Control Systems/Block Diagrams

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28.08.2021

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

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Control Systems/Block Diagrams

When designing or analyzing a system, often it is useful to model the system graphically. Block Diagrams

are a useful and simple method for analyzing a system graphically. A "block" looks on paper exactly what it

means:

When two or more systems are in series, they can be combined into a single representative system, with a

transfer function that is the product of the individual systems.

If we have two systems, f(t) and g(t), we can put them in series with one another so that the output of system

f(t) is the input to system g(t). Now, we can analyze them depending on whether we are using our classical

or modern methods.

If we define the output of the first system as h(t), we can define h(t) as:

Now, we can define the system output y(t) in terms of h(t) as:

We can expand h(t):

But, since convolution is associative, we can re-write this as:

Our system can be simplified therefore as such:

If two or more systems are in series with one another, the total transfer function of the series is the product

of all the individual system transfer functions.

In the time-domain we know that:

But, in the frequency domain we know that convolution becomes multiplication, so we can re-write this as: