## Simulink Integrator block: how to

### 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.

### 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]=0; t2=time[0]=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?