CD Discrete State-Space Function

Owning Palette: Implementation VIs and Functions

Installed With: Control Design and Simulation Module

Implements a system model in discrete state-space form. You define the system model by specifying the input, output, state, and direct transmission matrices.

Details  

Dialog Box Options

Block Diagram Inputs

Block Diagram Outputs

Place on the block diagram

Find on the Functions palette

Dialog Box Options

Parameter	Description
Polymorphic instance	Specifies whether this function is single-input single-output (SISO) or multiple-input multiple-output (MIMO). The default value is SISO.
Feedthrough	Configures the function to be either a Direct or Indirect feedthrough function. Enable this control by selecting a parameter from the Parameters list and then selecting Terminal from the Parameter source pull-down menu. If you select Configuration Dialog Box from the Parameter source pull-down menu, LabVIEW disables this control and calculates the feedthrough behavior automatically. Refer to the Details section for a description of the parameters that determine the feedthrough behavior of this function.
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 simulation diagram. The default value is Configuration Dialog Box. If you select Terminal, LabVIEW displays an input for that parameter on the simulation 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 simulation diagram. You then must set the value for this parameter inside the configuration dialog box.
State-Space	Specifies the state-space model. Load Model—Loads model information from a data file. Save Model—Saves model information to a data file. This file is compatible with the Control Design VIs and functions. Copy to Clipboard—Copies the current model definition to the clipboard. From the clipboard, you can paste the model on the block diagram or into another configuration dialog box of the same model form. Paste from Clipboard—Pastes model information from the clipboard to the configuration dialog box. Model Dimensions—Use this section to specify the number of inputs, states, and outputs of the system model. Inputs—Specifies the number of model inputs. States—Specifies the number of model states. Outputs—Specifies the number of model outputs. Φ—Specifies the n × n state matrix of the given system. Γ—Specifies the n × m input matrix of the given system. C—Specifies the r × n output matrix of the given system. D—Specifies the r × m direct transmission matrix of the given system. where m is the number of inputs n is the number of states r is the number of outputs
initial state (x0)	Specifies a vector of initial states for the system. This vector must be of length n, where n is the number of states.

Block Diagram Inputs

Parameter	Description
initial state (x0)	Specifies a vector of initial states for the system. This vector must be of length n, where n is the number of states.
initialize	Sets the model state(s) to 0, when TRUE.
input u(k)	Specifies the input to the system. input u(k) must be a vector of length m, where m is the number of inputs.
State-Space	Specifies a state-space model. This input accepts either a block diagram constant or a model you created using the Control Design VIs and functions.
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 current output of the system. This vector must be of length r, where r is the number of 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 a one-dimensional array that specifies the internal states. This array must be of length n, where n is the number of states. Each element of the array represents x[n].
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.

CD Discrete State-Space Details

The following equations define the state-space system.

where	u is the input vector
	y is the output vector
	x is the state vector
	Φ, Γ, C, D are the state-space matrices. Refer to the State-Space parameter help for more information about these matrices.

If you place this function outside a Simulation Loop, t_k = k * Sampling Time (s), for k = 0, 1, 2, ….

If you place this function inside a Simulation Loop, t_k = initial time + sample skew (s) + k * sample period (s), for k = 0, 1, 2, …

Feedthrough Behavior

The value you specify for the D matrix of the State-Space parameter determines the feedthrough behavior of this function.

• If the D matrix is nonzero, all input/output pairs have direct feedthrough behavior.
• If the D matrix is zero, the following input/output pairs have indirect feedthrough behavior.
  • input u(k) — output y(k)
  • input u(k) — state x(k)
  The remaining input/output pairs have direct feedthrough behavior.

When you use the configuration dialog box to configure the D matrix, LabVIEW verifies that the feedthrough behavior is correct. For example, if you set the Feedthrough parameter to Indirect, and you set the D matrix to nonzero, LabVIEW changes the Feedthrough parameter to Direct.

If you specify the value of the D matrix programmatically by wiring a value to the parameter terminal, LabVIEW does not adjust the feedthrough behavior for you. You must ensure that you specify the proper feedthrough behavior for the value of the D matrix that you specify.