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Control Automático de Procesos. Trabajo Práctico de Gabinete N° 1: Práctica intensiva de Introducción a Matlab. Alumna: Quevedo Sol Agustina >> A = [1,2,3 4,5,6 7,8,9] A= 1 4 7
2 5 8
3 6 9
>> A(1,2) ans = 2 >> VECTOR = [1,2,3] VECTOR = 1
2
3
>> MATRIZ = [1,2,3;4,5,6;7,8,9] MATRIZ = 1 4 7
2 5 8
3 6 9
>> eye (10) ans = 1 0 0 0 0 0 0
0 1 0 0 0 0 0
0 0 1 0 0 0 0
0 0 0 1 0 0 0
0 0 0 0 1 0 0
0 0 0 0 0 1 0
0 0 0 0 0 0 1
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0 0 0 0 1 0 0 0 0 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
>> ones (10) ans = 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
>> MATRIZ2 = [1 2 3 123 1 2 3] MATRIZ2 = 1 1 1
2 2 2
3 3 3
>> C = MATRIZ * MATRIZ2 C= 6 12 18 15 30 45 24 48 72 >> D = MATRIZ .* MATRIZ2 D= 1 4 9 4 10 18 7 16 27
>> det(MATRIZ)
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
ans = 6.6613e-16 >> det (C) ans = 0 >> det (MATRIZ2) ans = 0 >> inv(C) Warning: Matrix is singular to working precision. ans = Inf Inf Inf Inf Inf Inf Inf Inf Inf
>> C(:,2) ans = 12 30 48 >> VECTOR2 = 2*VECTOR VECTOR2 = 2
4
6
>> VECTOR2(:,2) ans = 4
>> P=[1,3,-2,0,1]
P= 1
3 -2
0
1
>> roots(P) ans = -3.5421 + 0.0000i 0.5446 + 0.4685i 0.5446 - 0.4685i -0.5470 + 0.0000i
raices = -3.5421 + 0.0000i 0.5446 + 0.4685i 0.5446 - 0.4685i -0.5470 + 0.0000i >> polyval (P,raices) ans = 1.0e-12 * -0.2807 + 0.0000i 0.0011 + 0.0003i 0.0011 - 0.0003i 0.0002 + 0.0000i >> P2 = [3 4 5] P2 = 3
4
5
>> P3 = [2 1 2] P3 = 2
1
2
>> PP = conv(P2,P3) PP =
6 11 20 13 10
>> [Q,R] = deconv (P2,P3) Q= 1.5000
R= 0 2.5000 2.0000 >> >> a=[2, 3; 5, -2] a= 2 3 5 -2 >> b=[4; 6] b= 4 6 >> s=inv(a)*b s= 1.3684 0.4211
>> t=solve('2*x^2+3*x-2') t= -2 1/2 >> [a,b] = solve('a^2 + a*b - b = 3','a^2 - 4*b - 5 = 0') a=
-1 - 2*2^(1/2) - 1 2*2^(1/2) - 1
b= -1 2^(1/2) + 1 1 - 2^(1/2) >> y=dsolve('Dy-x-y=0','y(0)=1', 'x') y= 2*exp(x) - x - 1 >> ezplot(y, 0, 2); grid on
>> int(sym('x*sin(x)')) ans = sin(x) - x*cos(x) >> s=int(sym('x*sin(x)'),0,pi)
s= pi >> syms x >> y=x^3-8 y= x^3 - 8 >> t=factor(y) t= (x - 2)*(x^2 + 2*x + 4) >> e=taylor(exp(x),x, 5) e= exp(5) + exp(5)*(x - 5) + (exp(5)*(x - 5)^2)/2 + (exp(5)*(x - 5)^3)/6 + (exp(5)*(x - 5)^4)/24 + (exp(5)*(x 5)^5)/120 >> e=taylor(exp(x),x, 5) e= exp(5) + exp(5)*(x - 5) + (exp(5)*(x - 5)^2)/2 + (exp(5)*(x - 5)^3)/6 + (exp(5)*(x - 5)^4)/24 + (exp(5)*(x 5)^5)/120 >> f='2*t+1'; t=3 t= 3 >> y=eval(f) y= 7 >> f=3*x^2+5*x f=
3*x^2 + 5*x >> t=factor(f) s=expand(t) t= x*(3*x + 5)
s= 3*x^2 + 5*x >> >> limit(sin(x)/x) ans = 1 >> x=-4:.01:4; y=sin(x); plot(x,y)
>> x=-1.5:.01:1.5; y=exp(-x.^2); plot(x,y)
>> t=0:.001:2*pi; x=cos(3*t); y=sin(2*t); plot(x,y)
>> function y=expcu(x) >> fplot ('expcu', [-1.5,1.5])
>> t=.01:.01:2*pi; x=cos(t); y=sin(t); z=t.^3; plot3(x,y,z)
>> mesh(eye(10))
>> xx=-2:.2:2; yy=xx yy = Columns 1 through 11 -2.0000 -1.8000 -1.6000 -1.4000 -1.2000 -1.0000 -0.8000 -0.6000 -0.4000 -0.2000 Columns 12 through 21 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000 2.0000 >> [x,y]=meshgrid(xx,yy); z=exp(-x.^2-y.^2); mesh(z)
0
>> colormap(cool)
>> shading flat
>> colormap (jet)
2 5 8
3 6 9
>> A(1,2) ans = 2 >> VECTOR = [1,2,3] VECTOR = 1
2
3
>> MATRIZ = [1,2,3;4,5,6;7,8,9] MATRIZ = 1 4 7
2 5 8
3 6 9
>> eye (10) ans = 1 0 0 0 0 0 0
0 1 0 0 0 0 0
0 0 1 0 0 0 0
0 0 0 1 0 0 0
0 0 0 0 1 0 0
0 0 0 0 0 1 0
0 0 0 0 0 0 1
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0 0 0 0 1 0 0 0 0 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
>> ones (10) ans = 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
>> MATRIZ2 = [1 2 3 123 1 2 3] MATRIZ2 = 1 1 1
2 2 2
3 3 3
>> C = MATRIZ * MATRIZ2 C= 6 12 18 15 30 45 24 48 72 >> D = MATRIZ .* MATRIZ2 D= 1 4 9 4 10 18 7 16 27
>> det(MATRIZ)
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
ans = 6.6613e-16 >> det (C) ans = 0 >> det (MATRIZ2) ans = 0 >> inv(C) Warning: Matrix is singular to working precision. ans = Inf Inf Inf Inf Inf Inf Inf Inf Inf
>> C(:,2) ans = 12 30 48 >> VECTOR2 = 2*VECTOR VECTOR2 = 2
4
6
>> VECTOR2(:,2) ans = 4
>> P=[1,3,-2,0,1]
P= 1
3 -2
0
1
>> roots(P) ans = -3.5421 + 0.0000i 0.5446 + 0.4685i 0.5446 - 0.4685i -0.5470 + 0.0000i
raices = -3.5421 + 0.0000i 0.5446 + 0.4685i 0.5446 - 0.4685i -0.5470 + 0.0000i >> polyval (P,raices) ans = 1.0e-12 * -0.2807 + 0.0000i 0.0011 + 0.0003i 0.0011 - 0.0003i 0.0002 + 0.0000i >> P2 = [3 4 5] P2 = 3
4
5
>> P3 = [2 1 2] P3 = 2
1
2
>> PP = conv(P2,P3) PP =
6 11 20 13 10
>> [Q,R] = deconv (P2,P3) Q= 1.5000
R= 0 2.5000 2.0000 >> >> a=[2, 3; 5, -2] a= 2 3 5 -2 >> b=[4; 6] b= 4 6 >> s=inv(a)*b s= 1.3684 0.4211
>> t=solve('2*x^2+3*x-2') t= -2 1/2 >> [a,b] = solve('a^2 + a*b - b = 3','a^2 - 4*b - 5 = 0') a=
-1 - 2*2^(1/2) - 1 2*2^(1/2) - 1
b= -1 2^(1/2) + 1 1 - 2^(1/2) >> y=dsolve('Dy-x-y=0','y(0)=1', 'x') y= 2*exp(x) - x - 1 >> ezplot(y, 0, 2); grid on
>> int(sym('x*sin(x)')) ans = sin(x) - x*cos(x) >> s=int(sym('x*sin(x)'),0,pi)
s= pi >> syms x >> y=x^3-8 y= x^3 - 8 >> t=factor(y) t= (x - 2)*(x^2 + 2*x + 4) >> e=taylor(exp(x),x, 5) e= exp(5) + exp(5)*(x - 5) + (exp(5)*(x - 5)^2)/2 + (exp(5)*(x - 5)^3)/6 + (exp(5)*(x - 5)^4)/24 + (exp(5)*(x 5)^5)/120 >> e=taylor(exp(x),x, 5) e= exp(5) + exp(5)*(x - 5) + (exp(5)*(x - 5)^2)/2 + (exp(5)*(x - 5)^3)/6 + (exp(5)*(x - 5)^4)/24 + (exp(5)*(x 5)^5)/120 >> f='2*t+1'; t=3 t= 3 >> y=eval(f) y= 7 >> f=3*x^2+5*x f=
3*x^2 + 5*x >> t=factor(f) s=expand(t) t= x*(3*x + 5)
s= 3*x^2 + 5*x >> >> limit(sin(x)/x) ans = 1 >> x=-4:.01:4; y=sin(x); plot(x,y)
>> x=-1.5:.01:1.5; y=exp(-x.^2); plot(x,y)
>> t=0:.001:2*pi; x=cos(3*t); y=sin(2*t); plot(x,y)
>> function y=expcu(x) >> fplot ('expcu', [-1.5,1.5])
>> t=.01:.01:2*pi; x=cos(t); y=sin(t); z=t.^3; plot3(x,y,z)
>> mesh(eye(10))
>> xx=-2:.2:2; yy=xx yy = Columns 1 through 11 -2.0000 -1.8000 -1.6000 -1.4000 -1.2000 -1.0000 -0.8000 -0.6000 -0.4000 -0.2000 Columns 12 through 21 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000 2.0000 >> [x,y]=meshgrid(xx,yy); z=exp(-x.^2-y.^2); mesh(z)
0
>> colormap(cool)
>> shading flat
>> colormap (jet)
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