Discrete Stochastic State-Space (Internal) (Control Design Toolkit)
Simulates a discrete-time stochastic state-space system model using internally-generated random samples of Gaussian-distributed noise vectors.
This function generates samples of the noise vectors using the model you wire to the Second-Order Statistics Noise Model input of this function.
| Dialog Box Options |
| Block Diagram Inputs |
| Block Diagram Outputs |
Dialog Box Options
| Parameter | Description |
|---|---|
| Initialize | Is TRUE if you want to restart the calculation from any initial values you provide. Initialize is FALSE if you do not want to restart this function. The default value is FALSE. |
| Input u(k) | Specifies the control action this function applies to the model. If you specify a vector of zeros for Input u(k) or do not wire a value to this parameter, this function does not apply a control action. |
| Stochastic State-Space Model | Specifies a mathematical representation of a stochastic system. You can construct a stochastic state-space model using the CD Construct Stochastic Model VI. |
| Second-Order Statistics Noise Model | Specifies a mathematical representation of the noise model of a stochastic state-space model. You can create a noise model using the CD Construct Noise Model VI. |
| Initial State x(0) | Specifies the initial state of the model. If you do not specify a value for this parameter, this function assumes an initial state of 0. |
| error in | Describes error conditions that occur before this VI or function runs. The default is no error. If an error occurred before this VI or function runs, the VI or function passes the error in value to error out. If an error occurs while this VI or function runs, it runs normally and sets its own error status in error out. Use the Simple Error Handler or General Error Handler VIs to display the description of the error code. Use error in and error out to check errors and to specify execution order by wiring error out from one node to error in of the next node. |
| Parameters | Lists all the parameters associated with this function. Select a parameter from this list to configure the parameter. When you select a parameter, the parameter and its associated Parameter source control appear in the Parameter Information section of the configuration dialog box. |
| Preview | Displays a graphical preview, if available, of the function output or configuration. |
| Parameter Information | Contains the parameters you can configure for this function. You must select a parameter from the Parameters list to make that parameter and its associated Parameter source control visible in the Parameter Information section of the configuration dialog box. |
| Parameter Source | Specifies whether you configure this parameter using the Configuration Dialog Box or a Terminal on the block diagram. The default value is Configuration Dialog Box. If you select Terminal, LabVIEW displays an input for that parameter on the block diagram, and you can wire values to that input to configure this function programmatically. If you select Configuration Dialog Box, LabVIEW removes that input from the block diagram. You then must set the value for this parameter inside the configuration dialog box. |
Block Diagram Inputs
| Parameter | Description |
|---|---|
| Initialize | Is TRUE if you want to restart the calculation from any initial values you provide. Initialize is FALSE if you do not want to restart this function. The default value is FALSE. |
| Input u(k) | Specifies the control action this function applies to the model. If you specify a vector of zeros for Input u(k) or do not wire a value to this parameter, this function does not apply a control action. |
| Stochastic State-Space Model | Specifies a mathematical representation of a stochastic system. You can construct a stochastic state-space model using the CD Construct Stochastic Model VI. |
| Second-Order Statistics Noise Model | Specifies a mathematical representation of the noise model of a stochastic state-space model. You can create a noise model using the CD Construct Noise Model VI. |
| Initial State x(0) | Specifies the initial state of the model. If you do not specify a value for this parameter, this function assumes an initial state of 0. |
| error in | Describes error conditions that occur before this VI or function runs. The default is no error. If an error occurred before this VI or function runs, the VI or function passes the error in value to error out. If an error occurs while this VI or function runs, it runs normally and sets its own error status in error out. Use the Simple Error Handler or General Error Handler VIs to display the description of the error code. Use error in and error out to check errors and to specify execution order by wiring error out from one node to error in of the next node. |
Block Diagram Outputs
| Parameter | Description |
|---|---|
| Output y(k) | Returns the values of the model output(s) at time k. The length of this vector is equal to the number of model outputs. |
| State x(k+1) | Returns the values of the model state(s) at time k + 1. The length of this vector is equal to the number of model states. |
| State x(k) | Returns the values of the model state(s) at time k. The length of this vector is equal to the number of model states. |
| error out | Contains error information. If error in indicates that an error occurred before this VI or function ran, error out contains the same error information. Otherwise, it describes the error status that this VI or function produces. Right-click the error out front panel indicator and select Explain Error from the shortcut menu for more information about the error. |
Discrete Stochastic State-Space (Internal) Details
This function adapts to changes in the Second-Order Statistics Noise Model, as long as the model dimensions do not change. Therefore, you can use this function to simulate linear time-variant (LTV) stochastic state-space models.
This function uses the Second-Order Statistics Noise Model to obtain the values of E{w(k)}, E{v(k)}, Q(k), R(k), and N(k). The following equations define these terms:
| where | δkl is the Kronecker delta function. The following equations defines this function: δkl = 1 when k = l; δkl = 0 when k ≠ l. |
| w(k) is the process noise vector. | |
| v(k) is the observation noise vector. | |
| Q(k) is the covariance matrix of w(k). | |
| R(k) is the covariance matrix of v(k). | |
| N(k) is the cross-covariance matrix of w(k) and v(k). If these noise vectors are uncorrelated, N(k) is a matrix of zeros. | |
| E{} denotes the expected mean of the enclosed term(s). |
This function also uses the Second-Order Statistics Noise Model to generate Gaussian-distributed temporally-uncorrelated random samples of w(k) and v(k) at each time step.