Discrete Zero-Pole-Gain Function

Simulation VI and Function

Discrete Zero-Pole-Gain Function

Owning Palette: Discrete Linear Systems Functions

Installed With: Control Design and Simulation Module

Implements a system model in discrete zero-pole-gain form. You define the system model by specifying the Zeros, Poles, and Gain of the zero-pole-gain equation.

Details Example

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.
Zeros-Poles-Gain	Specifies the zero-pole-gain 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 and outputs of the system model. You also use this section to specify the input-output location of the equation you want to edit. This section is available only if you select MIMO from the Polymorphic instance pull-down menu. Inputs—Specifies the number of model inputs. Outputs—Specifies the number of model outputs. Current Input—Specifies the current column of the Input-Output Model. Current Output—Specifies the current row of the Input-Output Model. Input-Output Model—Displays a graphical representation of the MIMO model. Click a cell to edit the equation at that input-output location. You also can use the Current Input and Current Output controls to specify the location of the equation you want to edit. Gain—Specifies a real value representing the common gain of the zero-pole-gain model. For MIMO models, Gain applies to the equation that the Current Input and Current Output parameters specify. Zeros—Specifies zeros of the zero-pole-gain model. For all zeros with an imaginary part, the conjugate complex number also must belong to this array. For MIMO models, Zeros applies to the equation that the Current Input and Current Output parameters specify. Poles—Specifies the poles of the zero-pole-gain model. For all poles with an imaginary part, the conjugate complex number also must belong to this array. For MIMO models, Poles applies to the equation that the Current Input and Current Output parameters specify.
sample period (s)	Specifies the length of the discrete time step, in seconds, of this function. The default value is –1. If you enter a value of –1, this function inherits the discrete time step you specify for the simulation diagram. Otherwise, the value of sample period (s) must be a multiple of the discrete time step you specify for the simulation diagram. This parameter is valid only when you place this function inside a Simulation Loop.
sample skew (s)	Specifies the length of time by which you want to delay the execution of this function. The default value is 0. The value of this parameter must satisfy the following relationship: 0 ≤ sample skew (s) ≤ sample period (s) This parameter is valid only when you place this function inside a Simulation Loop.
reset?	Sets the model state(s) to 0, when TRUE.

Block Diagram Inputs

Parameter	Description
sample period (s)	Specifies the length of the discrete time step, in seconds, of this function. The default value is –1. If you enter a value of –1, this function inherits the discrete time step you specify for the simulation diagram. Otherwise, the value of sample period (s) must be a multiple of the discrete time step you specify for the simulation diagram. This parameter is valid only when you place this function inside a Simulation Loop.
sample skew (s)	Specifies the length of time by which you want to delay the execution of this function. The default value is 0. The value of this parameter must satisfy the following relationship: 0 ≤ sample skew (s) ≤ sample period (s) This parameter is valid only when you place this function inside a Simulation Loop.
reset?	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.
Zeros-Poles-Gain	Specifies a zero-pole-gain model. This input accepts either a block diagram constant or a model you created using the Control Design VIs and functions.

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.

Discrete Zero-Pole-Gain Details

For SISO models, this function uses the following equation to calculate the output:

For MIMO models, this function calculates the output as H = [H_ij].

where	k is the gain
	Z[m] is the array of zeros
	P[n] is the array of poles
	m is the order of the numerator
	n is the order of the denominator
	z is the z-transform variable
	i is the index number of the input
	j is the index number of the output

The function is based on the Discrete Transfer Function, which is represented in zero-pole-gain notation.

Feedthrough Behavior

The values you specify for the Zeros and Poles subparameters determine the feedthrough behavior of this function. Given Z as the Zeros subparameter and P as the Poles subparameter:

If the order of Z = the order of P, the function has direct feedthrough behavior.
If the order of Z < the order of P, the input u(k) input has indirect feedthrough to the output y(k) output. All other input/output pairs have direct feedthrough behavior.
If the order of Z > the order of P, LabVIEW returns an error.

When you use the configuration dialog box to configure Z and P, LabVIEW verifies that the feedthrough behavior is correct. For example, if you set the Execution Mode parameter to Indirect, and you set the order of Z equal to the order of P, LabVIEW changes the Execution Mode parameter to Direct.

If you define the zero-pole-gain equation programmatically, LabVIEW does not adjust the feedthrough behavior for you. You must ensure that you specify the proper feedthrough behavior for the orders of Z and P you specify.

Example

Refer to the SimEx discrete zero-pole-gain VI in the labview\examples\Control and Simulation\Simulation\Discrete Linear directory for an example of using the Discrete Zero-Pole-Gain VI.

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