How to Store Time constant from "damp"

When I use damp(sys) it spits out poles, damping, frequency and time constant. When looking up the help damp I only see ways to store the frequency, damping and poles. Is there a way to store the time constant too?

Answer 1

[Star Strider]

The τ is relatively easy to calculate —

s = tf('s');
H = (s^2 - 2*s - 5) / (s^3 + 5*s^2 - 7*s - 20);

damp(H)                                                 % Output

                                                           
   Pole        Damping       Frequency      Time Constant  
                           (rad/seconds)      (seconds)    
                                                           
 -1.61e+00     1.00e+00       1.61e+00         6.23e-01    
  2.22e+00    -1.00e+00       2.22e+00        -4.51e-01    
 -5.61e+00     1.00e+00       5.61e+00         1.78e-01    

[wn,zeta,p] = damp(H)

wn = 3×1

1.6063 2.2186 5.6123

zeta = 3×1

1 -1 1

p = 3×1

-1.6063 2.2186 -5.6123

tau = 1./(wn.*zeta)                                     % Calculated

tau = 3×1

0.6226 -0.4507 0.1782

.

[Paul]

That is the time constant calculation in damp(), but it's only an approximation, and not the actual time constant for a pair of second order poles. In this example damp() is off by more than 0.1 seconds.

>> h = tf(1,[1 1.3 1]);
>> damp(h)
                                                                       
         Pole              Damping       Frequency      Time Constant  
                                       (rad/seconds)      (seconds)    
                                                                       
 -6.50e-01 + 7.60e-01i     6.50e-01       1.00e+00         1.54e+00    
 -6.50e-01 - 7.60e-01i     6.50e-01       1.00e+00         1.54e+00    
>> s=stepinfo(h,'RiseTimeThreshold',[0 0.63]);
>> s.RiseTime

ans =

    1.6848