1.16 Find closed loop transfer function from the open loop transfer function for a unity feedback

Problem: Given \[ L(s)=\frac {s}{(s+4)(s+5)}\] as the open loop transfer function, how to find \(G(s)\), the closed loop transfer function for a unity feedback?

Mathematica

Clear["Global`*"]; sys = TransferFunctionModel[ s/((s+4)(s+5)),s]
closedLoop = SystemsModelFeedbackConnect[sys];

 

The system wrapper can be removed in order to obtain the rational polynomial expression as follows

First[Flatten[closedLoop[[1,1]]/ closedLoop[[1,2]]]]

\[ \frac {s}{s^2+10 s+20} \]

 

Matlab

clear all; close all; s=tf('s'); sys=s/((s+4)*(s+5)); closedloop=feedback(sys,1)

Transfer function: s --------------- s^2 + 10 s + 20