How is the transfer function determined for a PID controller

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I'm reading a tutorial on PID controller, and the transfer function for a mass-spring damper system is given as follows:
where m = 1 , b = 10, k = 20. If a proportional gain is added to the controller, the new tranfser function becomes:
How is the new transfer function derived?

Accepted Answer

Sulaymon Eshkabilov
Sulaymon Eshkabilov on 9 Jul 2021
T = tf(Kp, [1 10 20+Kp]);

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