delayest

Estimate time delay (dead time) from data

Syntax

nk = delayest(Data)
nk = delayest(Data,na,nb,nkmin,nkmax,maxtest)
nk = delayest(___,Name,Value)


Description

nk = delayest(Data) estimates time delay from the single-output data Data. data can be in the form of a timetable, a comma-separated pair of numeric matrices, or an iddata object. It can also be an idfrd object defining frequency-response data.

If data is a timetable, the software assumes that the last variable is the single output. If the timetable contains more variables than you want to use, or the single output channel is not the last timetable variable, select specific input and output channels for the delay estimation by specifying the InputName and OutputName name-value arguments.

If data is in the form of a numeric matrix pair u,y, then u must be an Ns-by-Nu matrix and y must be an Ns-length column vector. Here, Ns is the number of samples and Nu is the number of inputs. Since u,y contains no sample time information, also specify the name-value arguments Ts and TimeUnit

nk is returned as an integer or a row vector of integers, containing the estimated time delay in samples from the input(s) to the output in Data.

The estimate is based on a comparison of ARX models with different delays:

$$\begin{array}{l}y(t)+a_{1}y(t-1)+\mathrm{...}+a_{na}y(t-na)=\\ b_{1}u(t-nk)+\mathrm{...}+b_{nb}u(t-nb-nk+1)+e(t)\end{array}$$

nk = delayest(Data,na,nb,nkmin,nkmax,maxtest) specifies additional options. The integer na is the order of the A polynomial (default 2). nb is a row vector of length equal to the number of inputs, containing the order(s) of the B polynomial(s) (default all 2). nkmin and nkmax are row vectors of the same length as the number of inputs, containing the smallest and largest delays to be tested. Defaults are nkmin = 0 and nkmax = nkmin+20. If nb, nkmax, and/or nkmin are entered as scalars in the multiple-input case, all inputs will be assigned the same values. maxtest is the largest number of tests allowed (default 10,000).

nk = delayest(___,Name,Value) uses additional model options specified by one or more name-value arguments.

The available arguments consist of InputName and OutputName, which are the input and output channel names. Use these arguments especially when data is a timetable that has more variables than you want to use. Also use OutputName to identify the output channels when the timetable data contains more than one output variable. Otherwise, the software interprets only the last variable as an output channel.

For example, specify the input and output signal variable names using sys = delayest(data,'InputName',["u1","u3"],'OutputName',"y1").

Version History

Introduced before R2006a

R2022b: Time-domain estimation data is accepted in the form of timetables and matrices

Most estimation, validation, analysis, and utility functions now accept time-domain input/output data in the form of a single timetable that contains both input and output data or a pair of matrices that contain the input and output data separately. These functions continue to accept iddata objects as a data source as well, for both time-domain and frequency-domain data.