Dariusz Rachowicz
3MMDI L5
Laboratorium z Automatyki
Sprawozdanie
Lab. nr 3
Temat: Badanie podstawowych elementów automatyki
1. Wstęp teoretyczny
Elementy automatyki:
k
a) Bezinercyjne G(s) =ð k =ð
1
b) Inercyjne
k
·ð I rzÄ™du G(s) =ð
Ts +ð1
k
·ð II rzedu G(s) =ð
(T1s +ð1)(T2s +ð1)
k
·ð Oscylacyjne G(s) =ð
T1s2 +ð T2s +ð1
2
kvð
o
G(s) =ð
2
s2 +ð 2xðvð s +ðvð
o o
c) Całkujące
k
·ð Idealne G(s) =ð
Ts
k
·ð Rzeczywiste G(s) =ð
s(Ts +ð1)
s(Ts +ð1)
·ð Izodromowe G(s) =ð
k
d) Różniczkujące
·ð Idealne G(s) =ð ks
ks
·ð Rzeczywiste G(s) =ð
Ts +ð1
e) OpózniajÄ…ce G(s) =ð ke-ðtðs
k- współczynnik wzmocnienia ; T stała czasowa
2. Wykresy
a. Bezinercyjny
k
G(s) =ð k =ð , k = 2, 20, 35
1
b. Inercyjny
·ð I rzÄ™du
T1= 4; 10; 20
k = 2; 20; 40
k
·ð II rzÄ™du G(s) =ð
(T1s +ð1)(T2s +ð1)
T2 = 3; 10; 30
Kod programu:
Zmiana T2:
>> k=2 >> k=2 >> k=2
>> T1=2 >> T1=2 >> T1=2
>> T2=3 >> T2=10 >> T2=30
>> s=tf('s') >> s=tf('s') >> s=tf('s')
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> >> >>
G=k/((T1*s+1)*(T2*s+1) G=k/((T1*s+1)*(T2*s+1) G=k/((T1*s+1)*(T2*s+1)
) ) )
G = G = G =
2 2 2
--------------- ----------------- -----------------
6 s^2 + 5 s + 1 20 s^2 + 12 s + 1 60 s^2 + 32 s + 1
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> ltiview(G) >> ltiview(G) >> ltiview(G)
Charakterystyki:
Skokowa, częstotliwościowa, częstotliwościowa logarytmiczna.
T1= 2, 20, 50
Kod programu:
>> k=2
>> T1=2 >> k=2
>> T2=3 >> T1=20 >> k=2
>> s=tf('s') >> T2=3 >> T1=50
Continuous-time >> s=tf('s') >> T2=3
transfer function. Continuous-time >> s=tf('s')
>> transfer function. Continuous-time
G=k/((T1*s+1)*(T2*s+1) >> transfer function.
) G=k/((T1*s+1)*(T2*s+1) >>
G = ) G=k/((T1*s+1)*(T2*s+1)
2 G = )
--------------- 2 G =
6 s^2 + 5 s + 1 ----------------- 2
Continuous-time 60 s^2 + 23 s + 1 ------------------
transfer function. Continuous-time 150 s^2 + 53 s + 1
>> ltiview(G) transfer function. Continuous-time
>> ltiview(G) transfer function.
>> ltiview(G)
Charakterystyki:
Skokowa, częstotliwościowa, częstotliwościowa logarytmiczna.
k = 2; 15;60
Kod programu:
>> k=2 >> k=15 >> k=60
>> T1=2 >> T1=2 >> T1=2
>> T2=3 >> T2=3 >> T2=3
>> s=tf('s') >> s=tf('s') >> s=tf('s')
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> >> >>
G=k/((T1*s+1)*(T2*s+1) G=k/((T1*s+1)*(T2*s+1) G=k/((T1*s+1)*(T2*s+1)
) ) )
G = G = G =
2 15 60
--------------- --------------- ---------------
6 s^2 + 5 s + 1 6 s^2 + 5 s + 1 6 s^2 + 5 s + 1
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> ltiview(G) >> ltiview(G) >> ltiview(G)
Charakterystyki:
Skokowa, częstotliwościowa, częstotliwościowa logarytmiczna.
2
kvð
o
·ð Oscylacyjne G(s) =ð
2
s2 +ð 2xðvð s +ðvð
o o
¾= 0,1; 0,5; 1
Kod programu:
>> k=10
>> om=3 >> k=10 >> k=10
>> ksi=0.1 >> om=3 >> om=3
>> s=tf('s') >> ksi=0.5 >> ksi=1
Continuous-time >> s=tf('s') >> s=tf('s')
transfer function. Continuous-time Continuous-time
>> transfer function. transfer function.
G=(k*om^2)/(s^2+2*ksi* >> >>
om*s+om^2) G=(k*om^2)/(s^2+2*ksi* G=(k*om^2)/(s^2+2*ksi*
G = om*s+om^2) om*s+om^2)
90 G = G =
--------------- 90 90
s^2 + 0.6 s + 9 ------------- -------------
Continuous-time s^2 + 3 s + 9 s^2 + 6 s + 9
transfer function. Continuous-time Continuous-time
>> ltiview(G) transfer function. transfer function.
>> ltiview(G) >> ltiview(G)
Charakterystyki:
Skokowa, częstotliwościowa, częstotliwościowa logarytmiczna.
k
·ð Oscylacyjne G(s) =ð
T1s2 +ð T2s +ð1
T = 4; 15; 40
2
Kod programu:
>> T1=5 >> T1=5 >> T1=5
>> T2=4 >> T2=15 >> T2=40
>> k=10 >> k=10 >> k=10
>> s=tf('s') >> s=tf('s') >> s=tf('s')
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> >> >>
G=k/(T1*s^2+T2*s+1) G=k/(T1*s^2+T2*s+1) G=k/(T1*s^2+T2*s+1)
G = G = G =
10 10 10
--------------- --------------- ---------------
5 s^2 + 4 s + 1 5 s^2 + 15 s + 1 5 s^2 + 40 s + 1
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> ltiview(G) >> ltiview(G) >> ltiview(G)
T1=5; 20; 70
Kod programu:
>> T1=5 >> T1=20 >> T1=70
>> T2=4 >> T2=4 >> T2=4
>> k=10 >> k=10 >> k=10
>> s=tf('s') >> s=tf('s') >> s=tf('s')
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> >> >>
G=k/(T1*s^2+T2*s+1) G=k/(T1*s^2+T2*s+1) G=k/(T1*s^2+T2*s+1)
G = G = G =
10 10 10
--------------- --------------- ---------------
5 s^2 + 4 s + 1 20 s^2 + 4 s + 1 70 s^2 + 4 s + 1
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> ltiview(G) >> ltiview(G) >> ltiview(G)
Charakterystyki:
Skokowa, częstotliwościowa, częstotliwościowa logarytmiczna.
k=10; 30; 50
Kod programu:
>> T1=5 >> T1=5 >> T1=5
>> T2=4 >> T2=4 >> T2=4
>> k=10 >> k=30 >> k=50
>> s=tf('s') >> s=tf('s') >> s=tf('s')
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> >> >>
G=k/(T1*s^2+T2*s+1) G=k/(T1*s^2+T2*s+1) G=k/(T1*s^2+T2*s+1)
G = G = G =
10 30 50
--------------- --------------- ---------------
5 s^2 + 4 s + 1 5 s^2 + 4 s + 1 5 s^2 + 4 s + 1
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> ltiview(G) >> ltiview(G) >> ltiview(G)
Charakterystyki:
Skokowa, częstotliwościowa, częstotliwościowa logarytmiczna.
c. Całkujące:
k
·ð Idealne G(s) =ð
Ts
T = 2; 25; 35
Kod programu:
>> T1=2 >> T1=25 >> T1=35
>> k=5 >> k=5 >> k=5
>> s=tf('s') >> s=tf('s') >> s=tf('s')
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> G=k/(T1*s) >> G=k/(T1*s) >> G=k/(T1*s)
G = G = G =
5 5 5
--- --- ---
2 s 25 s 35 s
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> ltiview(G) >> ltiview(G) >> ltiview(G)
Charakterystyki:
Skokowa, częstotliwościowa, częstotliwościowa logarytmiczna.
k = 5; 20; 40
Kod programu:
>> T1=2 >> T1=2 >> T1=2
>> k=5 >> k=20 >> k=5
>> s=tf('s') >> s=tf('s') >> s=tf('s')
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> G=k/(T1*s) >> G=k/(T1*s) >> G=k/(T1*s)
G = G = G =
5 20 40
--- --- ---
2 s 2 s 2 s
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> ltiview(G) >> ltiview(G) >> ltiview(G)
Charakterystyki:
Skokowa, częstotliwościowa, częstotliwościowa logarytmiczna.
k
·ð rzeczywiste G(s) =ð
s(Ts +ð1)
T=2; 10; 20
Charakterystyki:
k = 2; 10; 30
Charakterystyki:
s(Ts +ð1)
·ð Izodromowe G(s) =ð
k
T = 6; 17; 24
Kod programu:
>> T=6 >> T=17 >> T=24
>> k=3 >> k=3 >> k=3
>> s=tf('s') >> s=tf('s') >> s=tf('s')
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> G=(s*(T*s+1))/k >> G=(s*(T*s+1))/k >> G=(s*(T*s+1))/k
G = G = G =
6 s^2 + s 17 s^2 + s 24 s^2 + s
--------- --------- ---------
3 3 3
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> ltiview(G) >> ltiview(G) >> ltiview(G)
Charakterystyki:
k = 3; 18; 33
Kod programu:
>> T=6 >> T=6 >> T=6
>> k=3 >> k=18 >> k=33
>> s=tf('s') >> s=tf('s') >> s=tf('s')
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> G=(s*(T*s+1))/k >> G=(s*(T*s+1))/k >> G=(s*(T*s+1))/k
G = G = G =
6 s^2 + s 6 s^2 + s 6 s^2 + s
--------- --------- ---------
3 3 3
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> ltiview(G) >> ltiview(G) >> ltiview(G)
Charakterystyki:
d. Różniczkujące
·ð Idealne G(s) =ð ks
k = 7; 30; 90
Kod programu:
>> k=7 >> k=30 >> k=90
>> s=tf('s') >> s=tf('s') >> s=tf('s')
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> G=k*s >> G=k*s >> G=k*s
G = G = G =
7 s 30 s 90 s
Continuous-time Continuous-time Continuous-time
transfer function. transfer function. transfer function.
>> ltiview(G) >> ltiview(G) >> ltiview(G)
Charakterystyki:
ks
·ð Rzeczywiste G(s) =ð
Ts +ð1
k = 2; 20; 40
Schemat:
Charakterystyki:
T = 4; 20; 35
Charakterystyki:
c. OpózniajÄ…ce G(s) =ð ke-ðtðs
k = 1; 10; 20
Schemat:
Charakterystyki:
Ä = 2; 10; 20
Schemat:
Charakterystyki:
Wyszukiwarka