Analysis Interface for Linear Systems

滴水静禅天•2018-03-05•信息计算• 1192

Analysis Interface for Linear Systems

Modeling of Linear Systems

Simulink提供了各种用来对线性系统建模的工具诸如:转移函数,态空间和zpk模块等.这些模块既有连续的也由离散的.同时还有线性时变对象(LTI),诸如tf对象,ss对象和zpk对象.

G=tf(n,d) %n,d分别代表多项式分子系数和分母系数

G=ss(A,B,C,D);%ABCD为态空间描述矩阵

G=zpk(z,p,K)

采样数据系统同样可以使用相同的方法表达,采样间隔时间T=G.Ts

不带有延时的LTI对象可以用LTI系统模块(在控制系统工具箱),直接填写LTI变量即可,如果采用ss模型则还可以填写初始态参数.

带有初始条件的线性系统可以同通过Simulink Extras->Additional Linear中找到

Example 4.7 Consider the transfer function model
G(s) =s2 + 5/s2(s + 1)2((s + 2)2 + 9).
It might be complicated to enter such a model with the direct use of the tf() function presented
earlier, since manual expansion of the denominator polynomial should be made first. A simpler way
of using a transfer function representation will be shown. We can declare the Laplace operator s by
s = tf('s'), then the following commands can be entered to MATLAB, and the LTI object G can
be created in the MATLAB workspace. The variable G can be specified in Fig. 4.55(b) directly.

>> %转移函数的一种声明方式

>> s=tf('s');

>> G=(s^2+5)/(s^2*(s+1)^2*(s+2)^2+9)

G =

s^2 + 5

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

s^6 + 6 s^5 + 13 s^4 + 12 s^3 + 4 s^2 + 9

Continuous-time transfer function.

Example 4.8 Transfer function matrices of multivariable systems can also be represented by
an LTI object. Consider a 4 by 4 transfer function matrix [4]

对于上面的多变量系统使用低阶的模块处理非常困难,然而使用LTI则该系统则比较容易建模.

h1=tf(1,[4 1]); h2=tf(1,[5 1]); %其成员都是h1和h2的倍数;

h11=h1; h12=0.7*h2; h13=0.5*h2; h14=0.2*h2;

h21=0.6*h2; h22=h1; h23=0.4*h2; h24=0.35*h2;

h31=h24; h32=h23; h33=h1; h34=h21; h41=h14; h42=h13; h43=h12; h44=h1;

G=[h11,h12,h13,h14; h21,h22,h23,h24; h31,h32,h33,h34; h41,h42,h43,h44];

Example 4.9 Consider the discrete state space model given by

其采样间隔为T=0.1s,LTI中的变量G可以如下声明:

F=[0,-2,-2,-1.1; 0.5,1.8,0.8,0.5; 0.5,0.8,1.8,0.5; -0.5,-0.8,-0.7,0.4];
G=[0.1,0.1; 0.2,0.1; 0.3,0.1; 0.1,0]; C=[1 0 0 0]; G=ss(F,G,C,0,0.1)

Analysis Interface for Linear Systems

Matlab提供了很多分析工具,例如bode(G)用来分析系统的伯特图.nyquist(G)和nichols(G)用来绘制奈奎斯特图和尼古拉斯图.step(G)和impulse(G)用来画越截图和脉冲图

Analysis->Control Desgin ->Linear Analysis

4.6 Simulation of Continuous Nonlinear Stochastic Systems(连续非线性随机系统的仿真)

在第三章曾经提及对于由白噪音驱动的连续系统,随机数生成器不能直接使用.第三章的处理也仅仅是在线性系统中使用.利用文献中介绍的非线性随机性处理方法非常难以扩展.

4.6.1 Simulation of Random Signals in Simulink(随机信号的仿真)

在Source群组中的Band-Limited White Noise(带宽限定白噪声)模块可以用来模拟指定强度的白噪音输入.十几场该模块扮演了1/sqrt(Δt)*Rand()的脚色.

Example 4.10 Consider again the system model shown in Example 3.36. Approximate simulation methods can be used, and the Simulink model is constructed in Fig. 4.61(a). Selecting
T = 0.1s, the menu item Simulation → Simulation Parameters can be selected. A dialog box
shown in Fig. 4.34 is displayed. The fixed fourth-order Runge–Kutta algorithm can be selected, with
a step size of 0.1s. If the terminating time is assigned to 30 000T, the 1000 points Workspace I/O
item in the dialog box should be clicked to off. The simulation process can be invoked and the outputsignal can be returned to the MATLAB workspace under the name yout. The following statements
can be used to estimate the probability density function, as shown in Fig. 4.61(b). It can be seen that
the results agree well with theoretical results.