Control systems block diagram: Valid or Invalid?

[cnh1995]

Homework Statement

I have been helping a friend who is preparing for a national level EE exam. While going through the previous year question papers for this exam, he found this question.

Relevant Equations

Standard block diagram reduction techniques

I got the answer by simplifying the block diagram using standard block diagram reduction techniques and a bit of algebraic manipulation.

However, in the summing block between 1/s and G(s), they are subtracting both C(s) and C(s)/s at the same time (despite having different units)!

As per my understanding, addition/subtraction of two quantities is allowed only when their units are same. In the above diagram, C(s) and C(s)/s have different units and cannot be subtracted as shown in the diagram.

Am I missing something here or is the question actually incorrect?

Thanks in advance!

 

[Baluncore]

Am I missing something here or is the question actually incorrect?

The graph shows a signal path, let's call it voltage, with processes acting on the signal voltage. Those processes are time delays and arithmetic, that probably result in negative feedback.
1/s represents an integrator in the Laplace domain.

 

[cnh1995]

The graph shows a signal path, let's call it voltage, with processes acting on the signal voltage. Those processes are time delays and arithmetic, that probably result in negative feedback.
1/s represents an integrator in the Laplace domain.

Thanks for the response!

Suppose C(s) is a voltage signal.
In the diagram below, the blue feedback path directly goes to the summing block, indicating a voltage signal subtraction.

But the red feedback path also goes to the summing block and it is not a voltage signal (it is voltage* 1/s, or a flux signal more appropriately)

So this does not look like a valid block diagram to me.

 

[DaveE]

You might think of this diagram as an ODE. There's nothing wrong with saying $x(t) +\int{x(t)}\, dt ...$ in that context.

 

[Baluncore]

But the red feedback path also goes to the summing block and it is not a voltage signal (it is voltage* 1/s, or a flux signal more appropriately)

1/s, or s^-1 represents a pure integrator in the Laplace domain, it functions as a time delay or a low pass filter. It is not a 1/x reciprocal function.

 

[Filip Larsen]

Note that in practice you would have constant factors on each term that in principle convert to the "correct" unit, like for the often used PID control.