Оценка параметров переходных сигналов по экспериментальным данным.

1. Постановка задачи:

Проанализировать переходные сигналы при различных данных.

2. Текст программы:

>> t=0:0.1:360;

>> t1=t*pi/180;

>> U=30*sin(t1+30*pi/180);

>> plot(t,U),grid

U=250*sin(t1);

>> plot(t,U),grid

>> t=0:0.1:720;

>> t1=t*pi/180;

>> U=250*sin(t1);

>> U1=250*sin(t1-120*pi/180);

>> U2=250*sin(t1+120*pi/180);

>> plot(t,U,t,U1,t,U2),grid

>> alf=0:15:180;

>> bet=alf.*(pi/180);

>> H=[sin(bet)' cos(bet)' sin(2*bet)' cos(2*bet)' sin(3*bet)' cos(3*bet)']

H =

0 1.0000 0 1.0000 0 1.0000

0.2588 0.9659 0.5000 0.8660 0.7071 0.7071

0.5000 0.8660 0.8660 0.5000 1.0000 0.0000

0.7071 0.7071 1.0000 0.0000 0.7071 -0.7071

0.8660 0.5000 0.8660 -0.5000 0.0000 -1.0000

0.9659 0.2588 0.5000 -0.8660 -0.7071 -0.7071

1.0000 0.0000 0.0000 -1.0000 -1.0000 -0.0000

0.9659 -0.2588 -0.5000 -0.8660 -0.7071 0.7071

0.8660 -0.5000 -0.8660 -0.5000 -0.0000 1.0000

0.7071 -0.7071 -1.0000 -0.0000 0.7071 0.7071

0.5000 -0.8660 -0.8660 0.5000 1.0000 0.0000

0.2588 -0.9659 -0.5000 0.8660 0.7071 -0.7071

0.0000 -1.0000 -0.0000 1.0000 0.0000 -1.0000

>> rank(H)

ans =

6

>> y1=[12.7 33.8 52.0 60.9 57.8 45.7 31.1 20.1 15.6 15.1 13.0 4.2 -12.7]';

>> x=(H'*H)^-1*H'*y1

x =

42.3858

22.5645

-0.0418

0.0059

11.3261

-9.8647

>> U1m=(x(1)^2+x(2)^2)^0.5

U1m =

48.0178

>> Q1=atan(x(2)/x(1))*180/pi

Q1 =

28.0291

>> U2m=(x(3)^2+x(4)^2)^0.5

U2m =

0.0422

>> Q2=atan(x(4)/x(3))*180/pi

Q2 =

-7.9760

>> U3m=(x(5)^2+x(6)^2)^0.5

U3m =

15.0197

>> Q3=atan(x(6)/x(5))*180/pi

Q3 =

-41.0550

>> y=[12.6937 33.7823 52.0270 60.8661 57.8116 45.7234 31.0608 20.1415 15.5952 15.0802 12.9958 4.1658 -12.6937]';

>> z=y-y1

z =

-0.0063

-0.0177

0.0270

-0.0339

0.0116

0.0234

-0.0392

0.0415

-0.0048

-0.0198

-0.0042

-0.0342

0.0063

>> j=0.5*z'*z

j =

0.0039

> j=0.5*(norm(z,'fro'))^2

j =

0.0039

Решение задач модели цепи постоянного и переменного тока.

1. Постановка задачи:

Получение навыков в решении моделей цепей переменного и постоянного тока.

2. Текст программы:

Цепь постоянного тока

>> r1=20; r2=5; r3=10; r4=10; r5=5;

>> r6=2; r7=1; e1=200; e2=80; e4=30; e6=38; e7=60;

>> g11=1/r1+1/r2+1/r7; g12=-1/r1; g13=-1/r2;

>> g22=1/r1+1/r4+1/r5+1/r3; g21=g12; g23=-1/r3;

>> g33=1/r6+1/r3+1/r2; g31=g13; g32=g23;

>> i11=2+e7/r7+e2/r2-e1/r1;

>> i22=-2+e1/r1-e4/r4;

>> i33=-e2/r2-e6/r6;

>> G=[g11 g12 g13; g21 g22 g23; g31 g32 g33]

G =

1.2500 -0.0500 -0.2000

-0.0500 0.4500 -0.1000

-0.2000 -0.1000 0.8000

>> pause,

>> IVG=inv(G)

IVG =

0.8424 0.1444 0.2286

0.1444 2.3105 0.3249

0.2286 0.3249 1.3478

>> pause,

>> I=[i11 i22 i33]

I =

68

5

-35

>> pause,

>> U=IVG*I

U =

50.0000

10.0000

-30.0000

>> pause

>> F=[U(1,1)-U(2,1),U(3,1)-U(1,1),U(2,1)-U(3,1),U(2,1),U(2,1),U(3,1),-U(1,1)];

>> E=[e1, e2, 0, e4, 0, e6, e7];

>> GG=[1/r1, 1/r2, 1/r3, 1/r4, 1/r5, 1/r6, 1/r7];

>> GD=diag(GG,0);

>> IV=GD*(F'+E')

IV =

12.0000

0

4.0000

4.0000

2.0000

4.0000

10.0000

Цепь переменного тока

>> i=sqrt(-1);

>> E1=24*exp(i*0); E2=12*exp(i*(pi/2));

>> X1=-2; X2=2; X3=-2; R1=5; R2=5;

>> Y11=1/(i*X1)+1/R1+1/R2;

>> abs(Y11);

>> fi(180/pi)*angle(Y11);

>> Y12=-1/R2; Y21=-1/R2;

>> Y22=1/R2+1/(i*X3)+1/(i*X2);

>> Y1=1/(i*X1); Y2=1/(i*X2);

>> Y4=1/(i*X3);

>> YA=[Y11 Y12; Y21 Y22];

>> Y=inv(YA);

>> E=[E1*Y1; E2*Y2];

>> F=Y*E;

>> I=[E1-F(1,1); F(1,1); F(1,1)-F(2,1);F(2,1);E2-F(2,1)].*[Y1; 1/R1; 1/R2; Y4; Y2]

I =

-1.0345 - 0.4138i

4.9655 - 0.4138i

-6.0000 - 0.0000i

1.0345 +27.4138i

7.0345 +27.4138i

>> pause

>> ia=(E1-F(1,1))*Y1; ib=F(1,1)*(1/R1);

>> ic=(F(1,1)-F(2,1))*(1/R2); id=F(2,1)*Y4;

>> ie=(E2-F(2,1))*Y2;

>> IV=I;

>> I1=abs(IV(1,1));

>> k=(180/pi);

>> FI1=k*angle(IV(1,1));

>> I2=abs(IV(2,1));

>> FI2=k*angle(IV(2,1));

>> I3=abs(IV(3,1));

>> FI3=k*angle(IV(3,1));

>> I4=abs(IV(4,1));

>> FI4=k*angle(IV(4,1));

>> abs(ie);

>> k*angle(ie);

>> I5=abs(IV(5,1));

>> FI5=k*angle(IV(5,1));

>> Imod=[I1 I2 I3 I4 I5]

Imod =

1.1142 4.9827 6.0000 27.4333 28.3019

>> pause,

>> Angles=[FI1 FI2 FI3 FI4 FI5]

Angles =

-158.1986 -4.7636 -180.0000 87.8389 75.6082

>> pause,

>> Pi=E1*(IV(1,1))'+E2*(IV(5,1))'

Pi =

3.0414e+002 +9.4345e+001i

>> pause,

>> Pc=((abs(IV(1,1)))^2)*(i*X1)+((abs(IV(2,1)))^2)*R1+((abs(IV(3,1)))^2)*R2+((abs(IV(4,1)))^2)*(i*X3)+((abs(IV(5,1)))^2)*(i*X2)

Pc =

3.0414e+002 +9.4345e+001i

>> DM=(ia)*(ia)'*(i*X1)+(ib)*(ib)'*R1+(ic)*(ic)'*R2+(id)*(id)'*(i*X3)+(ie)*(ie)'*(i*X2);

>> pause

>> error=Pi-Pc

error =

-1.1369e-013 -3.1264e-013i

>> p1=IV(1,1)

p1 =

-1.0345 - 0.4138i

>> pt1=IV(2,1)+IV(3,1)

pt1 =

-1.0345 - 0.4138i

>> pause

>> p2=IV(3,1)

p2 =

-6.0000 - 0.0000i

>> pt2=-IV(5,1)+IV(4,1)

pt2 =

-6