I have a question regarding a control loop system which is subject to disturbance, unfortunately I missed a couple of lectures on the subject and now am scratching my head as to how to do it. The loop is shown below.

enter image description here

\$D(s)=\frac{K}{s+10},\$ \$M_p(s)=\frac{M_o}{s},\$ \$G(s)=\frac{s+3}{s^2+4s+5},\$ \$I(s)=\frac{1}{s}\$

\$K_t\$ isn't used for now so that can be ignored. \$M_p\$ is a step input disturbance.

Anyway, the question in hand is asking for the steady state error assuming the system to be stable, and I am simply struggling with getting the initial T.F. in order to get this.
It is given that I need to determine \$\frac{\theta(s)}{M_p(s)}\$ and furthermore am given that this is: $$\frac{(s+3)(s+10)}{s(s+10)(s^2+4s+5)+K(s+3)}$$

But I baffled as to how to get to this result, any ideas?
After this I know what to do but I just want to know how to get to this stage in the first place.

  • 1
    \$\begingroup\$ Forward path is G(s)I(s), feedback path is D(s). Assume \$\theta_{ref}=0\$. To see this, re-draw the block diagram with the input signal of interest, \$M_p\$, on the left. \$\endgroup\$
    – Chu
    Commented Apr 28, 2016 at 9:31
  • \$\begingroup\$ \$\theta=G\cdot I(M_p+D\cdot (\theta_{ref}-\theta ))\$, can you take it from here? \$\endgroup\$ Commented Apr 28, 2016 at 9:55
  • \$\begingroup\$ @VladimirCravero Yeah I can get that I struggle to get \$\frac{\theta}{M_p}\$ on its own though... \$\endgroup\$
    – MrPhooky
    Commented Apr 28, 2016 at 10:10
  • 2
    \$\begingroup\$ Hint 2: \$\theta\cdot(1+D\cdot G\cdot I)=M_p\cdot G\cdot I\$, using \$\theta_{ref}=0\$. If you can't get it from here you need to exercise on algebra, not control systems. \$\endgroup\$ Commented Apr 28, 2016 at 10:20
  • \$\begingroup\$ Then plug in all the other formula! \$\endgroup\$
    – Andy aka
    Commented Apr 28, 2016 at 10:24

1 Answer 1


Just redraw the diagram like this: -

enter image description here

I've used Y instead of theta for my own convenience.

You get Y = I.G(M - Y.D) which reduces to \$\dfrac{Y}{M} = \dfrac{1}{\frac{1}{G.I} + D}\$

I can see that if you plug the expressions for G, I and D in you get the correct answer.


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.