MATLAB CONTROL SYSTEM TOOLBOX 9 Guia do Utilizador descarregar pdf (Página 31)

100

101

Operations on LTI Models

1-11

Operations on LTI Models

You can perform simple matrix operations, such as addition, multiplication, or

concatenation on LTI models. See C hapter 3, “Operations on LTI M odels” for

more information. Thanks to MATLAB object-oriented programming

capabilities, these operations assume appropriatefunctionalities when applied

to LTI models. For example, addition performs a parallel interconnection. Type

tf(1,[1 0]) + tf([1 1],[1 2])% 1/s + (s+1)/(s+2)

and MATLAB responds:

Transfer function

s^2 + 2 s + 2

-------------

s^2 + 2 s

Multiplication performs a series interconnection. Type

2 * tf(1,[1 0])*tf([1 1],[1 2])% 2*1/s*(s+1)/(s+2)

and MATLAB responds

Transfer function:

2 s + 2

---------

s^2 + 2 s

If the operands are models of different types, t he resulting model t ype is

determined by precedence rules; see “Precedence Rules” on page 2-5 for more

information. State-space models have highest precedence while transfer

functions have lowest precedence. Hence the sum of a transfer function and a

state-space model is always a state-space model.

Other available operations include system inversion, transposition, and

pertransposition; see “Inversion and Related Operations” on page 3-13.

Matrix-like indexing for extracting subsystems is also supported; see

“Extracting and Modifying Subsystems” on page 3-5 for more information. For

instance, if

sys is a MIMO system with two inputs and three outputs,

sys(3,1)

1 2 ... 26 27 28 29 30 31 32 33 34 35 36 ... 648 649

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