1. .
2. .
3. .
4. k, kd, k -, - ϲ-.
5. (, , ).
6. .
7. .
MATLAB.
MatLab - . MatLab, , , .
MatLab , MATLAB for Windows ( 4.0), Matlab, :
Signal Processing Toolbox " ",
Optimization Toolbox "",
Neural Network Yoolbox " ",
Control System Yoolbox" ";
SplineToolbox "";
SIMULINK (Dynamic System Simulation Software) " "
MatLab , , , toolbox ( ). , m-, . - MatLab MATLAB for Windows ( 4.0), - Matlab, Signal.
MatLab .
matlab
Matlab
Matlab . : ACOT, PLOT, EIG, CEIL, CUMSUM, BALANCE, MAX, SORT, SUM, MIN, RATS.
:
1: F(x) .
0,01.
ABS - ABS() . -, ABS() , .
PLOT - . PLOT(X,Y) X ( - , - ). X Y , , .
|
|
:
x = -10:0.01:10;
y=acot(x)+2*(x-2).^2-abs(4*x-3);
Warning: Divide by zero.
(Type "warning off MATLAB:divideByZero" to suppress this warning.)
> In C:\MATLAB6p5\toolbox\matlab\elfun\acot.m at line 8
plot(x,y);
EIG
EIG (A, B) , A .
[V,D]=E1G(A,B) D, , V, , A*V=B*V*D.
2: .
a =
1.0000 1.2000 2.0000
1.2000 1.0000 0.4000
2.0000 0.4000 2.0000
b =
1 -1 2
1 2 1
2 0 3
eig(a,b)
ans =
0.6693
2.0000
2.3307
>>a=[1 1.2 2;1.2 1 0.4;2 0.4 2];
>> [v,d]=eig(a);
>> eig(a)
ans =
-0.8649
0.9128
3.9521
>> [v,d]=eig(a)
v =
-0.7780 -0.1099 0.6186
0.3960 -0.8502 0.3470
0.4878 0.5149 0.7049
d =
-0.8649 0 0
0 0.9128 0
0 0 3.9521
ROUND
ROUND (). , , .
CEIL(A)
ceil(). , , .
3: .
round (). :
a=[1 1.2 2;1.2 1 0.4;2 0.4 2];y=round(a)
y =
1 1 2
1 1 0
2 0 2
ceil().
a =
1.0000 1.2000 2.0000
1.2000 1.0000 0.4000
2.0000 0.4000 2.0000
ceil(a)
ans =
1 2 2
2 1 1
2 1 2
RATS
rats(A) .
4: . . ( 2 ).
:
a=[1 1.2 2;1.2 1 0.4;2 0.4 2]
a =
1.0000 1.2000 2.0000
1.2000 1.0000 0.4000
2.0000 0.4000 2.0000
>> c=rats(a)
c =
1 6/5 2
6/5 1 2/5
2 2/5 2
5: (, , ). :
a =
3 1 1
1 2 3
-2 5 -2
b =
1 -1 2
1 2 1
2 0 3
1) : c=a+b
c =
4 0 3
2 4 4
0 5 1
2) : c=a*b
c =
6 -1 10
9 3 13
-1 12 -5
3) :
3.1) c=a/b
c =
-13.0000 -6.0000 11.0000
8.0000 5.0000 -6.0000
9.0000 7.0000 -9.0000
c=b/a
c =
-0.0577 0.4423 -0.3654
0.3462 0.3462 0.1923
0.2115 0.7115 -0.3269
3.2) c=a\b
c =
0.1923 -0.6346 0.5385
0.4615 0.0769 0.6923
-0.0385 0.8269 -0.3077
c=b\a
c =
-31 13 -25
6 -2 6
20 -7 16
CUMSUM - CUMSUM(X) X. - , CUMSUM(X) , n- n X. X CUMSUM(X) , .
|
|
6: . :
a =
3 1 1
1 2 3
-2 5 -2
cumsum(a), , . :
a=[3 1 1;1 2 3;-2 5 -2];cumsum(a)
ans =
3 1 1
4 3 4
2 8 2
BALANCE.
BALANCE , , .. .
[T,Ab]=BALANCE(A) T, , Ab= T\A*T. BALANCE(A) Ab.
7: .., .
a =
3 1 1
1 2 3
-2 5 -2
>>balance(a)
ans =
3 1 1
1 2 3
-2 5 -2
MAX - MAX(X) X () - -, . [Y,I] = () Y , I .
MIN - MIN .
8: .
a =
3 1 1
1 2 3
-2 5 -2
max() min(), .
[y,i]=max(a)
y =
3 5 3
i =
1 3 2
[y,i]=min(a)
y =
-2 1 -2
i =
3 1 3
SORT
SORT(X) X . [Y,I] = SORT(X) I, ( , ) Y). X , Y=(I). X , .
9: . : a=[3 1 1;1 2 3;-2 5 -2];
sort(), .
sort(a)
ans =
-2 1 -2
1 2 1
3 5 3
SUM
SUM(X) X . X SUM(X) - X. SUM(D/AG(X)) X.
10. - .
:
a =
-13 -8 -3 2 7
0 -1 7 -3 -13
-13 -8 3 4 -1
-13 -9 4 -1 -6
-26 -17 7 3 -7
- sum(), . sum() - . :
a=[-13 -8 -3 2 7;0 -1 7 -3 -13;-13 -8 3 4 -1;-13 -9 4 -1 -6;-26 -17 7 3 -7];
y=sum(a)
y =
-65 -43 18 5 -20
11. . :
b_1=[-2.8;-26.3;-16.8;-29.1;-45.9]
b_1 =
-2.8000
-26.3000
-16.8000
-29.1000
-45.9000
b_2=[-1.8;-26.1;-15.8;-29.77;-46.9]
b_2 =
-1.8000
-26.1000
-15.8000
-29.7700
-46.9000
:
a =
-13 -8 -3 2 7
0 -1 7 -3 -13
-13 -8 3 4 -1
-13 -9 4 -1 -6
-26 -17 7 3 -7
b1 : 1=[A, b1]. b1, .. -.
A_1=[a;b_1']
A_1 =
-13.0000 -8.0000 -3.0000 2.0000 7.0000
0 -1.0000 7.0000 -3.0000 -13.0000
-13.0000 -8.0000 3.0000 4.0000 -1.0000
-13.0000 -9.0000 4.0000 -1.0000 -6.0000
-26.0000 -17.0000 7.0000 3.0000 -7.0000
-2.8000 -26.3000 -16.8000 -29.1000 -45.9000
|
|
b2 , :
A_2=[a,b_2]
A_2 =
-13.0000 -8.0000 -3.0000 2.0000 7.0000 -1.8000
0 -1.0000 7.0000 -3.0000 -13.0000 -26.1000
-13.0000 -8.0000 3.0000 4.0000 -1.0000 -15.8000
-13.0000 -9.0000 4.0000 -1.0000 -6.0000 -29.7700
-26.0000 -17.0000 7.0000 3.0000 -7.0000 -46.9000
SOLVE
solve, .
12 .
:
MatLab :
[x,y]=solve('acot(x)+2*(y-2)^2=5','y-abs(4*x-3)=3')
x =
0.64631476499002086240204017407305
y =
3.4147409400399165503918393037078
MatLab. MatLab , . MatLab .
. ACOT, PLOT, EIG, CEIL, CUMSUM, BALANCE, MAX, SORT, SUM, MIN. , .
MatLab , , , toolbox ( ).
.
1. .. . .- : , 2003.-128.
2. .. - MATLAB for Windows.-: , 2001.-142.
3. . MATLAB / . ...- .-: , 1994.
Allbest.ru
1
http://apeshnik.narod.ru/matlab/part1.htm
I. MATLAB
1. , (+, -).
2. , (*, /).
3. (^).
4. (sqrt): sqrt(16+9)
5. , .
6. %
7. : t=(0:0.5:7)' %
8. (: a = [1 2 3;4 5 6]):
;
;
-;
-.
9. :
, (+, -);
(*);
(inv), (pinv);
(/);
(^);
(').
c : tril().
c : triu().
¾ : fliplr(A).
¾ : flipud(A).
¾ 900 : rot90(A).
¾ 900 : rot90(A,-1).
¾ 900 : rot90(A,k), k = 1, 2,... , 900.
¾ .. .
¾ n: eye(n).
|
|
¾ : eye(size(A)).
¾ n´m: ones(n,m). : ones(n).
¾ : ones(size(A)).
¾ n´m: zeros(n,m). : zeros(n).
¾ : zeros(size(A)).
¾ n: pascal(n). -.
¾ : diag(A).
¾ : trace(A).
¾ sum diag: sum(diag(A)).
¾ n (n>2): magic(n).
¾ MATLAB: - , .
¾ : diag(diag(A)).
¾ - : diag(P).
¾ - N: diag(N).
¾ , diag.
¾ : eig(A).
¾ : A = [1 2 3;4 5 6]; A(:,2:3) 2- 3-
¾ rand (, rand(3,4))
¾ randn (, randn(2,5))
¾ : help--.
¾ ( ):
(: [1 2 3;4 5 6].^2) .
.9 .
8. : poly(A).
9. : poly(sym(A)). .
10. ( s): poly(sym(A),sym('s')).
11. .. 1.26, 1.27, 1.28.
12. : poly(eig(A)).
13. , : poly(P).
14. , : poly2sym(P). .
II. , , .
1. : size(A).
2. : length(P).
3. size , length ( ).
4. : disp(A), disp(P), disp(a), - ( , , =2+3i).
5. : - , isprime(a) 1 (), 0 (). ( ).
6. 2... : primes(a). . primes(a) , 2... .
7. : sign(a). sign , , .
8. : round(a).
9. abs: abs((3-5)/2), abs(-2^3)
III. .
1. N : factor(N).
2. : sum(P). .
3. : sum(A). , .
4. : prod(P).
5. : prod(A).
6. : perms(P).
- -.
2-D MATLAB.
- , MATLAB m- ( m). - ( ) MATLAB, m-.
|
|
1. .
1.
10. MATLAB : = [1 2 3;4 5 6] = [1,2,3;4,5,6];
11. : 1 = ';
12. b = [10 20 30;40 50 60];
13. 1 b: = 1*b;
14. ' 1 b:' disp(' 1 b: ');
15. , Enter;
16. , () ;.
17. .
18. 1-6 -. edit. , . 1-6 - (, Lab1). - .
19. MATLAB.
20. - . - Enter;
21. - edit (, Lab1).
22. - . %. .. % , .. , %, , MATLAB.
23. - . : inv(c).
2.
, .
:
(1)
, () , .. .
F(t):
(2)
[0, 1],
1. , .
1.1. 18 , 2:
% , 1
% [0, 1]
%
% -
%
1.2. 18 expinv:
p2=rand(18,1);
T=expinv(p2,0.5)
t2=sort(T)
1.3. 18 exprnd:
for k=1:18
y(k)=exprnd(0.5);
end
R=sort(y) % R
1.1, 1.2, 1.3 - , MATLAB m. m- () MATLAB.
.
() MATLAB DISTTOOL (disttool).
DISTTOOL . DISTTOOL : cdf ( ), pdf ( ).
() MATLAB RANDTOOL(randtool).
RANDTOOL .
. 2-D MATLAB.
2.1. :
t=0:0.01:2*pi; y=3*(1+sin(t)); polar(t,y)
2.2. hold on: t=0:0.01:2*pi;y1=3*(1+sin(t));y2=3*(1-sin(t));
polar(t,y1),hold on,polar(t,y2,'r')
2.3. hold on:
t=0:0.01:2*pi;y1=3*(1+sin(t));y2=3*(1-sin(t));
y3=3*(1+cos(t)); y4=3*(1-cos(t));
polar(t,y1),hold on,polar(t,y2,'r'),polar(t,y3,'g'),polar(t,y4,'k')
2.4. :
t=0:0.01:2*pi; y=sin(t);
plot(t,y),grid
2.5. gtext:
t=0:0.01:2*pi;y=sin(t);plot(t,y),grid,gtext('t'),gtext('y')
% (t y) .
2.6. fplot.
% sin(t) sin(x) .. :
fplot('sin(t)',[-3*pi 3*pi]),grid % MATLAB
% sin(t) t -0.7 0.7
fplot('sin(t)',[-3*pi,3*pi,-0.7,0.7]),grid
% : sin(t), exp(-0.5t), 3cos(t)
fplot('[sin(t),exp(-0.5*t),3*cos(t)]',[-1,10,-4 5]),grid
: fplot :
.
2.7. title, xlabel, ylabel:
t=0:0.01:2*pi;y=sin(t);
plot(t,y),grid,title(''),xlabel(''),
ylabel(''),gtext('t'),gtext('y')
fplot('[sin(t),3*cos(t)]',[-1,10,-4,5]),grid,title('y_1-sin(t), y_2-3cos(t)'),gtext('y_1'),gtext('y_2')
% .
2.8. legend:
t=0:0.01:2*pi;y1=sin(t);y2=cos(t);
plot(t,y1,'r'),grid,hold on,plot(t,y2), legend('s1','c2')
2.9. legend :
: legend('s1','c2', 2);
: legend('s1','c2', 3);
: legend('s1','c2', 4);
: legend('s1','c2', 1)
: legend('s1','c2');
: legend('s1','c2', -1);
2.10. funtool.
MATLAB funtool (Enter). : , , , ..
% , .1.:
1.
(-) (-)
y yellow
m magenta -
c cyan - r red
g green
b blue ()
w white k black
. .2.8, .
: .2.8 , 1. fplot, :
fplot('sin(t)',[-5,5],'r'),grid, hold on,fplot('3*cos(t)',[-5 5],'g') %
% , .2.
2.
( )
point
o
circle
x
x-mark
*
star
s
suare
d
diamond
v
triangle (down)
()
^
triangle (up)
()
<
triangle (left)
()
>
triangle (right)
()
p
pentagram
h
hexagram
-
solid
:
dotted
(:)
-.
dashdot
-
--
dashed
: .2.7 , 2., .2.8 , 1, 2.
3.
1.1 1.2 .
1- F1:
t1=sort(x);
F1=1-exp(-2*t1);
plot(t1,F1),grid
2- F2:
p2=rand(48,1);
T=expinv(p2,0.5); % 0.5
t2=sort(T);
F2=1-exp(-2*t2);
plot(t2,F2),grid
3- F3:
p3=rand(48,1);
T3=expinv(p2,0.5); % 0.5
t3=sort(T3);
F3=expcdf(t3,0.5); % expcdf
plot(t3,F3),grid
4. .
:
(3)
m , t .
. . .
3- f3:
p3=rand(48,1);
T3=expinv(p2,0.5); % 0.5
t3=sort(T3);
f3=exppdf(t3,0.5); % exppdf
plot(t3,f3),grid
.
1. F1, F2, F3 .
2. f1, f
6
http://apeshnik.narod.ru/matlab/part6.htm
.
ss, initial, dss, lsim, MATLAB.
: MATLAB . , .
(1)
n- , U r- , Y m- , A n´n , n´r , m´n , D m´r (A, B, C, D ).
(1) , .. , ( ) .
(2)
n´n, . [].
1. ss.
(1) A, B, C, D .
. , 3- .
%
A=[-1.23 0 0;2.5 -0.56 0;0 3 -2.3];
B=[4;0;0];
C=[0 0 3.3];
D=0; % D
% s1
s1=ss(A,B,C,D)
%
a =
x1 x2 x3
x1 -1.23 0 0
x2 2.5 -0.56 0
x3 0 3 -2.3
b =
u1
x1 4
x2 0
x3 0
c =
x1 x2 x3
y1 0 0 3.3
d =
u1
y1 0
Continuous-time system.
% s1
eig(s1) % pole
ans =
-2.3000
-0.5600
-1.2300
%
Y.
step(s1,15),grid % 0 15 .
impulse(s1,12),grid % 0 12 .
. :
[0 0 1], [0 0 5], [1 0 0], [0 1 0], [1 1 1].
% size, dcgain
s1=ss(A,B,C,D); %
size(s1)
State-space model with 1 input(s), 1 output(s),and 3 state(s).
% size(s1): 1 , 1 ,
dcgain(s1) % s1
ans =
62.4905
% :
[0 0 1], [0 0 0.3], [0 0 5], [1 0 0], [0 1 0], [1 1 1].
2. .
2.1. tf.
tf(s1)
Transfer function:
--------------------------------
s^3 + 4.09 s^2 + 4.806 s + 1.584
% : 99/1.584=62.5
2.2. zpk.
zpk(s1)
Zero/pole/gain:
-------------------------
(s+2.3) (s+1.23) (s+0.56)
% :
99/(2.3*1.23*0.56)
ans =
62.4905
%
3. initial.
(1), , ..
(3)
(3) Y (1) ss ( s1).
% s1 (0): .. - [10; 10; 10].
% [10; 10; 10]
initial(s1,[10;10;10],15),grid % 0 15
initial(s1,[10;10;10],[0:0.1:7]),grid % 0 7 0.1
% ( ) .
% s1 s2
A1=[-1.23 0 0;2.5 -0.56 0;0 3 -2.3];
B1=[4;0;0];
C1=[0 0 3.3];
D1=0;
A2=[-3 0 0;5 -2.56 0;0 3.3 -1.3];
B2=[3;0;0];
C2=[0 0 3.3];
D2=0;
s1=ss(A1,B1,C1,D1);
s2=ss(A2,B2,C2,D2);
% initial
initial(s1,s2,[10;10;10],9),grid,legend('s1','s2')
% ( )
.
¾ (1) (3) initial.
¾ initial : [-10,-10,10], [1,1, 10], [10, 10, 1], [1, 1, -1], [0,0,10].
¾
¾ s1 s2 2: [0,0,-3.3], [0 0 1], [12 13 -10], [5 0 0], [0 5 0]
. initial , .
4. dss.
, , , . MATLAB dss, ss .
.
(4)
(4) :
(5)
,.
(4) . step.
%
A=[-0.2 0 0;3 -0.5 0;0 6 -1.8];
B=[5;0;0]; C=[0 0 1]; D=0;
E=[2.5 0 0;0 1.07 0;0 0 1.3];
% dss.
ds1=dss(A,B,C,D,E);
% 0 12.
step(ds1,12),grid,title('ds1')
% ss A,B,C,D
s1=ss(A,B,C,D);
step(s1,12),grid,title('s1')
% dss ss , dss .
.
¾ 4 , .. dss: 12=[2.5 0 0;0 1.07 0;1 0 1.3]; E13=[2.5 0 0.7;0 1.07 0;1 0 1.3]; E14=[1.5 0 0.7;0 1.07 0;1 0 1.3]; E16=[0.989 0 0;0 0.989 0;0 0 0.989] : 7 100.
¾ , dss, initial impulse.
5. lsim.
lsim , ss.
1. (4) [0 21] .
%
A=[-0.2 0 0;3 -0.5 0;0 6 -1.8];
B=[5;0;0]; C=[0 0 1]; D=0;
s22=ss(A,B,C,D); % ss-
t=0:0.1:21;
u=2*ones(length(t),1); % -, 2
%
step(s22,22,'k'),grid,hold on,lsim(s22,u,t,[0;0;0],'m.')
% step , lsim "" .
u=10*exp(-0.1*t).*cos(t); %
%
step(s22,22,'k'),grid,hold on,lsim(s22,u,t,[0;0;0],'m.')
2. .
(6)
(6) , (4), ,
MATLAB B=[5 0;0 20;0 0].
A=[-0.2 0 0;3 -0.5 0;0 6 -1.8];
B=[5 0;0 20;0 0];
C=[0 0 1]; D=0;
s33=ss(A,B,C,D);
dcgain(s33) %
ans =
500.0000 133.3333
%
step(s33,21),title(' U_1, U_2')
% lsim
t=0:0.1:41;
u1=ones([length(t),1]);
u2=ones([length(t),1]);
u=[u1, u2]; % : u=ones(length(t),2)
%
lsim(s33,u,t,[0;0;0]),grid,title(' 2- ')
% 500+133.3333=633.3333
.
¾ , (500) 200 . step lsim.
¾ step lsim : [0,1,0], [1,0,0],[1,1,1].
¾ lsim (6) ode45.
step.
step Y, . plot.
(6) :
A=[-0.2 0 0;3 -0.5 0;0 6 -1.8];
B=[5 0;0 20;0 0];
C=[0 0 1]; D=0;
s44=ss(A,B,C,D);
% s44 A, B, C, D
% step
[y,t,x]=step(s1,21); % 0 21
% y,t,x
size(y),size(t),size(x)
ans =
101 1 2 % Y
ans =
101 1 % t
ans =
101 3 2 %
Y , ( ). ( ) . 101 .
Y, X plot.
%
plot(t,y(:,1,1),'r'), grid, hold on, plot(t,y(:,1,2)), legend('Y_1','Y_2')
%
plot(t,x(:,:,1)),grid,legend('X_1','X_2','X_3'),title(' 1- ')
%
plot(t,x(:,:,2)),grid,legend('X_1','X_2','X_3'),title(' 2- ')
% , 2- ( 6 3- ).
.
¾ step (6) .
¾ step (6) . : 2, 10, 20, 0.2.
lsim.
(6) :
% ss- . lsim.
[y1,t1,x1]=lsim(s1,u,T,[0;0;0]);%
size(y1),size(t1),size(x1)
ans =
211 1 %
ans =
211 1 % ( )
ans =
211 3 %
% lsim ()
%
plot(t1,y1), grid, title(' ')
plot(t1,x1), grid, title(' '),legend('x_1','x_2','x_3')
.
¾ lsim :,,,. , , lsim.
¾ [0, 50] : [1, 0, 0], [0, 1, 0], [1, 1, 1].
impulse.
% (6)
[Y0,T0,X0]=impulse(s1,25); % 0 25
size(Y0),size(T0),size(X0)
ans =
101 1 2 %
ans =
101 1 %
ans =
101 3 2 %
%
plot(T0,Y0(:,:,1),'r'), grid, hold on, plot(T0,Y0(:,:,2),'m'), legend(' u_1',' u_2')
%
5
http://apeshnik.narod.ru/matlab/part5.htm
MATLAB.
MATLAB laplace.
1.1. syms x y t; %
f1 = t; % -;
L1 = laplace(f1) % ;
f2 = sym('10'); % f2 = 10 ;
L2 = laplace(f2) % ;
f3 = sym('3')*t + sym('7'); % ;
L3 = laplace(f3) % ;
f4 = exp(-t); % ( );
L4 = laplace(f4) % ;
f5 = exp(t); % ( );
L5 = laplace(f5) % ;
L6 = laplace(exp(t))
f6 = sin(x);
L6 = laplace(f6) % sin(x);
L7 = laplace(cos(x)) % cos(x);
.
. .
:
(1)
m £ n .
tf. % . help tf;
2.1. W1:
. (2)
2.2. MATLAB ( -):
W1=tf(12,[1 2 3 1])
% :
Transfer function:
---------------------
s^3 + 2 s^2 + 3 s + 1
2.3.. W2:
. (3)
MATLAB :
W2=tf([3 5 4],[1 2 3 1])
% :
Transfer function:
3 s^2 + 5 s + 4
---------------------
s^3 + 2 s^2 + 3 s + 1
zpk (zero-pole-gain), k gain.
, .
2.4. , 7.7, . .
MATLAB :
W3=zpk([],[-3.3,-0.25,-12.7],7.7)
% :
Zero/pole/gain:
7.7
-------------------------
(s+3.3) (s+12.7) (s+0.25)
% [],
%
2.5. , 7.7, .
MATLAB :
W4=zpk([4,-5],[-3.3,-0.25,-12.7],7.7)
% :
Zero/pole/gain:
7.7 (s-4) (s+5)
-------------------------
(s+3.3) (s+12.7) (s+0.25)
2.6. .
2.6.1. W4 :
% MATLAB :
w44=tf(W4)
% :
Transfer function:
7.7 s^2 + 7.7 s - 154
---------------------------------
s^3 + 16.25 s^2 + 45.91 s + 10.48
2.6.2. :
% MATLAB :
.
W5=tf(10,[1,3,2])
% :
Transfer function:
-------------
s^2 + 3 s + 2
% , , 10, .
% w55:
w55=zpk(W5) %
%
Zero/pole/gain:
---------
(s+2)(s+1)
% W2 :
w22=zpk(W2) %
%
Zero/pole/gain:
3 (s^2 + 1.667s + 1.333)
--------------------------------
(s+0.4302) (s^2 + 1.57s + 2.325)
% (1) SISO (single input single output).
2.7. .
, , . "", , "", , .. ( ).
eig.
2.7.1. W5 w55.
eig(W5) % W5
ans =
-2
-1
eig(w55) % w55
ans =
-2
-1
% . w55 ,
%
2.7.2. W2 w22.
eig(W2) % W2
ans =
-0.7849 + 1.3071i
-0.7849 - 1.3071i
-0.4302
eig(w22) %w22 , W2
ans =
-0.7849 + 1.3071i
-0.7849 - 1.3071i
-0.4302
% . w22.
2.7.3. .
, 6.78 zpk w66:
w66=zpk([],[-6.78,-6.78,-6.78],7)
%
eig(w66)
ans =
-6.7800
-6.7800
-6.7800
%
2.7.4. .
.
- zpk.
w77=zpk([],[-5+2.3*i,-5-2.3*i,-5.7],6)
Zero/pole/gain:
---------------------------
(s+5.7) (s^2 + 10s + 30.29)
% , -5.7, -: -5+2.3i; -5-2.3i,
% i ( j ).
, w77, :
W77=tf(w77)
Transfer function:
--------------------------------
s^3 + 15.7 s^2 + 87.29 s + 172.7