Bode Diagrams for Transfer Function: (s+2)/(s*(s+10)*(s^2+2s+2))

[UnteljentEnginyr]

So I have a midterm on Bode Diagrams and Root-Locus on Thursday...and I can not do either. At this point I am only focusing on the Bode diagrams because they are a bit easier and I want to master them now so that I can devote the rest of my time to the Root-Locus.

Say I have the transfer function

(s+2)/(s*(s+10)*(s^2+2s+2)).

In Bode form, this becomes

(jw/2+1)/(10*jw*(jw/10+1)*((jw)^2/2+jw+1))

I am sorry for the difficulty when looking at the function...I have no way of making it look better.

Could someone walk me through a problem like this?

This is what I know:
-The break points will occur and 2, 10, and some other value derived from the polynomial expression.
-The slope of the asymptotes will be plus or mine 1, depending on if the break point is in the denominator(-1) or numerator (+1)...the slope of the first will be -1 because of the (jw)^-1 term.

What I don't know:
-The break point of the polynomial (and imaginary) expression
-How to go from the magnitude plot to the phase plot
-what the intercept at the magnitude axis (y-axis) will be...is it random or is there an actual way to find it.

I have done the bode plot in Matlab...but I can't really make out changes in slope well, nor can I get an accurate Magnitude axis intercept.

I hope this makes sense. And look forward to my questions from Root-Locus.

 

[enigma]

I'm moving this to homework help where you may get a better viewing.

Sorry I can't help... I blasted controls from my memory shortly after passing the course.

 

[thechris]

bode is all about approximations.

unless the teacher has explicitly shown you how to do 2nd order terms in class, i wouldn't worry too much --- second order terms are a bit harder to do. in my control systems class, the teacher did a lot with RL and bode, but mainly wanted us to show info on gain and phase margins instead of making pretty pictures!

magnitude and phase plots are realistically separate -- an important fact for control systems where "transport lag" becomes a big factor of the phase, and yet doens't affect magnitude!

but assumeing no lag, sure you can do it. you just need to find the poles and zeros on the plot. again, easy for 1st order terms, but not as easy for second order terms.

in matlab, look at the margin command -- it will give you the gain and phase margin and frequencies!