idsim (System Identification Toolbox)

Simulate systems specified in theta format.

y = idsim([u e],th)
[y, ysd] = idsim(u,th)

Description

th describes an arbitrary model in the theta format. idsim returns y containing the simulated output, corresponding to the input sequence u (one column for each input) and the noise e. If e is omitted, a noise-free simulation is obtained.

The noise-sequence e is scaled by

, where

is the noise variance (loss function) as specified by th. To achieve the correct noise effect, give e zero mean and unit variance.

For multi-output systems simulated with noise, e should have as many columns as the numbers of outputs. The noise is again scaled using the noise covariance matrix in th.

The second output argument is the standard deviation of the simulated output. This option is however not available for state-space models.

If th is a continuous-time model, it is first converted to discrete time with sampling interval abs(T). See "Some Special Topics" on page 3-68 in the User's Guide.

Examples

Simulate a given system th0 (for example created by poly2th):

e = randn(500,1);
u = idinput(500,'prbs');
y = idsim([u e],th0);

Validate a model by comparing a measured output y with one simulated using an estimated model th:

yh = idsim(u,th);
plot([y yh])

Algorithm

In case the model is of input-output type, idsim uses the MATLAB filter function. For state-space models, it uses ltitr.