Control Systems/Block Diagrams

Systems in Series

Series Transfer Functions

---

28.08.2021

Control Systems/Block Diagrams - Wikibooks, open books for an open world

https://en.wikibooks.org/wiki/Control_Systems/Block_Diagrams

2/5

[Series state equation]

[Series output equation]

We can represent our system in the frequency domain as:

If we have two systems in series (say system F and system G), where the output of F is the input to system G,

we can write out the state-space equations for each individual system.

System 1:

System 2:

And  we  can  write  substitute  these  equations  together  form  the  complete  response  of  system  H,  that  has

input u, and output y

G

:

Blocks may not be placed in parallel without the use of an adder. Blocks connected by an adder as shown

above have a total transfer function of:

Since  the  Laplace  transform  is  linear,  we  can  easily  transfer  this  to  the  time  domain  by  converting  the

multiplication to convolution:

The state-space equations, with non-zero A, B, C, and D matrices conceptually model the following system: