idssdata

State-space data of identified system

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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,dx0] = idssdata(sys)
[A,B,C,D,K,___] = idssdata(sys,j1,...,jN)
[A,B,C,D,K,___] = idssdata(sys,'cell')

Description

[A,B,C,D,K] = idssdata(sys) returns the A,B,C,D and K matrices of the identified state-space model sys.

[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,dx0] = idssdata(sys) returns the uncertainties in the system matrices for sys.

[A,B,C,D,K,___] = idssdata(sys,j1,...,jN) returns data for the j1, ..., jn entries in the model array sys.

[A,B,C,D,K,___] = idssdata(sys,'cell') returns data for all the entries in the model array sys as separate cells in cell arrays.

Input Arguments

sys

Identified 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

Integer indices of N entries in the array sys of identified systems.

Output Arguments

A,B,C,D,K

State-space matrices that represent sys as:

x[k+1]=Ax[k]+Bu[k]+Ke[k];x[0]=x0;y[k]=Cx[k]+Du[k]+e[k];

If sys is an array of identified models, then A,B,C,D,K are multi-dimension arrays. To access the state-space matrix, say A, for the k-th entry of sys, use A(:,:,k).

x0

Initial state.

If sys is an idss or idgrey model, then x0 is the value obtained during estimation. It is also stored using the Report.Parameters property of sys.

For other model types, x0 is zero.

If sys is an array of identified models, then x0 contains a column for each entry in sys.

dA,dB,dC,dD,dK

Uncertainties associated with the state-space matrices A,B,C,D,K.

The uncertainty matrices represents 1 standard deviation of uncertainty.

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

dx0

Uncertainty associated with the initial state.

dx0 represents 1 standard deviation of uncertainty.

If sys is an array of identified models, then dx0 contains a column for each entry in sys.

Examples

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Open Live Script

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);
Open Live Script

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.

Open Live Script

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.

Open Live Script

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);
Open Live Script

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.

See Also

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Introduced in R2012a

System Identification Toolbox Documentation
Support