G(w)| or Ku like before, so I am not really sure where the concept that Ku = infinity comes from for those specific settings

[thomasjohnston]

In pole analysis, where does the 1+ GKu = 0 come from?