Can I calculate the settling time in MATLAB?

I have many closed loop transfer functions that are in similar form to this one:

I want to calculate the settling time up until 2% of the final value. I have many of those transfer functions so hopefully whatever method you guys suggest I can use it to automate this process for all.

Answer 1

[Star Strider]

Perhaps this —

s = tf('s');
G = (7507.852*s^3 - 37030.228*s^2 - 70479.368*s + 100001.744) / (s^5 + 50*s^4 + 1000*s^3 + 10000.585*s^2 + 9997.664*s + 10001.744);

figure
stepplot(G)
grid

s = stepinfo(G)

s = struct with fields:
         RiseTime: 2.3370
    TransientTime: 8.1185
     SettlingTime: 8.4958
      SettlingMin: 9.0200
      SettlingMax: 12.8592
        Overshoot: 28.6117
       Undershoot: 59.0919
             Peak: 12.8592
         PeakTime: 3.6890

Settling_Time = s.SettlingTime

Settling_Time = 8.4958

From the documentation:

By default, SettlingTime measures the time it takes for the error to stay below 2% of |yfinal – yinit|.

That would appear to meet your requirement for it.

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