CD Controllability Matrix VI

Owning Palette: State-Space Model Analysis VIs

Requires: Control Design and Simulation Module

Calculates the Controllability Matrix of the State-Space Model. You can use the controllability matrix Q to determine if the given system is controllable. A system of order n is controllable if Q is full rank, meaning the rank of Q is equal to n. This VI also determines if the given system is stabilizable. A system is stabilizable if all the unstable eigenvalues are controllable.

Details  

	State-Space Model contains a mathematical representation of and information about the system for which this VI determines controllability matrix.
	Tolerance is the threshold this VI uses to determine if the controllability matrix is row rank deficient. The default is 1E–6.
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	Controllability Matrix is the matrix Q for a system with system matrix A of order n, and input matrix B. The following equation defines the controllability matrix.
	If Is Controllable? is TRUE, the system is controllable.
	If Is Stabilizable? is TRUE, the system is stabilizable. A system is stabilizable if all unstable eigenvalues are controllable.
	error out contains error information. This output provides standard error out functionality.

CD Controllability Matrix 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.