idssdata

State-space data for identified system

Syntax

[A,B,C,D,K] = idssdata(sys)

[A,B,C,D,K,x0] = idssdata(sys)

[A,B,C,D,K,x0,dA,dB,dC,dD,dK] = idssdata(sys)

[A,B,C,D,K,x0,dA,dB,dC,dD,dK,dx0] = idssdata(sys)

[___] = idssdata(sys,j1,...,jN)

[___] = idssdata(sys,'cell')

Description

[A,B,C,D,K] = idssdata(sys) returns the A, B, C, D, and K state-space matrices for the identified model sys. If sys is not an idss or idgrey model, then it is first converted to an idss model.

[A,B,C,D,K,x0] = idssdata(sys) returns the initial state values, x0.

[A,B,C,D,K,x0,dA,dB,dC,dD,dK] = idssdata(sys) returns the uncertainties in the system matrices.

[A,B,C,D,K,x0,dA,dB,dC,dD,dK,dx0] = idssdata(sys) returns the uncertainties in the initial states.

[___] = idssdata(sys,j1,...,jN) returns data for the j1,...,jN entries in the model array sys. Use this syntax when sys is a model array.

[___] = idssdata(sys,'cell') returns data for all the entries in the model array sys as separate cells in cell arrays. Use this syntax when sys is a model array.

Examples

Obtain Identified State-Space Matrices

Obtain the identified state-space matrices for a model estimated from data.

Identify a model using data.

load icEngine.mat
data = iddata(y,u,0.04);
sys = n4sid(data,4,'InputDelay',2);

data is an iddata object representing data sampled at a sampling rate of 0.04 seconds.

sys is an idss model representing the identified system.

Obtain identified state-space matrices of sys.

[A,B,C,D,K] = idssdata(sys);

Obtain Initial State of Identified Model

Obtain the initial state associated with an identified model.

Identify a model using data.

load icEngine.mat
data = iddata(y,u,0.04);
sys = n4sid(data,4,'InputDelay',2);

data is an iddata object representing data sampled at a sampling rate of 0.04 seconds.

sys is an idss model representing the identified system.

Obtain the initial state associated with sys.

[A,B,C,D,K,x0] = idssdata(sys);

A, B, C, D and K represent the state-space matrices of the identified model sys. x0 is the initial state identified for sys.

Obtain Uncertainty Data of State-Space Matrices of Identified Model

Obtain the uncertainty matrices of the state-space matrices of an identified model.

Identify a model using data.

load icEngine.mat
data = iddata(y,u,0.04);
sys = n4sid(data,4,'InputDelay',2);

data is an iddata object representing data sampled at a sampling rate of 0.04 seconds.

sys is an idss model representing the identified system.

Obtain the uncertainty matrices associated with the state-space matrices of sys.

[A,B,C,D,K,x0,dA,dB,dC,dD,dx0] = idssdata(sys);

dA, dB, dC, dD and dK represent the uncertainty associated with the state-space matrices of the identified model sys. dx0 represents the uncertainty associated with the estimated initial state.

Obtain State-Space Matrices for Multiple Identified Models

Obtain the state-space matrices for multiple models from an array of identified models.

Identify multiple models using data.

load icEngine.mat
data = iddata(y,u,0.04);
sys2 = n4sid(data,2,'InputDelay',2);
sys3 = n4sid(data,3,'InputDelay',2);
sys4 = n4sid(data,4,'InputDelay',2);
sys = stack(1,sys2,sys3,sys4);

data is an iddata object representing data sampled at a sampling rate of 0.04 seconds.

sys is an array of idss models. The first entry of sys is a second-order identified system. The second and third entries of sys are third- and fourth-order identified systems, respectively.

Obtain the state-space matrices for the first and third entries of sys.

[A,B,C,D,K,x0] = idssdata(sys,1);
[A,B,C,D,K,x0] = idssdata(sys,3);

Obtain State-Space Matrices for Identified Model as Cell Array

Obtain the state-space matrices of an array of identified models in cell arrays.

Identify multiple models using data.

load icEngine.mat
data = iddata(y,u,0.04);
sys3 = n4sid(data,3,'InputDelay',2);
sys4 = n4sid(data,4,'InputDelay',2);
sys = stack(1,sys3,sys4);

data is an iddata object representing data sampled at a sampling rate of 0.04 seconds.

sys is an array of idss models. The first entry of sys is a third-order identified system and the second entry is a fourth-order identified system.

Obtain the state-space matrices of sys in cell arrays.

[A,B,C,D,K,x0] = idssdata(sys,'cell');

A, B, C, D and K are cell arrays containing the state-space matrices of the individual entries of the identified model array sys. x0 is a cell array containing the estimated initial state of the individual entries of the identified model array sys.

Input Arguments

sys — Identified linear model

idss | idtf | idproc | idpoly | idgrey | model array

Identified linear model, specified as one of the following model objects.

• idss — State-space model

• idtf — Transfer function model

• idproc — Process model

• idpoly — Polynomial model

• idgrey — Linear grey-box model

If sys is not an identified state-space model (idss or idgrey), then it is first converted to an idss model. This conversion results in a loss of the model uncertainty information.

sys can be an array of identified models.

j1,...,jN — Model array indices

integers

Model array indices, specified as integers. Specify up to N indices, where N is the number of models in sys.

Output Arguments

A, B, C, D, K — State-space matrices

arrays | cell array

State-space matrices that represent sys as:

$$\begin{array}{l}x[k+1]=Ax[k]+Bu[k]+Ke[k];x[0]=x0;\\ y[k]=Cx[k]+Du[k]+e[k];\end{array}$$

If sys is an array of identified models and you do not specify the 'cell' input option, then A, B, C, D, and K are multi-dimensional arrays. To access a state-space matrix, such as A, for the ith entry in sys, use A(:,:,i).

If sys is an array of identified models and you specify the 'cell' input option, then A, B, C, D, and K are cell arrays with one entry for each model in sys.

x0 — Initial states

column vector | matrix | cell array

Initial states, returned as a column vector or array.

If sys is an idss or idgrey model, then x0 contains the initial state values obtained during estimation. These values are stored in the Report.Parameters property of sys.

For other model types, x0 is zero.

If sys is an array of identified models and you do not specify the 'cell' input option, then x0 contains one column for each entry in sys.

If sys is an array of identified models and you specify the 'cell' input option, then x0 is a cell array with one entry for each model in sys.

dA, dB, dC, dD, dK — Uncertainties associated with the state-space matrices

arrays | cell arrays

Uncertainties associated with the state-space matrices A, B, C, D, and K. The uncertainty matrices represent one standard deviation of uncertainty.

If sys is an array of identified models, then dA, dB, dC, dD, and dK are multi-dimensional arrays. To access the state-space matrix, say A, for the k-th entry of sys, use A(:,:,k).

If sys is an array of identified models and you do not specify the 'cell' input option, then dA, dB, dC, dD, and dK are multi-dimensional arrays. To access a state-space matrix, such as dA, for the ith entry in sys, use dA(:,:,i).

If sys is an array of identified models and you specify the 'cell' input option, then dA, dB, dC, dD, and dK are cell arrays with one entry for each model in sys.

dx0 — Uncertainties associated with the initial states

column vector | matrix | cell array

Uncertainty associated with the initial states, returned as a column vector or array. dx0 represents one standard deviation of uncertainty.

If sys is an array of identified models and you do not specify the 'cell' input option, then dx0 contains one column for each entry in sys.

If sys is an array of identified models and you specify the 'cell' input option, then dx0 is a cell array with one entry for each model in sys.

Version History

Introduced in R2012a