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zero

Zeros and gain of SISO dynamic system

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Syntax

z =zero(sys)
[Z,gain] = zero(sys)
[Z,gain] = zero(sys,J1,...,JN)

Description

example

Z= zero(sys)返回单输入单输出（SISO）动态系统模型的零，sys。The output is expressed as the reciprocal of the time units specified insys.TimeUnit。

example

[Z,gain] = zero(sys)also returns the zero-pole-gain ofsys。

example

[Z,gain] = zero(sys,J1、……Jn）returns the zeros and gain of the entries in the model arraysys与下标J1，...，JN。

Examples

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打开实时脚本

Compute the zeros of the following transfer function:

s y s ( s ) = 4 。 2 s 2 + 0 。 2 5 s - 0 。 0 0 4 s 2 + 9 。 6 s + 1 7 

sys = tf([4.2,0.25,-0.004],[1,9.6,17]); Z = zero(sys)
z =2×1-0.0726 0.0131
打开实时脚本

Calculate the zero locations and zero-pole gain of the following transfer function:

s y s ( s ) = 4 。 2 s 2 + 0 。 2 5 s - 0 。 0 0 4 s 2 + 9 。 6 s + 1 7 

sys = tf([4.2,0.25,-0.004],[1,9.6,17]); [z,gain] = zero(sys)
z =2×1-0.0726 0.0131
gain = 4.2000

The zero locations are expressed in 第二 - 1 , because the time unit of the transfer function (H.TimeUnit) is seconds.

打开实时脚本

对于此示例，加载一个3 x-1的传输函数模型。

load('tfarray.mat',“系统”）；尺寸（系统）
3x1 array of transfer functions. Each model has 1 outputs and 1 inputs.

Find the zeros and gain values of the models in the array.

[Z, gain] = zero(sys); Z(:,:,1,1)
ans = 0x1 empty double column vector
增益（：，：，1,1）
ans = 1

zeroreturns an array each for the zeros and the gain values respectively. Here,Z(:,:,1,1)和增益（：，：，1,1）corresponds to the zero and the gain value of the first model in the array, that is,sys（：，：，1,1）。

Input Arguments

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Dynamic system, specified as a SISO dynamic system model, or an array of SISO dynamic system models. Dynamic systems that you can use include continuous-time or discrete-time numeric LTI models such astf,ZPK, orssmodels.

Ifsysis a generalized state-space modelgenss或者an uncertain state-space modelUSS,zeroreturns the zeros of the current or nominal value ofsys。Ifsysis an array of models,zeroreturns the zeros of the model corresponding to its subscriptJ1，...，JNinsys。For more information on model arrays, seeModel Arrays。

Indices of models in array whose zeros you want to extract, specified as a positive integer. You can provide as many indices as there are array dimensions insys。例如，如果sys是一个动态系统模型的4 x-5数组，以下命令在数组中提取零（2,3）的零。

z =zero(sys,2,3);

Output Arguments

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Zeros of the dynamic system, returned as a column vector or an array. Ifsysis:

  • 然后一个模型Z是动态系统模型的零的列矢量sys

  • A model array, thenZis an array containing the zeros of each model insys

Zis expressed as the reciprocal of the time units specified insys.TimeUnit。For example, zero is expressed in 1/minute ifsys.TimeUnit='minutes'。

动态系统的零极生成，作为标量返回。换句话说，gainis the value ofK当模型写入时ZPKform.

提示

  • Ifsyshas internal delays,zerosets all internal delays to zero, creating a zero-order Padé approximation. This approximation ensures that the system has a finite number of zeros.zeroreturns an error if setting internal delays to zero creates singular algebraic loops. To assess the stability of models with internal delays, usestep或者impulse。

  • 要计算多输入，多输出（MIMO）系统的传输零，请使用tzero。

Version History

在R2006a之前引入

See Also

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