"Principles of Automation" Module2 transfer function and block diagram algebra

★★★ : Must see before the exam

★ : More important

1 transfer function

1.1 Form of transfer function

Evan Form (First Polynomial)

Second order systems use this form

Bode form (tail one polynomial)

First-order systems often use this form

For a high-order systematized second-order system, it is necessary to form Bode form before discarding the real poles

★2.2 Define important transfer functions

Open loop transfer function

Open loop transfer function is a concept about system transfer function. Generally speaking, it has two interpretations in automatic control system.

The first describes the dynamic properties of open loop systems (systems with no feedback). It is the ratio of the Laplace transform of the system output to the Laplace transform of the system input in an open loop system, that is, the open loop transfer function C(s)/R(s) of the system.

The second is in the closed-loop system: as shown in figure (typical structure of feedback control system), it is assumed that the system has single input R(s) and single output C(s), forward channel transfer function G1(s)G2(s), and feedback (reverse channel) is negative feedback H(s) : The open loop transfer function of the system can be obtained by multiplying the forward channel transfer function and the feedback channel transfer function. Then the open loop transfer function is equivalent to B(s)/R(s), namely H(s)G1(s)G2(s). The “disconnect” mentioned above refers to the disconnect of the feedback signal into the node (the output end of the feedback channel).

In this case, the open loop transfer function is for the closed loop system, not for the open loop system.