CD Minimal Realization VI

Owning Palette: Model Reduction VIs

Requires: Control Design and Simulation Module

Simplifies the model by using the minimum order possible to fully describe the dynamic system. Wire data to the State-Space Model input to determine the polymorphic instance to use or manually select the instance.

Details  

CD Minimal Realization (State-Space)

	State-Space Model contains a mathematical representation of and information about the original state-space model this VI reduces.
	Tolerance specifies the threshold this VI uses to determine modes to eliminate. For state-space models, Tolerance specifies the controllability and observability thresholds. For transfer function and zero-pole-gain models, Tolerance also specifies zero-pole cancellation closeness. The default is 1E–12.
	error in describes error conditions that occur before this node runs. With the following exception, this input provides standard error in functionality. This node runs normally even if an error occurred before this node runs.
	Reduced Model represents the minimal realization of the system model. To access and modify the data in the model, use the Model Information VIs.
	Number of States Removed returns the number of states this VI removes from the model to generate a minimal realization of the original state-space model.
	error out contains error information. This output provides standard error out functionality.

CD Minimal Realization (Transfer Function)

For transfer function models, this VI searches for the closest zero to each pole of the dynamic system. If the closest zero is within the threshold that the Tolerance specifies, this VI removes the zero-pole pair and reduces the system order.

	Transfer Function Model contains a mathematical representation of and information about the original transfer function model this VI reduces.
	Tolerance specifies the threshold this VI uses to determine modes to eliminate. For state-space models, Tolerance specifies the controllability and observability thresholds. For transfer function and zero-pole-gain models, Tolerance also specifies zero-pole cancellation closeness. The default is 1E–12.
	error in describes error conditions that occur before this node runs. With the following exception, this input provides standard error in functionality. This node runs normally even if an error occurred before this node runs.
	Reduced Model represents the minimal realization of the system model. To access and modify the data in the model, use the Model Information VIs.
	Number of Poles-Zeros Removed returns the number of pole-zero pairs this VI removes from each input-output pair of a model. The ijth element of this parameter corresponds to the number of pole-zero pairs this VI removes from the equation at the ith output and jth input location.
	error out contains error information. This output provides standard error out functionality.

CD Minimal Realization (Zero-Pole-Gain)

For zero-pole-gain models, this VI searches for the closest zero to each pole of the dynamic system. If the closest zero is within the threshold the Tolerance specifies, this VI removes the zero-pole pair and reduces the system order.

	Zero-Pole-Gain Model contains a mathematical representation of and information about the original zero-pole-gain model this VI reduces.
	Tolerance specifies the threshold this VI uses to determine modes to eliminate. For state-space models, Tolerance specifies the controllability and observability thresholds. For transfer function and zero-pole-gain models, Tolerance also specifies zero-pole cancellation closeness. The default is 1E–12.
	error in describes error conditions that occur before this node runs. With the following exception, this input provides standard error in functionality. This node runs normally even if an error occurred before this node runs.
	Reduced Model represents the minimal realization of the system model. To access and modify the data in the model, use the Model Information VIs.
	Number of Poles-Zeros Removed returns the number of pole-zero pairs this VI removes from each input-output pair of a model. The ijth element of this parameter corresponds to the number of pole-zero pairs this VI removes from the equation at the ith output and jth input location.
	error out contains error information. This output provides standard error out functionality.

CD Minimal Realization Details

A minimal realization for a state-space model is a state-space representation in which you remove all states that are not observable or controllable. A minimal realization for transfer function and zero-pole-gain models is a representation where you use zero-pole cancellations to reduce the number of modes required to describe the system dynamics.

For state-space models, this VI uses the staircase transformation to first obtain a group of controllable states. After identifying the controllable states, this VI uses the staircase transformation again to specify which of the controllable states also are observable. The minimal realization consists of the controllable and observable states of the system.

This VI supports delays. Refer to the LabVIEW Control Design User Manual for more information about delays.