Getting Started | ![]() ![]() |
Constructing MIMO Transfer Functions
MIMO transfer functions are two-dimensional arrays of elementary SISO transfer functions. There are two ways to specify MIMO transfer function models:
tf
with cell array arguments
Concatenation of SISO Models
Consider the following single-input, two-output transfer function.
You can specify by concatenation of its SISO entries. For instance,
This syntax mimics standard matrix concatenation and tends to be easier and more readable for MIMO systems with many inputs and/or outputs. See Model Interconnection Functions in "Creating and Manipulating Models" online for more details on concatenation operations for LTI systems.
Using the tf Function with Cell Arrays
Alternatively, to define MIMO transfer functions using tf
, you need two cell arrays (say, N
and D
) to represent the sets of numerator and denominator polynomials, respectively. See the Structures and Cell Arrays in the MATLAB online documentation for more details on cell arrays.
For example, for the rational transfer matrix , the two cell arrays
N
and D
should contain the row-vector representations of the polynomial entries of
You can specify this MIMO transfer matrix by typing
The Control System Toolbox responds with
Transfer function from input to output... s - 1 #1: ----- s + 1 s + 2 #2: ------------- s^2 + 4 s + 5
Notice that both N
and D
have the same dimensions as H. For a general MIMO transfer matrix , the cell array entries
N{i,j}
and D{i,j}
should be row-vector representations of the numerator and denominator of , the
entry of the transfer matrix
.
![]() | MIMO Example: Jet Transport Aircraft | Accessing I/O Pairs in MIMO Systems | ![]() |