# Unit Step Response of an Integrator

Desinging a very basic 1st order integrator with the continous transfer function:

$$H(s) = -1 / (0.001 s)$$ [No zeros, one pole at origin]

I was expecting the unit step response to be positive-slope. However in my Python code I get a negative slope.

num = (0 , -1)
den = (0.001 , 0)
Hs = sig.lti(num,den)
t, s = sig.step(Hs)
plt.plot(t,s)


Provides:

• $H(s)$ has a negative sign, that's why. – Matt L. Dec 4 '18 at 12:40
• That's the sign for more coffee needed. – Malcolm Rest Dec 4 '18 at 12:49
• I'll drink to that! :-) – Peter K. Dec 4 '18 at 13:01

Your integrator has a negative sign:

$$H(s)=-\frac{1000}{s}\tag{1}$$

That's why its step response also has a negative sign:

$$y(t)=-1000\int_{-\infty}^tu(\tau)d\tau=-1000\cdot t\cdot u(t)\tag{2}$$

where $$u(t)$$ is the unit step.

• Man! Do we really need to post answer for a single negative sign ;-))) – Fat32 Dec 4 '18 at 18:25
• @Fat32: One yes, otherwise it keeps popping up as unanswered, two or three, probably not :) – Matt L. Dec 4 '18 at 20:37
• that's a reason i bitched on the meta about SE always regurgitating unanswered questions. sometimes they're unanswered because the question is useless. hopefully the OP will check-mark Matt's answer and then SE will be satisfied that it's answered and we all can move on. – robert bristow-johnson Dec 4 '18 at 22:44
• @robertbristow-johnson: Yes, what we can do about it is suggesting to close bad questions, and answer all others. – Matt L. Dec 5 '18 at 8:27