Accurate rise time with stepinfo()

I have the following code:

g = tf([0 0 5000],[1 200 5000]);
step(g); grid on;
S = stepinfo(step(g),'RiseTimeLimits',[0 0.632])

the figure producued by step(g) is here:

from looking at this, it is obvious that the rise time to 63.2% of the steady state output is approximately 0.04. However, the stepinfo() command says the rise time is

RiseTime: 74.6661

This number makes no sense at all. Is there something I am missing? I have used stepinfo() before and got accurate results but this has me stumped.

Answer 1

[Star Strider]

From the documentation for stepinfo:

• RiseTime — Time it takes for the response to rise from 10% to 90% of the steady-state response.

If you want the time constant τ use step with this calling syntax:

[y,tOut] = step(sys)

then interpolate (if necessary) to get the time constant:

g = tf([0 0 5000],[1 200 5000]);
[y,tOut] = step(g); 
tau = interp1(y, tOut, exp(-0.5))

producing:

tau =
   0.038246779260296

.

[Evan Hine]

thanks this makes much more sense!

[Star Strider]

As always, my pleasure!

Note that this works because the system is overdamped (or appears to be, I didn’t do the maths to analyse that in detail). If it had overshoot, it would be necessary to find the time of the (first) peak, and then use only the time and amplitude values up to that point to interpolate the time constant.

Also, a small correction:

tau = interp1(y, tOut, 1-exp(-1))

producing:

tau =
   0.040550205799629

.

[Paul]

Note that this solution assumes that the final value of the response is unity. I think that the time constant is typically taken as 63% to the steady state, whatever that steady state value may be.

[Star Strider]

Only in this situation. I do not intend it to generalise to all such situations.

I quote from my Comment:

‘Note that this works because the system is overdamped (or appears to be, I didn’t do the maths to analyse that in detail). If it had overshoot, it would be necessary to find the time of the (first) peak, and then use only the time and amplitude values up to that point to interpolate the time constant.’

Answer 2

[Paul]

The first input to stepinfo is incorrect. It should just be g

>> S = stepinfo(g,'RiseTimeLimits',[0 0.632])

S = 

  struct with fields:

        RiseTime: 4.0539e-02
    SettlingTime: 1.3999e-01
     SettlingMin: 6.3697e-01
     SettlingMax: 9.9839e-01
       Overshoot: 0
      Undershoot: 0
            Peak: 9.9839e-01
        PeakTime: 2.2606e-01