Simulink Integrator block: how to

Asked by soko loko

soko loko (view profile)

on 19 Dec 2013
Latest activity Commented on by soko loko

soko loko (view profile)

on 20 Dec 2013
Hi:
I'm trying to figure out how exactly the integrator block (Simulink) works, I mean, How can be calculated manually? (e.g. if a ramp signal is integrated, a parabola is obtained)
Thanks.

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Answer by Andreas Goser

Andreas Goser (view profile)

on 19 Dec 2013

Simplified, it is new_value equals old_value plus increase and the increase is gradient divided by step size. The question now is how deep you are in math, e.g. for an university student of engineering I would recommend different material than if you are going to college.

soko loko

soko loko (view profile)

on 19 Dec 2013
Thank you for the response. By the way, I'm a mechatronics engineering student. Could you describe the above calculations with equations? How is the gradient obtained?

ES (view profile)

on 19 Dec 2013

What do you mean by how exactly? integration of ramp is indeed a parabola.. example y=mx, integration of y=integration(mx)=(mx^2/2) which is indeed a parabola's equation..

soko loko

soko loko (view profile)

on 20 Dec 2013
Thank you. What I dont understand is what equation is Simulink solving since only values are entereing to the integrator and not an equation.
ES

ES (view profile)

on 20 Dec 2013
You dont need an equation to integrate. As I said before, integration is merely area under curve. suppose your sample time is 0.1 seconds, so your time signal is [0,0.1,0.2,0.3,0.4,...]. Your Actual Signal may be [0,4,2.3,-3.4,3,...]. corresponding to the time values defined above. lets assume t1=time=0; t2=time=0.1; dt=t2-t1=0.1; signal has changed from 0.4 t0 2.3. This region is almost a trapezoid. area under this curve is a the area of trapezium within these lines(x=0 [for y-axis or t1=0],y=0[for x-axis], x=0.1 [for t2=0.1] and y=mx+c where m=2.3/0.4 indicating slope].. Thus the total area is calculated as an summation of such tiny areas.
Now what I have described above is simple, it is called trapezoidal integration. The normal integration is similar in concept but more continuous and more generic.
soko loko

soko loko (view profile)

on 20 Dec 2013
Thank you for the explanation!. I was able to reproduce the behavior of the integrator block in Excel using the Euler method. By the way, speaking generally, what method is best the trapezoidal or Euler method?