Solution 2.39a: Integrators vs Differentiators

[stanigator]

For the question (problem 2.39a) stated in the picture attached to this message, I don't understand why integrators should be used in favour of differentiator for the block diagram representing the differential equation system. Is this b/c of the nature of the differentiator electronics too susceptible to environmental noise?

 

[ranger]

In addition to what you mention of the susceptibility to noise, another point comes to mind. The differentiator would represent an unstable system with regards to certain types of bounded inputs. An example of this would be a step input. This input would result in the unbounded output with the characteristics of an impulse. That is, the derivative of a unit step, $u(t)$, is in fact the unit impulse function, $\delta(t)$:

$$\frac{du}{dt} = \delta(t)$$