0
$\begingroup$

There is a system with two controllers in series having the transfer functions G1(s) and G2(s) which is separated by a summing point through which the disturbance D(s) enters the system. The output from the 2nd controller is fed back through another element having the transfer function H(s). The closed loop transfer function CD is given by the formula CD/D(s) = G2(s) / (1 + G1(s) * G2(s) * H(s)).

Can someone help me figure out how we get to this final formula.enter image description here

I included the diagram too. It is from the book Modern Control Engineering by Katsuhiko Ogata.

$\endgroup$

1 Answer 1

0
$\begingroup$

Assume $R(s) = 0$. Now the left most summing junction can be removed from the diagram taking care to shift the -ve sign to the remaining summing junction.

The above assumption is valid since transfer functions are derived for SISO systems. So, the other inputs are allowed to be assumed zero (or constant as the case may be).

Then redraw the diagram with $G_2$ in $\text{forward}$ path and both $H(s)$ and $G_1(s)$ in $\text{feedback}$ path (with negative feedback).

Now the closed loop transfer function is given by $$ \frac{\text{forward}}{1 + \text{forward} \cdot \text{feedback}} $$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.