自控实验

实验名称：线性系统的时域分析方法1

实验目的：

1.传递函数的代数式与零极点式互换

2.由开环传递函数求闭环传递函数的方法

3.系统的单位阶跃响应图和单位控制响应图的画法

实验仪器设备：

PC机，MATLAB软件

实验原理及步骤：

1．tf2zpk 函数说明

>> help tf2zpk

tf2zpk Discrete-time transfer function to zero-pole conversion.

[Z,P,K] = tf2zpk(NUM,DEN) finds the zeros, poles, and gain:

(z-Z(1))(z-Z(2))...(z-Z(n))

H(z) = K ---------------------------

(z-P(1))(z-P(2))...(z-P(n))

from a single-input, single-output transfer function in polynomial form:

NUM(z)

H(z) = --------

DEN(z)

EXAMPLE:

[b,a] = butter(3,.4);

[z,p,k] = tf2zpk(b,a)

翻译：

Tf2zpk 离散传递函数zero-pole转换

[Z,P,K] = tf2zpk(NUM,DEN)找到零点、极点并且得到：

(z-Z(1))(z-Z(2))...(z-Z(n))

H(z) = K ---------------------------

(z-P(1))(z-P(2))...(z-P(n))

对于从单变量多项式形式的传递函数：

NUM(z)

H(z) = --------

DEN(z)

例如：[b,a] = butter(3,.4);

[z,p,k] = tf2zpk(b,a)

2．expand函数说明

>> help expand

--- help for sweepset/expand ---

expand Expand records into sweeps

S = expand(S,t) turns each record into a sweep by replicating it N

times. The number of times to replicate each record is specified by the

(1-by-NUMRECS) vector t.

Overloaded methods:

sym/expand

dtree/expand

翻译：

帮助sweepset/扩展

扩大记录扩展到扫描

S = expand(S,t) 通过复制N次把每一个记录变成一个扫描。复制每个记录的次数是指定的通过(1-by-NUMRECS) 向量t。

重载的方法：sym/expand dtree/expand

3．feedback 函数说明

>> help feedback

feedback Feedback connection of two input/output systems.

M = feedback(M1,M2) computes a closed-loop model M for the feedback loop:

u --->O---->[ M1 ]----+---> y

| | y = M * u

+-----[ M2 ]<---+

Negative feedback is assumed and the model M maps u to y. To apply

positive feedback, use the syntax M = feedback(M1,M2,+1).

M = feedback(M1,M2,FEEDIN,FEEDOUT,SIGN) builds the more general feedback interconnection:

+------+

v --------->| |--------> z

| M1 |

u --->O---->| |----+---> y

| +------+ |

| |

+-----[ M2 ]<---+

The vector FEEDIN contains indices into the input vector of M1 and

specifies which inputs u are involved in the feedback loop. Similarly,

FEEDOUT specifies which outputs y of M1 are used for feedback. If SIGN=1

then positive feedback is used. If SIGN=-1 or SIGN is omitted, then

negative feedback is used. In all cases, the resulting model M has the

same inputs and outputs as M1 (with their order preserved).

If M1 and M2 are arrays of models, feedback returns a model array M of

the same dimensions where

M(:,:,k) = feedback(M1(:,:,k),M2(:,:,k)) .

For dynamic systems SYS1 and SYS2,

SYS = feedback(SYS1,SYS2,'name')

connects SYS1 and SYS2 by matching their I/O names. The I/O names of

SYS1 and SYS2 must be fully defined.

See also lft, parallel, series, connect, InputOutputModel, DynamicSystem.

Overloaded methods:

InputOutputModel/feedback

iddata/feedback

翻译：

Feedback 反馈连接的两个输入/输出系统。

M = feedback(M1,M2) 计算一个闭环反馈回路模型M

u --->O---->[ M1 ]----+---> y

| | y = M * u

+-----[ M2 ]<---+

负反馈是假定的并且模型M是u映射到y。运用正反馈，使用语句M = feedback(M1,M2,+1).

M = feedback(M1,M2,FEEDIN,FEEDOUT,SIGN) 构建更多一般的反馈。

连接：

+------+

v --------->| |--------> z

| M1 |

u --->O---->| |----+---> y

| +------+ |

| |

+-----[ M2 ]<---+

向量FEEDIN包含指标输入向量的M1和指定输入u参与的反馈循环。同样的，FEEOUT 指定输出向量M1的y用于反馈。如果SIGN=1，然后使用正反馈，如果SIGN=-1或者SIGN省略，用于负反馈。在所有情况下，所产生的模型M有相同的输入和输出作为M1（命令保存）。

如果M1和M2是一个数组模型，反馈返回一个相同维数的数组的模型M M(:,:,k) = feedback(M1(:,:,k),M2(:,:,k)) .

对于动态系统SYS1和SYS2, SYS = feedback(SYS1,SYS2,'name')

连接SYS1和SYS2通过匹配它们的I/O名字，SYS1和SYS2的I/O

名字必须完全定义。

重载方法： InputOutputModel/feedback iddata/feedback

实验内容：

1.将传递函数=)(s G 368

17979143877238323423+++++++s s s s s s s 转化为零极点表达式 >> num=[3 38 72 87];

>> den=[3 14 79 179 368];

>> sys=tf(num,den)

sys =

3 s^3 + 38 s^2 + 72 s + 87

-------------------------------------

3 s^

4 + 14 s^3 + 79 s^2 + 179 s + 368

Continuous-time transfer function.

>> [z p k]=tf2zp(num,den)

z =

-10.6725 + 0.0000i

-0.9971 + 1.3127i

-0.9971 - 1.3127i

p =

-0.4934 + 3.6870i

-0.4934 - 3.6870i

-1.8399 + 2.3409i

-1.8399 - 2.3409i

k =

1

2. 画出开环传递函G(s)=

10

2132++s s 的单位阶跃响应图和单位脉冲响应图 >> num=[13];

>> den=[1 2 10];

>> sys=tf(num,den)

sys =

13

--------------

s^2 + 2 s + 10

Continuous-time transfer function.

>> t=0:0.05:2.5;

>> step(sys,t)

>> grid on

>> impulse(sys,t)

>> grid on

自动控制原理实验报告

院系：电子信息工程系

专业班级：电信1301

学号：1305141031

姓名：汪敏

指导教师：孙锴