SI Estimate State-Space Model from FRF VI

Owning Palette: Frequency-Domain Model Estimation VIs

Requires: Advanced Signal Processing Toolkit or Control Design and Simulation Module

Estimates the parameters of a discrete state-space model for an unknown system by using a frequency response function (FRF). Wire data to the FRF magnitude and FRF phase inputs to determine the polymorphic instance to use or manually select the instance.

You can obtain the FRF of a dynamic system by using the SI Estimate FRF VI. You can wire the FRF magnitude and FRF phase outputs of the SI Estimate FRF VI to the FRF magnitude and FRF phase inputs of the SI Estimate State-Space Model from FRF VI.

Details  Examples

SI Estimate Discrete State-Space Model from FRF (SISO Arbitrary)

	structure selector specifies whether this VI computes the D matrix and the initial states of the state-space model you want to estimate. D matrix? specifies whether this VI estimates the D matrix of the model. If D matrix? is TRUE, this VI estimates the D matrix. If D matrix? is FALSE, the D matrix is 0. The default is FALSE. initial states? specifies whether this VI estimates the initial states of the model. If initial states? is TRUE, this VI estimates the initial states. If initial states? is FALSE, this VI sets the value of initial states to 0. The default is FALSE.
	FRF format specifies the format of the FRF magnitude and the FRF phase. Note  If you use the SI Estimate FRF VI to estimate the FRF, specify the same FRF format settings for this parameter as you do for the SI Estimate FRF VI. dB on? specifies whether magnitude is in decibels or in a linear scale. The default is FALSE, which specifies that this VI expresses magnitude in a linear scale. unwrap phase? specifies whether the phase is unwrapped. The default is FALSE, which specifies that the phase is wrapped. convert to degree? specifies whether the unit of phase is in radians or degrees. The default is FALSE, which means the phase is in radians.
	FRF magnitude specifies the magnitude of the averaged frequency response and frequency scale. frequency specifies the frequencies, in hertz, at which this VI evaluates the averaged frequency response. magnitude specifies the magnitude of the averaged frequency response. Use dB on? to specify the unit of magnitude.
	FRF phase specifies the phase of the averaged frequency response and frequency scale. frequency specifies the frequencies, in hertz, at which this VI evaluates the averaged frequency response. phase specifies the phase of the averaged frequency response. Use unwrap phase? to specify whether the phase is unwrapped. Use convert to degrees? to specify the unit of phase.
	number of states specifies the number of states of the system model. The value of number of states must be greater than 0. The default is 4.
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	sampling rate (Hz) specifies the sampling frequency, in hertz, of the estimated discrete system model. The value of sampling rate must be greater than 0. The default value is twice the highest frequency of the FRF data.
	noise subspace specifies the percentage of the noise subspace in the whole space, which is the combination of the signal subspace and the noise subspace. The default is 50.
	system model out returns information about the model structure, nominal or estimated parameters, identification result, and so on. Use the Model Management VIs to retrieve the information system model out contains. Note  You can use a customized system model probe to view model information that flows through system model wires when you debug a block diagram created with the System Identification VIs. Right-click a system model wire and select Custom Probe»SI System Model from the shortcut menu to use the system model probe.
	coefficients of state-space model returns the coefficients of the state-space model. A returns the state matrix of the system model. B returns the input matrix of the system model. C returns the output matrix of the system model. D returns the direct transmission matrix of the system model.
	initial states returns the initial states of the state-space model. The length of initial states equals the number of states of the system model.
	error out contains error information. This output provides standard error out functionality.

SI Estimate Discrete State-Space Model from FRF (SISO Uniform)

	structure selector specifies whether this VI computes the D matrix and the initial states of the state-space model you want to estimate. D matrix? specifies whether this VI estimates the D matrix of the model. If D matrix? is TRUE, this VI estimates the D matrix. If D matrix? is FALSE, the D matrix is 0. The default is FALSE. initial states? specifies whether this VI estimates the initial states of the model. If initial states? is TRUE, this VI estimates the initial states. If initial states? is FALSE, this VI sets the value of initial states to 0. The default is FALSE.
	FRF format specifies the format of the FRF magnitude and the FRF phase. Note  If you use the SI Estimate FRF VI to estimate the FRF, specify the same FRF format settings for this parameter as you do for the SI Estimate FRF VI. dB on? specifies whether magnitude is in decibels or in a linear scale. The default is FALSE, which specifies that this VI expresses magnitude in a linear scale. unwrap phase? specifies whether the phase is unwrapped. The default is FALSE, which specifies that the phase is wrapped. convert to degree? specifies whether the unit of phase is in radians or degrees. The default is FALSE, which means the phase is in radians.
	FRF magnitude specifies the magnitude of the averaged frequency response and frequency scale. f0 specifies the starting frequency of the spectrum, in hertz. df specifies the frequency increment of the spectrum, in hertz. magnitude specifies the magnitude of the averaged frequency response. Use dB on? to specify the unit of magnitude.
	FRF phase specifies the phase of the averaged frequency response and frequency scale. f0 specifies the starting frequency of the spectrum, in hertz. df specifies the frequency increment of the spectrum, in hertz. phase specifies the phase of the averaged frequency response. Use unwrap phase? to specify whether the phase is unwrapped. Use convert to degrees? to specify the unit of phase.
	number of states specifies the number of states of the system model. The value of number of states must be greater than 0. The default is 4.
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	sampling rate (Hz) specifies the sampling frequency, in hertz, of the estimated discrete system model. The value of sampling rate must be greater than 0. The default value is twice the highest frequency of the FRF data.
	noise subspace specifies the percentage of the noise subspace in the whole space, which is the combination of the signal subspace and the noise subspace. The default is 50.
	system model out returns information about the model structure, nominal or estimated parameters, identification result, and so on. Use the Model Management VIs to retrieve the information system model out contains. Note  You can use a customized system model probe to view model information that flows through system model wires when you debug a block diagram created with the System Identification VIs. Right-click a system model wire and select Custom Probe»SI System Model from the shortcut menu to use the system model probe.
	coefficients of state-space model returns the coefficients of the state-space model. A returns the state matrix of the system model. B returns the input matrix of the system model. C returns the output matrix of the system model. D returns the direct transmission matrix of the system model.
	initial states returns the initial states of the state-space model. The length of initial states equals the number of states of the system model.
	error out contains error information. This output provides standard error out functionality.

SI Estimate Discrete State-Space Model from FRF (MIMO Arbitrary)

	structure selector specifies whether this VI computes the D matrix and the initial states of the state-space model you want to estimate. D matrix? specifies whether this VI estimates the D matrix of the model. If D matrix? is TRUE, this VI estimates the D matrix. If D matrix? is FALSE, the D matrix is 0. The default is FALSE. initial states? specifies whether this VI estimates the initial states of the model. If initial states? is TRUE, this VI estimates the initial states. If initial states? is FALSE, this VI sets the value of initial states to 0. The default is FALSE.
	FRF format specifies the format of the FRF magnitude and the FRF phase. Note  If you use the SI Estimate FRF VI to estimate the FRF, specify the same FRF format settings for this parameter as you do for the SI Estimate FRF VI. dB on? specifies whether magnitude is in decibels or in a linear scale. The default is FALSE, which specifies that this VI expresses magnitude in a linear scale. unwrap phase? specifies whether the phase is unwrapped. The default is FALSE, which specifies that the phase is wrapped. convert to degree? specifies whether the unit of phase is in radians or degrees. The default is FALSE, which means the phase is in radians.
	FRF magnitude specifies the magnitude of the averaged frequency response and frequency scale. frequency specifies the frequencies, in hertz, at which this VI evaluates the averaged frequency response. magnitude specifies the magnitude of the averaged frequency response. Use dB on? to specify the unit of magnitude.
	FRF phase specifies the phase of the averaged frequency response and frequency scale. frequency specifies the frequencies, in hertz, at which this VI evaluates the averaged frequency response. phase specifies the phase of the averaged frequency response. Use unwrap phase? to specify whether the phase is unwrapped. Use convert to degrees? to specify the unit of phase.
	number of states specifies the number of states of the system model. The value of number of states must be greater than 0. The default is 4.
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	sampling rate (Hz) specifies the sampling frequency, in hertz, of the estimated discrete system model. The value of sampling rate must be greater than 0. The default value is twice the highest frequency of the FRF data.
	noise subspace specifies the percentage of the noise subspace in the whole space, which is the combination of the signal subspace and the noise subspace. The default is 50.
	system model out returns information about the model structure, nominal or estimated parameters, identification result, and so on. Use the Model Management VIs to retrieve the information system model out contains. Note  You can use a customized system model probe to view model information that flows through system model wires when you debug a block diagram created with the System Identification VIs. Right-click a system model wire and select Custom Probe»SI System Model from the shortcut menu to use the system model probe.
	coefficients of state-space model returns the coefficients of the state-space model. A returns the state matrix of the system model. B returns the input matrix of the system model. C returns the output matrix of the system model. D returns the direct transmission matrix of the system model.
	initial states returns the initial states of the state-space model. The length of initial states equals the number of states of the system model.
	error out contains error information. This output provides standard error out functionality.

SI Estimate Discrete State-Space Model from FRF (MIMO Uniform)

	structure selector specifies whether this VI computes the D matrix and the initial states of the state-space model you want to estimate. D matrix? specifies whether this VI estimates the D matrix of the model. If D matrix? is TRUE, this VI estimates the D matrix. If D matrix? is FALSE, the D matrix is 0. The default is FALSE. initial states? specifies whether this VI estimates the initial states of the model. If initial states? is TRUE, this VI estimates the initial states. If initial states? is FALSE, this VI sets the value of initial states to 0. The default is FALSE.
	FRF format specifies the format of the FRF magnitude and the FRF phase. Note  If you use the SI Estimate FRF VI to estimate the FRF, specify the same FRF format settings for this parameter as you do for the SI Estimate FRF VI. dB on? specifies whether magnitude is in decibels or in a linear scale. The default is FALSE, which specifies that this VI expresses magnitude in a linear scale. unwrap phase? specifies whether the phase is unwrapped. The default is FALSE, which specifies that the phase is wrapped. convert to degree? specifies whether the unit of phase is in radians or degrees. The default is FALSE, which means the phase is in radians.
	FRF magnitude specifies the magnitude of the averaged frequency response and frequency scale. f0 specifies the starting frequency of the spectrum, in hertz. df specifies the frequency increment of the spectrum, in hertz. magnitude specifies the magnitude of the averaged frequency response. Use dB on? to specify the unit of magnitude.
	FRF phase specifies the phase of the averaged frequency response and frequency scale. f0 specifies the starting frequency of the spectrum, in hertz. df specifies the frequency increment of the spectrum, in hertz. phase specifies the phase of the averaged frequency response. Use unwrap phase? to specify whether the phase is unwrapped. Use convert to degrees? to specify the unit of phase.
	number of states specifies the number of states of the system model. The value of number of states must be greater than 0. The default is 4.
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	sampling rate (Hz) specifies the sampling frequency, in hertz, of the estimated discrete system model. The value of sampling rate must be greater than 0. The default value is twice the highest frequency of the FRF data.
	noise subspace specifies the percentage of the noise subspace in the whole space, which is the combination of the signal subspace and the noise subspace. The default is 50.
	system model out returns information about the model structure, nominal or estimated parameters, identification result, and so on. Use the Model Management VIs to retrieve the information system model out contains. Note  You can use a customized system model probe to view model information that flows through system model wires when you debug a block diagram created with the System Identification VIs. Right-click a system model wire and select Custom Probe»SI System Model from the shortcut menu to use the system model probe.
	coefficients of state-space model returns the coefficients of the state-space model. A returns the state matrix of the system model. B returns the input matrix of the system model. C returns the output matrix of the system model. D returns the direct transmission matrix of the system model.
	initial states returns the initial states of the state-space model. The length of initial states equals the number of states of the system model.
	error out contains error information. This output provides standard error out functionality.

SI Estimate State-Space Model from FRF Details

If the frequency-domain data you wire to the FRF magnitude and FRF phase inputs is spaced uniformly, use the Uniform polymorphic instance of this VI. In this situation, you must specify the starting frequency f0 and the frequency increment df. If this data is spaced arbitrarily, use the Arbitrary polymorphic instance of this VI.

Note  You also can use the Arbitrary polymorphic instance if the frequency-domain data you wire to the FRF magnitude and FRF phase inputs is spaced uniformly.

When you estimate MIMO systems, you must wire a 2D array to FRF magnitude and FRF phase. Each column of the 2D array corresponds to an input signal of the MIMO system. Each row of the 2D array corresponds to an output signal of the MIMO system. For example, if the MIMO system has three input signals and five output signals, the 2D array must contain three columns and five rows. The first column of the 2D array corresponds to the first input signal of the MIMO system. The second row of the 2D array corresponds to the second output signal of the MIMO system.

Examples

Refer to the following VIs for examples of using the SI Estimate State-Space Model from FRF VI:

• Estimate State-Space Model from FRFs VI: labview\examples\System Identification\Getting Started\Frequency Domain Identification.llb
• Flexible Arm (Frequency Domain) VI: labview\examples\System Identification\Industry Applications\Mechanical Systems.llb