CD State Similarity Transform VI

Owning Palette: State-Space Model Analysis VIs

Requires: Control Design and Simulation Module

Applies a similarity transformation on State-Space Model using the given Transformation Matrix (T).

Details  

	State-Space Model contains a mathematical representation of and information about a system that this VI transforms into the specified similarity transformation.
	Transformation Matrix (T) is the matrix T that this VI uses to transform the system. T must be an invertible matrix.
	Transformation determines the type of realization this VI uses in the resulting state-space model. 0 Direct (default)—Specifies that this VI uses a direct transformation as defined by the following equation: where x is the state of the original model and is the state of the transformed model. 1 Inverse—Specifies that this VI uses an inverse transformation as defined by the following equation: where is the state of the original model and x is the state of the transformed model.
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	Transformed Model returns the model that results from applying the similarity transform to the State-Space Model.
	Inverse Transformation Matrix returns the inverse of the Transformation Matrix (T).
	error out contains error information. This output provides standard error out functionality.

CD State Similarity Transform Details

This VI does not support delays unless the delays are part of the mathematical model that represents the dynamic system. To account for the delays in the synthesis of the controller, you must incorporate the delays into the mathematical model of the dynamic system using the CD Convert Delay with Pade Approximation VI (continuous models) or the CD Convert Delay to Poles at Origin VI (discrete models). Refer to the LabVIEW Control Design User Manual for more information about delays and the limitations of Pade Approximation.

Direct Case:
If the system matrices for the original state-space model are given by (A, B, C, D), then the system matrices of the transformed model are given by (, , , ) where:

Inverse Case:
If the system matrices for the original state-space model are given by (, , , ), then the system matrices of the transformed model are given by (A, B, C, D), where: