sigma (Control Design and Simulation Module, MathScript Function)

Member of the frqrsp class.

Syntax

sigma(SysIn, attributes)

sigma(SysIn, attributes, [wmin wmax])

sigma(SysIn, attributes, [wmin wmax], type)

sigma(SysIn, attributes, wlist)

sigma(SysIn, attributes, wlist, type)

[magSV, wout] = sigma(SysIn)

[magSV, wout] = sigma(SysIn, [wmin wmax])

[magSV, wout] = sigma(SysIn, [wmin wmax], type)

[magSV, wout] = sigma(SysIn, attributes, wlist)

[magSV, wout] = sigma(SysIn, attributes, wlist, type)

Description

Creates a plot of the singular values of the frequency response of a system model. You also can use this function to calculate the singular values. This function converts transfer function and zero-pole-gain models into state-space models before calculating the singular values. If you do not specify an output, this function creates a plot.

Examples

Inputs

Name	Description
SysIn	Specifies a linear time-invariant (LTI) model in transfer function, zero-pole-gain, or state-space form.
attributes	Specifies valid plot attributes. Order the plot attributes by color, point-style, and line-style. For example, 'bo-' specifies that the plot is blue, marks points with circles, and uses solid lines. attributes is a string that can take a combination of the following values: 'b' Colors the plot blue. 'c' Colors the plot cyan. 'g' Colors the plot green. 'k' Colors the plot black. 'm' Colors the plot magenta. 'r' Colors the plot red. 'y' Colors the plot yellow. '.' Marks points with dots. 'o' Marks points with circles. 'x' Marks points with crosses. '+' Marks points with plus signs. '*' Marks points with asterisks. '-' Uses solid lines. ':' Uses dotted lines. '-.' Uses dashed and dotted lines. '--' Uses dashed lines.
wmin	Specifies the initial frequency, in radians/second, this function uses to calculate the singular values of the SysIn model. The default value is 1E-8. You also can use the wlist input to specify exact frequencies instead of a range. wmin is a real scalar.
wmax	Specifies the final frequency, in radians/second, this function uses to calculate the singular values of the SysIn model. The default value is 1000. You also can use the wlist input to specify exact frequencies instead of a range. wmax is a real scalar.
wlist	Specifies the frequency values, in radians/second, at which this function calculates the singular values. If you specify only two elements for this input, this function treats those elements as wmin and wmax. Therefore, you must specify at least three elements for the wlist input. wlist is a real vector consisting of three or more elements.
type	Specifies the type of singular value decomposition this function performs. type is an integer that takes the following values: 0 (Default) Specifies that this function calculates the singular value decomposition of H, where H is the SysIn model. 1 Specifies that this function calculates the singular value decomposition of inv(H). 2 Specifies that this function calculates the singular value decomposition of I + H, where I is the identity matrix. 3 Specifies that this function calculates the singular value decomposition of I + inv(H).

Outputs

Name	Description
magSV	Returns the singular value magnitude at different frequencies. The n-th column of this parameter corresponds to the n-th row of the wout parameter. magSV is a real matrix.
wout	Returns the frequencies, in radians/second, at which this function calculates the singular values. The n-th row of this parameter corresponds to the n-th column of the magSV parameter. wout is a real vector.

Examples

A = [-0.2, 0;0, -0.4]
B = [1, 0;0, 1]
C = [1, 0;0, 1]
D = [0, 0;0, 0]
SysIn = ss(A, B, C, D)
sigma(SysIn, 3)

Related Topics

bode
nichols
nyquist