阶跃响应采样数据如下表所示，求出传递函数的估计值。
四支僵劲不能动
| | | | | |
0 | 0 | 0.20 | 0.0338 | 0.90 | 0.4409 通分是什么意思 |
0.02 | 0.0001 | 0.22 | 0.0395 | 1.00 | 0.4924 |
0.04 | 0.0005 | 0.24 | 0.0480 | 1.50 | 0.6904 |
0.06 | 0.0014 | 0.26 | 0.0571 | 2.00 | 0.8121 |
0.08 | 0.0031 | 0.28 | 0.0668 | 2.50 | 0.8860 |
0.10 | 0.0057 | 0.30 | 做饭教程0.0771 | 3.00 | 0.9309 |
0.12 | 宁为玉碎不为瓦全的意思0.0091 | 小诗一首 0.50 | 0.1979 | 3.50 | 0.9581 |
0.14 | 0.0135 | 0.60 | 0.2624 | 4.00 | 0.9746 |
0.16 | 0.0187 | 0.70 | 0.3253 | 5.00 | 0.9907 |
0.18 | 0.0248 | 0.80 | 0.3851 | | |
| | | | | |
解:
MATLAB程序如下：
t=[0:0.02:0.30 0.50:0.10:1.00 1.50:0.50:4.00 5.00];
yt=[0 0.0001 0.0005 0.0014 0.0031 0.0057 0.0091 0.0135 0.0187 0.0248 0.0338 ...
0.0395 0.0480 0.0571 0.0668 0.0771 0.1979 0.2624 0.3253 0.3851 0.4409 ...
0.4924 0.6904 0.8121 0.8860 0.9309 0.9581 0.9746 0.9907];
yinf=1;
%firstly fitting euqation
y1=log(yinf-yt);
p=polyfit(t,y1,1);
alpha=-p(1);
A=-exp(p(2));
yt1=yinf+A*exp(-alpha*t);
figure(1)
plot(t,yt,'*',t,yt1)
grid on;
figure(2)
plot(t,p(1)*t+p(2),t,y1,'*');
grid on;
e1=yt1-yt;
figure(3)
plot(t,e1)
grid on;
shg
a1=find(abs(e1)<=0.05);
a11=find(t(a1)>1.0);
y11=log(yinf-yt(a1(a11(1)):29));
p=polyfit(t(a1(a11(1)):29),y11,1);
alpha=-p(1);
A=-exp(p(2));
figure(4)
plot(t,p(1)*t+p(2),t,y1,'*');
grid on;
yt11=yinf+A*exp(-alpha*t);
figure(5)
plot(t,yt,'*',t,yt11)
grid on;
%condly fitting euqation
ys2=yt-yt11;
a2=find(ys2>=0.0001);
y2=log(ys2(a2));
t2=t(a2);
p2=polyfit(t2,y2,1);
beta=-p2(1);
B=exp(p2(2));
yt2=yt11+B*exp(-beta*t);
figure(6)
plot(t,yt,'*',t,yt2)
grid on;
e2=yt2-yt;
figure(7)
plot(t,e2)
grid on;
shg
b=find(abs(e2)<=0.001);
b2=find(t(b)>0.5);
我是美术生y22=log(ys2(b(b2(1)):29));
p=polyfit(t(b(b2(1)):29),y22,1);
beta=-p2(1);
B=exp(p2(2));
yt22=yt11+B*exp(-beta*t);
figure(8)招工简章
plot(t,e2)
grid on;
shg
figure(9)
plot(t,yt,班主任办公室'*',t,yt22)
grid on;
hold on;
e2=yt22-yt;
syms xf
f=(x+alpha)*(x+beta)+A*(x+beta)*x+B*(x+alpha)*x;
