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State-space model with identifiable parameters
sys = idss(A,B,C,D) creates a state-space model with identifiable parameters. A, B, C, and D are the initial values of the state-space matrices. By default, sys is discrete-time model with unspecified sampling time and no state disturbance element.
sys = idss(A,B,C,D,K,x0) creates a state-space model with initial state values given by the vector x0.
sys = idss(A,B,C,D,K,x0,Ts) creates a state-space model with sampling time Ts. Use Ts = 0 to create a continuous-time model.
sys = idss(___,Name,Value) creates a state-space model using additional options specified by one or more Name,Value pair arguments.
sys = idss(sys0) converts any dynamic system model, sys0, to idss model form.
An idss model represents a system as a continuous-time or discrete-time state-space model with identifiable (estimable) coefficients.
A state-space model of a system with input vector u, output vector y, and disturbance e takes the following form in continuous time:
In discrete time, the state-space model takes the form:
For idss models, the elements of the state-space matrices A, B, C, and D can be estimable parameters. The elements of the state disturbance K can also be estimable parameters. The idss model stores the values of these matrix elements in the a, b, c, d, and k properties of the model.
There are three ways to obtain an idss model.
Estimate the idss model based on input-output measurements of a system, using n4sid or ssest. These estimation commands estimate the values of the estimable elements of the state-space matrices. The estimated values are stored in the a, b, c, d, and k properties of the resulting idss model. The Report property of the resulting model stores information about the estimation, such as handling of initial state values and options used in estimation.
When you obtain an idss model by estimation, you can extract estimated coefficients and their uncertainties from the model using commands such as idssdata, getpar, or getcov.
Create an idss model using the idss command.
You can create an idss model to configure an initial parameterization for estimation of a state-space model to fit measured response data. When you do so, you can specify constraints on one or more of the state-space matrix elements. For example, you can fix the values of some elements, or specify minimum or maximum values for the free elements. You can then use the configured model as an input argument to an estimation command (n4sid or ssest) to estimate parameter values with those constraints.
Convert an existing dynamic system model to an idss model using the idss command.
To configure an idss model in a desired form, such as a companion or modal form, use state transformation commands such as canon and ss2ss.
A,B,C,D |
Initial values of the state-space matrices. For a system with N_{y} outputs, N_{u} inputs, and N_{x} states, specify initial values of the state-space matrix elements as follows:
Use NaN for any matrix element whose initial value is not known. |
K |
Initial value of the state disturbance matrix. Specify K as an N_{x}-by-N_{y} matrix. Use NaN for any matrix element whose initial value is not known. Default: N_{x}-by-N_{y} zero matrix. |
x0 |
Initial state values. Specify the initial condition as a column vector of N_{x} values. Default: N_{x} column vector of zeros. |
Ts |
Sampling time. For continuous-time models, Ts = 0. For discrete-time models, Ts is a positive scalar representing the sampling period expressed in the unit specified by the TimeUnit property of the model. To denote a discrete-time model with unspecified sampling time, set Ts = -1. Default: –1 (discrete-time model with unspecified sampling time) |
sys0 |
Dynamic system. Any dynamic system to convert to an idss model:
For the syntax sys = idss(sys0,'split'), sys0 must be a numeric (non-identified) tf, zpk, or ss model object. Also, sys0 must have at least as many inputs as outputs. Finally, the subsystem sys0(:,Ny+1:Ny+Nu) must contain a non-zero feedthrough term (the subsystem must be biproper). |
Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.
Use Name,Value arguments to specify additional properties of idss models during model creation. For example, idss(A,B,C,D,'InputName','Voltage') creates an idss model with the InputName property set to Voltage.
Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.
idss objects properties include:
<argumentlist> </argumentlist>idgrey | idpoly | idproc | idssdata | idtf | n4sid | pem | ssest | ssestOptions | translatecov