Creating and Manipulating Models

Building LTI Arrays Using tf, zpk, ss, and frd

You can also build LTI arrays using the tf, zpk, ss, and frd constructors. You do this by using multidimensional arrays in the input arguments for these functions.

Specifying Arrays of TF models tf

For TF models, use

• sys = tf(num,den)
  

where

• Both num and den are multidimensional cell arrays the same size as sys (see "size and ndims" on page 4-9).
• sys(i,j,n1,...,nK) is the (i, j) entry of the transfer matrix for the model located in the position of the array.
• num(i,j,n1,...,nK) is a row vector representing the numerator polynomial of sys(i,j,n1,...,nK).
• den(i,j,n1,...,nK) is a row vector representing denominator polynomial of sys(i,j,n1,...,nK).

See "MIMO Transfer Function Models" on page 2-10 for related information on the specification of single TF models.

Specifying Arrays of ZPK Models Using zpk

For ZPK models, use

• sys = zpk(zeros,poles,gains)
  

where

• Both zeros and poles are multidimensional cell arrays whose cell entries contain the vectors of zeros and poles for each I/O pair of each model in the LTI array.
• gains is a multidimensional array containing the scalar gains for each I/O pair of each model in the array.
• The dimensions (and their lengths) of zeros, poles, and gains, determine those of the LTI array, sys.

Specifying Arrays of SS Models Using ss

To specify arrays of SS models, use

• sys = ss(a,b,c,d)
  

where a, b, c, and d are real-valued multidimensional arrays of appropriate dimensions. All models in the resulting array of SS models have the same number of states, outputs, and inputs.

Note    You cannot use the ss constructor to build an array of state-space models with different numbers of states. Use stack to build such LTI arrays.

The Size of LTI Array Data for SS Models

The size of the model data for arrays of state-space models is summarized in the following table.

Data	Size (Data)
a
b
c
d

where

• is the maximum of the number of states in each model in the array.
• is the number of inputs in each model.
• is the number of outputs in each model.
• are the lengths of the array dimensions.

Specifying Arrays of FRD Models Using frd

To specify a K-dimensional array of p-output, m-input FRD models for which are the lengths of the array dimensions, use

• sys = frd(response,frequency,units)
  

where

• frequency is a real vector of n frequency data points common to all FRD models in the LTI array.
• response is a p-by-m-by-n-by--by--by- complex-valued multidimensional array.
• units is the optional string specifying 'rad/s' or 'Hz'.

Note that for specifying an LTI array of SISO FRD models, response can also be a multidimensional array of 1-by-n matrices whose remaining dimensions determine the array dimensions of the FRD.

Building LTI Arrays Using the stack Function

Indexing Into LTI Arrays