examen sistemas de control digital 2014
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Examen Sistemas de Control Digital 2014-A
Bo Gp(s)y(t)e(t)
T
>> a1FTLA
Ingrese numerador y denominador de Gp(s)
Entre coeficientes del numerador : num = 1
Entre coeficientes del denominador : den = [1 1 0]
Entre tiempo de muestreo : T = .1
LA FUNCION DE TRANSF. DISCRETA DE LA PLANTA :
Gp(z) =
Transfer function:
0.004837 z + 0.004679
----------------------
z^2 - 1.905 z + 0.9048
Sampling time (seconds): 0.1
MATLAB
>> a2Yz
Gp(z)=
Transfer function:
0.004837 z + 0.004679
----------------------
z^2 - 1.905 z + 0.9048
Sampling time (seconds): 0.1
Y(z)= E(z) x Gp(z)
Y(z)=
Transfer function:
0.004837 z^2 + 0.004679 z
---------------------------------
z^3 - 2.905 z^2 + 2.81 z - 0.9048
Sampling time (seconds): 0.1
MATLAB
LA FUNCION DE TRANSF. DISCRETA DE LA PLANTA : G(z) =
Transfer function:
0.004837 z + 0.004679
----------------------
z^2 - 1.905 z + 0.9048
Sampling time (seconds): 0.1
EcuaCaract =
z^2 + ((5577163280430809*K)/1152921504606846976 - 8578625086068125/4503599627370496)*z + (2697167718797289*K)/576460752303423488 + 4075025458697629/4503599627370496
an =
(2697167718797289*K)/576460752303423488 + 4075025458697629/4503599627370496
a0 =
1
SEGUN PRIMER CRITERIO
Limite1 =
18285831196708992/899055906265763
Max1 =
20.3389
SEGUN SEGUNDO CRITERIO
Pz1 =
(10971498718025387*K)/1152921504606846976
Min2 =
0
Min2 =
0
SEGUN TERCER CRITERIO
Pz2 =
8578625086068125/2251799813685248 - (182827842836231*K)/1152921504606846976
Max2 =
4392256044066880000/182827842836231
Max2 =
2.4024e+004
EL RANGO DE LA GANANCIA K PARA QUE HAYA ESTABILIDAD ES :
Max =
20.3389
Min =
0
R-H
MATLAB
LA MATRIZ DE ROUTH ES :
W2 = a0 a2
W1 = a1 0
W0 = b1 0
RENGLONES : W2 y W1
EL ARREGLO DE ROUTH ES :
ans =
1.0000 0
20.0167 0
0 0
EL SISTEMA ES ESTABLE PARA UN K =
K =
0
LA MATRIZ DE ROUTH ES :
W2 = a0 a2
W1 = a1 0
W0 = b1 0
RENGLONES : W2 y W1
EL ARREGLO DE ROUTH ES :
ans =
1.0000 19.0468
-0.0310 0
19.0468 0
EL SISTEMA ES INESTABLE PARA K =
K =
21
>> b1b3
Gp(z)=
Transfer function:
0.004837 z + 0.004679
----------------------
z^2 - 1.905 z + 0.9048
Sampling time (seconds): 0.1
H(z)=
Transfer function:
0.004837 z + 0.004679
---------------------
z^2 - 1.9 z + 0.9095
Sampling time (seconds): 0.1
Y(z)= E(z) x H(z)
Y(z)=
Transfer function:
0.004837 z^2 + 0.004679 z
-------------------------------
z^3 - 2.9 z^2 + 2.81 z - 0.9095
Sampling time (seconds): 0.1
MATLAB
SP =
Columns 1 through 8
0 0.0048 0.0139 0.0220 0.0291 0.0353 0.0406 0.0451
Columns 9 through 16
0.0487 0.0515 0.0536 0.0550 0.0557 0.0559 0.0555 0.0546
Columns 17 through 24
0.0532 0.0515 0.0495 0.0471 0.0445 0.0418 0.0389 0.0358
Columns 25 through 32
0.0328 0.0296 0.0265 0.0234 0.0204 0.0174 0.0146 0.0119
Columns 33 through 40
0.0093 0.0068 0.0045 0.0024 0.0004 -0.0014 -0.0030 -0.0044
Columns 41 through 48
-0.0057 -0.0068 -0.0077 -0.0085 -0.0091 -0.0096 -0.0099 -0.0102
Columns 49 through 56
-0.0103 -0.0103 -0.0102 -0.0100 -0.0097 -0.0094 -0.0090 -0.0085
Columns 57 through 64
-0.0080 -0.0075 -0.0070 -0.0064 -0.0059 -0.0053 -0.0047 -0.0041
Columns 65 through 72
-0.0036 -0.0031 -0.0025 -0.0020 -0.0016 -0.0011 -0.0007 -0.0003
Columns 73 through 80
0.0000 0.0003 0.0006 0.0009 0.0011 0.0013 0.0015 0.0016
Columns 81 through 88
0.0017 0.0018 0.0018 0.0019 0.0019 0.0019 0.0019 0.0018
Columns 89 through 96
0.0018 0.0017 0.0016 0.0015 0.0015 0.0014 0.0013 0.0012
Columns 97 through 101
0.0010 0.0009 0.0008 0.0007 0.0006
EXTRA
Y(z)=
Transfer function:
0.002419 z^2 + 0.004758 z + 0.002339
------------------------------------
z^4 - 2.9 z^3 + 2.81 z^2 - 0.9095 z
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