How to find closed loop transfer function and use it to identify τ and k?

I have to answer a few questions on transfer functions using Matlab. The first question, which I solved without Matlab, gives a time response graph for an LR circuit, and asks me to find the first order transfer function. I ended up with G(s) = 2/(s+2). The next question says "determine the CLTF if the system has unity negative feedback and calculate the new values for τ and k. I'm stuck with this part - I know that the general CLTF for negative feedback is G/(1+GH), and I know that H = 1 because it is a unity system.

This is as far as I can get, so any help with this is appreciated! Parts I'm struggling with are:

• Is G(s) in the negative feedback system the same as the G(s) I worked out already? These two questions are part of the same question but I can't tell if they follow on from each other or if they're separate. This is all the info the questions give so I can't think what else G(s) should be in the feedback system
• I obtained a CLTF for the system using G(s) = 2/(s+2) and H(s) = 1, and got CLTF = 2/(s+4), but as I sid above I'm not sure I'm using the correct value for G(s), because when I try to work backwards to find τ and k, I get the same values as before
• Most importantly - if these values are wrong, which I believe they are, how do I use Matlab to obtain new values for τ and k?

Thanks!

[Ameer Hamza]

This question is not directly related to MATLAB and more appropriate for a forum relaetd to control system, e.g., https://engineering.stackexchange.com/. You will have a better chance of getting a response there.

Answer 1

[Raynier Suresh]

To find closed loop transfer function from an open loop transfer function (G) considering a negative feedback system you can use “feedback(G,1)”. To find K and T for your system you can compare the closed loop equation with the general form K/(ST+1) since your system is a first order system. To get more information about your open loop or closed loop system for a step input use “stepinfo(sys)”, where “sys” is the transfer function.

Referring to the following links might be useful :

Feedback : https://www.mathworks.com/help/control/ref/feedback.html

Stepinfo : https://www.mathworks.com/help/control/ref/stepinfo.html