Find the approximate phase plot for each of the following tr

Find the approximate phase plot for each of the following transfer function by applying the straight line approximation. Don\'t plot more than one or two points for each pole of zero. Use Matlab to plot the exact plot. a) G(s) (100)^2/s^2+20s+(100)^2 b) G(s) = S-1/s(s+10), and G(s) = s+3/s^2(s-10).

Solution

the transfer function has to be written in the form :

(a)

   MySys=tf(10000*[1],[1 20 10000]);

   bode(MySys);

for bode plot use >>>>>>>>>>>>>bode(MySys)

                  >>>>>>>>>>>>sysdat(MySys)

>>>>>>>>>>>>>>>slbode(MySys)   %%% straight line approximation

[rn,rd,imas,rhps,c,bf,ft,dr]=sysdat(n,d)

It computes the break frequencies,bf factor types,ft, (linear or quadratic) and damping ratios,dr,for the factors of the frequency response defined by the numerator and denominator coefficients n and d. It also computes the gain constant,c.

The second matlab function :[am,ph]=slbode(w,c,bf,ft,dr)

computes samples for the Bode amplitude and phase response straight-line approximations.These samples are output in the row array variables am and ph.Inputs are the factor parameters computed by sysdat and the frequency row array w. There should be an equal number of samples computed in each decade of frequency change.

a) s=tf(\'s\');

x=100^2/(s^2+20*s+10000);

bode(x);

b) s=tf(\'s\');
x=(s-1)/(s*(s+10));
bode(x);

c) s=tf(\'s\');
x=(s+3)/(s^2*(s-10));
bode(x)

for straight line approximation use above mentioned functions >>>> sysdat    & slbode