th2mod, theta format (Model Predictive Control Toolbox)

Converts a SISO or MISO model from the theta format (as used in the System Identification Toolbox) to one in the MPC mod format. Can also combine such models to form a MIMO system.

Syntax

umod = th2mod(th) 
[umod,emod] = th2mod(th1,th2,...,thN)

Description
The System Identification Toolbox allows you to identify single-input, single-output (SISO) and multi-input, single-output (MISO) transfer functions from data. The MISO form relating an output, y, to m inputs, u1 to um, and a noise input, e, is:

where A, Bi, C, D, and Fi are polynomials in the forward-shift operator, z.

The System Identification Toolbox automatically stores such models in a special format, the theta format. See the System Identification Toolbox User's Guide for details.

th2mod converts one or more MISO theta models into the MPC mod format, which you can then use with the MPC Toolbox functions. If you supply a single input argument, th, and a single output argument, umod, then umod will model the response of a single output, y, to m inputs, u1 to um, where m

1. The value of m depends on the number of inputs included in the input model, th. Note that umod will reflect the values of the A(z), B(z), and F(z) polynomials in eq. 1.

If you supply a second output argument, emod, it will model the response of y to the noise, e, i.e., the A(z), C(z) and D(z) polynomials in eq. 1.

If you supply p input models (1

8), tfd2mod assumes that they define a MIMO system in the following form:

The p output variables have independent noise inputs. In this case, each of the p input models must include the same number of inputs, m. The p outputs are arranged in parallel in the resulting umod output model (and the emod model, if used).

If the th models are auto-regressive (i.e., m = 0), then umod will be set to an empty matrix and only emod will be nonempty.

Example
The following commands create three SISO theta models using the mktheta command (System Identification Toolbox), then converts them to the equivalent mod form:

th1=mktheta([1 0 -.2],[0 0 -1]);
th2=mktheta([1 -.8 .1],[0 -.5 .3],1,1,1);
th3=mktheta([1 -.2],[0 1],[1 2 0],[1 -1.2 .3], 1);
[umod,emod]=th2mod(th1,th2,th3)

The results are:

umod =
1.0000    5.0000    1.0000         0         0    3.0000         0
   NaN         0    0.2000         0         0         0    1.0000
     0    1.0000         0         0         0         0         0
     0         0         0    0.8000   -0.1000         0    1.0000
     0         0         0    1.0000         0         0         0
     0         0         0         0         0    2.0000    1.0000
     0         0   -1.0000         0         0         0         0
     0         0         0   -0.5000    0.3000         0         0
     0         0         0         0         0    1.0000
emod =
 Columns 1 through 7 
1.0000    7.0000    3.0000         0         0    3.0000         0
   NaN         0    0.2000         0         0         0         0
     0    1.0000         0         0         0         0         0
     0         0         0    0.8000   -0.1000         0         0
     0         0         0    1.0000         0         0         0
     0         0         0         0         0    1.4000   -0.5400
     0         0         0         0         0    1.0000         0
     0         0         0         0         0         0    1.0000
     0         0    0.2000         0         0         0         0
     0         0         0    0.8000   -0.1000         0         0
     0         0         0         0         0    3.4000   -0.5400
  Columns 8 through 11 
     0         0         0         0
     0    1.0000         0         0
     0         0         0         0
     0         0    1.0000         0
     0         0         0         0
0.0600         0         0    1.0000
     0         0         0         0
     0         0         0         0
     0    1.0000         0         0
     0         0    1.0000         0
    0.0600         0         0    1.0000

Restriction
The System Identification Toolbox must be installed to use this function.

See Also
mod

tfd2step validmod