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Construct Linear Time Invariant (LTI) Models

2-9

Construct Linear Time Invariant (LTI) Models

In this section...

“Transfer Function Models” on page 2-9

“Zero/Pole/Gain Models” on page 2-10

“State-Space Models” on page 2-10

“LTI Object Properties” on page 2-12

“LTI Model Characteristics” on page 2-15

Model Predictive Control Toolbox software supports the same LTI model formats as does

Control System Toolbox™ software. You can use whichever is most convenient for your

application. It's also easy to convert from one format to another.

The following topics describe the three model formats and the commands used to

construct them:

• “Transfer Function Models” on page 2-9

• “Zero/Pole/Gain Models” on page 2-10

• “State-Space Models” on page 2-10

• “LTI Object Properties” on page 2-12

• “Specify Multi-Input Multi-Output (MIMO) Plants” on page 2-17

• “LTI Model Characteristics” on page 2-15

For more details, see the Control System Toolbox documentation.

Transfer Function Models

A transfer function (TF) relates a particular input/output pair. For example, if u(t) is a

plant input and y(t) is an output, the transfer function relating them might be:

Y s

U s

G s

s s

( )

= =

+ +

1 5

This TF consists of a numerator polynomial, s+2, a denominator polynomial, s

+s+10, and

a delay, which is 1.5 time units here. You can define G using Control System Toolbox tf

function:

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