| System Identification Toolbox | |
nk and InputDelay
What's the difference between the properties nk and InputDelay? InputDelay is defined for all idmodel and idfrd objects, while nk is defined for idarx, idpoly as well as for 'Free' and 'Canonical' idss models. Both properties indicate a delay from the input channels to the outputs. For idarx, nk is a matrix, describing the delays in the different input/output channels, but otherwise both nk and InputDelay describe the delay from a certain input channel to all the output channels.
InputDelay is really a flag that tells the model to append the input delays as time lags, when the model is simulated, or as phase lags when the frequency functions are computed. The InputDelay does not show up when the model is represented in state-space form, nor as transfer functions, nor in the input-output polynomials. InputDelay can be used both for continuous and discrete time models. In the latter case, the InputDelay is measured in number of samples. Moreover InputDelay may assume negative values, in order to handle noncausal models.
The property nk, on the other hand, is a model structure property, requiring the model to contain the indicated number of delays whatever the parameter values. This means that the state-space matrices, the transfer functions, etc., will show these delays in an explicit manner. Consequently, nk is not defined for continuous-time models.
Otherwise the two properties can be used in the same way
give identical bode-plots (up to minor variations due to end-effects in the data records), while A1 and A2 are different. In fact while A1 is of size 4-by-4, the matrix A2 is of size 7-by-7, since three extra states are required to accommodate the extra 2+1 input delays.
Note that setting nk to a certain value for a given model gives a model structure that has the indicated delay for any parameter values. The impulse response of the model may however change (not only be shifted) by this assignment.
| | No Covariance | Linear Regression Models | |