Get input/output delay information for idnlarx model structure
DELAYS = getDelayInfo(MODEL)
DELAYS = getDelayInfo(MODEL,TYPE)
DELAYS = getDelayInfo(MODEL) obtains the maximum delay in each input and output variable of an idnlarx model.
DELAYS = getDelayInfo(MODEL,TYPE) lets you choose between obtaining maximum delays across all input and output variables or maximum delays for each output variable individually. When delays are obtained for each output variable individually a matrix is returned, where each row is a vector containing ny+nu maximum delays for each output variable, and:
ny is the number of outputs of MODEL.
nu is the number of inputs of MODEL.
Delay information is useful for determining the number of states in the model. For nonlinear ARX models, the states are related to the set of delayed input and output variables that define the model structure (regressors). For example, if an input or output variable p has a maximum delay of D samples, then it contributes D elements to the state vector:
p(t-1), p(t-2), ...p(t-D)
The number of states of a nonlinear ARX model equals the sum of the maximum delays of each input and output variable. For more information about the definition of states for idnlarx models, see Definition of idnlarx States
getDelayInfo accepts the following arguments:
MODEL: idnlarx model.
TYPE: (Optional) Specifies whether to obtain channel delays 'channelwise' or 'all' as follows:
'all': Default value. DELAYS contains the maximum delays across each output (vector of ny+nu entries, where [ny, nu] = size(MODEL)).
'channelwise': DELAYS contains delay values separated for each output (ny-by-(ny+nu) matrix).
DELAYS: Contains delay information in a vector of length ny+nu arranged with output channels preceding the input channels, i.e., [y1, y2,.., u1, u2,..].
In the following example you create a 2-output, 3-input nonlinear ARX model, then verify the number of delays using getDelayInfo.
Create an idnlarx model.
M = idnlarx([2 0 2 2 1 1 0 0; 1 0 1 5 0 1 1 0],... 'linear');
Compute the maximum delays for each output variable individually.
Del = getDelayInfo(M,'channelwise') Del = 2 0 2 1 0 1 0 1 5 0
The matrix Del contains the maximum delays for the first and second output of the model M. You can interpret the contents of matrix Del as follows:
In the dynamics for the output 1 (y1) of model M, the maximum delays for each input/output channel are as follows: y1: 2, y2: 0, u1: 2, u2: 1, u3:0.
Similarly, in the dynamics for the output 2 (y2) of the model, the maximum delays in channels y1, y2, u1, u2, u3 are 1, 0, 1, 5, and 0 respectively.
You can find the maximum delays for all the input and output variables in the order (y1, y2, u1, u2, u3) by executing the command
Del = 2 0 2 5 0
Note: The maximum delay across all output equations can be obtained by executing MaxDel = max(Del,,1). Since input u2 has 5 delays (the 4th entry in Del, there are 5 terms corresponding to u5 in the state vector ((u5(t-1), ...u5(t-5). Applying this definition to all I/O channels, the complete state vector for model M becomes:
X(t) = [y1(t-1), y1(t-2), u1(t-1), u1(t-2), u2(t-1), u2(t-2), u2(t-3), u2(t-4), u2(t-5)]