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damp

Natural frequency and damping ratio

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Syntax

damp(sys)
[wn,zeta] = damp(sys)
[WN，Zeta，P] =潮湿（SYS）

描述

example

damp(sys)显示线性模型极线的阻尼比，固有频率和时间常数sys。对于离散时间模型，该表还包括每个极点的大小。杆子以频率值的增加顺序排序。

example

[wn,zeta] = damp(sys)返回固有频率wn， 和damping ratioszeta的the poles ofsys。

example

[wn,zeta,p] = damp(sys)also returns the polesp的sys。

例子

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打开实时脚本

For this example, consider the following continuous-time transfer function:

s y s ( s ) = 2 s 2 + 5 s + 1 s 3 + 2 s - 3 。

创建连续的时间传输函数。

sys = tf（[2,5,1]，[1,0,2，-3]）;

Display the natural frequencies, damping ratios, time constants, and poles ofsys。

damp(sys)
Pole Damping Frequency Time Constant (rad/seconds) (seconds) 1.00e+00 -1.00e+00 1.00e+00 -1.00e+00 -5.00e-01 + 1.66e+00i 2.89e-01 1.73e+00 2.00e+00 -5.00e-01 - 1.66e+00i 2.89e-01 1.73e+00 2.00e+00

The poles ofsyscontain an unstable pole and a pair of complex conjugates that lie int he left-half of the s-plane. The corresponding damping ratio for the unstable pole is -1, which is called a driving force instead of a damping force since it increases the oscillations of the system, driving the system to instability.

打开实时脚本

在此示例中，考虑以下离散时间传输函数，示例时间为0.01秒：

s y s ( z ) = 5 z 2 + 3 z + 1 z 3 + 6 z 2 + 4 z + 4 。

创建离散时间传输函数。

sys = tf([5 3 1],[1 6 4 4],0.01)
sys = 5 z^2 + 3 z + 1 --------------------- z^3 + 6 z^2 + 4 z + 4 Sample time: 0.01 seconds Discrete-time transfer function.

显示有关极点的信息sys使用dampcommand.

damp(sys)
Pole Magnitude Damping Frequency Time Constant (rad/seconds) (seconds) -3.02e-01 + 8.06e-01i 8.61e-01 7.74e-02 1.93e+02 6.68e-02 -3.02e-01 - 8.06e-01i 8.61e-01 7.74e-02 1.93e+02 6.68e-02 -5.40e+00 5.40e+00 -4.73e-01 3.57e+02 -5.93e-03

TheMagnitudecolumn displays the discrete-time pole magnitudes. The阻尼,Frequency， 和Time Constantcolumns display values calculated using the equivalent continuous-time poles.

打开实时脚本

在此示例中，创建一个具有两个输出和一个输入的离散时间零极增益模型。使用0.1秒的样品时间。

sys = zpk({0;-0.5},{0.3;[0.1+1i,0.1-1i]},[1;2],0.1)
sys = From input to output... z 1: ------- (z-0.3) 2 (z+0.5) 2: ------------------- (z^2 - 0.2z + 1.01) Sample time: 0.1 seconds Discrete-time zero/pole/gain model.

计算零极增益模型的固有频率和阻尼比sys。

[wn,zeta] = damp(sys)
wn =3×112.0397 14.7114 14.7114
zeta =3×11.0000 -0.0034 -0.0034

Each entry inwn和zeta对应于I/O的组合数sys。zetais ordered in increasing order of natural frequency values inwn。

打开实时脚本

在此示例中，计算以下状态空间模型的固有频率，阻尼比和极点：

A = [ - 2 - 1 1 - 2 ] , B = [ 1 1 2 - 1 ] , C = [ 1 0 ] , D = [ 0 1 ] 。

使用状态空间矩阵创建状态空间模型。

A = [-2 -1;1 -2]; B = [1 1;2 -1]; C = [1 0]; D = [0 1]; sys = ss(A,B,C,D);

利用dampto compute the natural frequencies, damping ratio and poles ofsys。

[WN，Zeta，P] =潮湿（SYS）
wn =2×12.2361 2.2361
zeta =2×10.8944 0.8944
p =2×1complex-2.0000 + 1.0000i -2.0000 - 1.0000i

The poles ofsys是位于S平面左半部分的复杂缀合物。相应的阻尼比小于1。因此，sysis an underdamped system.

Input Arguments

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Linear dynamic system, specified as a SISO, or MIMO dynamic system model. Dynamic systems that you can use include:

  • Continuous-time or discrete-time numeric LTI models, such astf,ZPK, orssmodels.

  • 普遍或不确定的LTI模型，例如genss或者USS（强大的控制工具箱）models. (Using uncertain models requires Robust Control Toolbox™ software.)

    damp假设

    • current values of the tunable components for tunable control design blocks.

    • 不确定控制设计块的标称模型值。

Output Arguments

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Natural frequency of each pole ofsys，以频率值的上升顺序排序作为向量返回。频率以倒数的单位表示TimeUnitproperty ofsys。

如果sysis a discrete-time model with specified sample time,wn包含等效连续极线的固有频率。如果未指定样品时间，则damp假设a sample time value of 1 and calculateswn因此。有关更多信息，请参阅算法。

每个极点的阻尼比，返回为矢量，以与wn。

如果sysis a discrete-time model with specified sample time,zeta包含阻尼ratios of the equivalent continuous-time poles. If the sample time is not specified, thendamp假设a sample time value of 1 and calculateszeta因此。有关更多信息，请参阅算法。

动态系统模型的电线杆，作为向量返回，以与wn。p与输出相同极(sys), except for the order. For more information on poles, see极。

算法

dampcomputes the natural frequency, time constant, and damping ratio of the system poles as defined in the following table:

Continuous Time Discrete Time with Sample Time Ts
杆位置

s

z

Equivalent Continuous-Time Pole

Not applicable

s = l n ( z ) T s

Natural Frequency

ω n = | s |

ω n = | s | = | l n ( z ) T s |

阻尼Ratio

ζ = − c o s ( ∠ s )

ζ = − c o s ( ∠ s ) = − c o s ( ∠ l n ( z ) )

Time Constant

τ = 1 ω n ζ

τ = 1 ω n ζ

如果未指定样品时间，则damp假设a sample time value of 1 and calculateszeta因此。

Version History

在R2006a之前引入

See Also

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