CD Damping Ratio and Natural Frequency VI

Owning Palette: Dynamic Characteristics VIs

Requires: Control Design and Simulation Module

Gives the damping ratios and natural frequencies for each pole of the input system. Wire data to the State-Space Model input to determine the polymorphic instance to use or manually select the instance.

Details  

CD Damping Ratio and Natural Frequency (State-Space)

	State-Space Model contains a mathematical representation of and information about the system of which this VI determines damping ratio and natural frequency.
	Frequency Unit specifies the units of frequency, either in Hertz or radians/seconds, to use in calculating the natural frequencies. 0 Hz 1 rad/s (default)
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	Damping Ratios returns the damping ratios for each pole in the system.
	Natural Frequencies returns the natural frequencies for each pole in the system.
	Poles returns the eigenvalues of state matrix A in state-space models.
	error out contains error information. This output provides standard error out functionality.

CD Damping Ratio and Natural Frequency (Transfer Function)

	Transfer Function Model contains a mathematical representation of and information about the system of which this VI determines damping ratio and natural frequency.
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	Damping Ratios returns the damping ratios for each pole in the system.
	Natural Frequencies returns the natural frequencies for each pole in the system.
	Poles returns the roots of the denominator in transfer function models.
	error out contains error information. This output provides standard error out functionality.

CD Damping Ratio and Natural Frequency (Zero-Pole-Gain)

	Zero-Pole-Gain Model contains a mathematical representation of and information about the system of which this VI determines damping ratio and natural frequency.
	Frequency Unit specifies the units of frequency, either in Hertz or radians/seconds, to use in calculating the natural frequencies. 0 Hz 1 rad/s (default)
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	Damping Ratios returns the damping ratios for each pole in the system.
	Natural Frequencies returns the natural frequencies for each pole in the system.
	Poles returns the poles in zero-pole-gain models.
	error out contains error information. This output provides standard error out functionality.

CD Damping Ratio and Natural Frequency (Complex Roots)

	Roots contains the complex roots for a polynomial.
	Sampling Time (s) specifies the sampling time of the model. Sampling Time (s) defines whether the model represents a continuous-time system or a discrete-time system. If the model represents a continuous-time system, Sampling Time (s) must equal 0. If the model represents a discrete-time system, Sampling Time (s) must be greater than 0 and equal to the sampling rate, in seconds, of the discrete system. A value of -1 specifies that Sampling Time (s) is irrelevant. The default is 0.
	Frequency Unit specifies the units of frequency, either in Hertz or radians/seconds, to use in calculating the natural frequencies. 0 Hz 1 rad/s (default)
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	Damping Ratios returns the damping ratios for each pole in the system.
	Natural Frequencies returns the natural frequencies for each pole in the system.
	error out contains error information. This output provides standard error out functionality.

CD Damping Ratio and Natural Frequency Details

The CD Damping Ratio and Natural Frequency VI provides the following response based on each pole of the system:

Wn = sqrt ( Re*2 + IM*2))
Damp = - cos(arcTan (Im/Re))

or for discrete models:

Wn = Ln (sqrt ( Re*2 + IM*2))) / dT
Damp = – cos(arcTan (Im/Re))

Notice that if the pole is real, Wn = Re and Damp = 1.

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 when calculating the dynamic characteristics of a system, 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.