# How do I get the closed-loop transfer function of the system, fitted with a PID controller, if the input valve has a transfer function?

How do I get the closed-loop transfer function of the system, fitted with a PID controller, if the input valve has a transfer function given by:

$$\frac{Q(s)}{P(s)} = \frac{Kv}{(Tv*S+I)}$$

Where Kv is a constant of proportionality between the steady-state discharge and the pressure on the input valve. Tv is the time constant of the input valve.

I'm not sure how I'm meant to use the input valve transfer function to work out the closed-loop system transfer function.

Could anyone help explain the steps?

• Voting to close as too broad, because this is the result you get about 1/3 of the way through a year-long introductory course in control theory. A short answer simply wouldn't make sense. – TimWescott Oct 14 '19 at 19:46
• I hadn't done a year long course only six weeks and I wasn't taught this! – MelanieW403 Oct 14 '19 at 19:50
• I would appreciate at least some basic idea understanding this part of control theory! – MelanieW403 Oct 14 '19 at 19:51
• First: I feel for you, particularly if this task has been thrust upon you with a time limit. Second, unfortunately, this sort of open-ended question is not a good fit for Stackexchange. They want nice convenient question/answer pairs; this isn't going to work that way. You're going to get an answer that you don't understand, you'll need clarification, etc. I suggest a different venue -- reddit.com/r/controltheory has a crew that will help you, particularly if you start by declaring whether you're doing homework or work-work, and long in-depth threads are not frowned upon. – TimWescott Oct 14 '19 at 19:57
• Thanks, Ill definetely check it out! – MelanieW403 Oct 14 '19 at 20:01