Реферат: Исследования устойчивости и качества процессов управления линейных стационарных САУ
МАИ
кафедра 301
Лабораторная работа №2
по курсу
“Основы теорииавтоматического управления”.
Исследование устойчивости икачества процессов
управления линейных стационарных САУ.
группа 03-302 Домнинский М.А.
М.1996.
Задание.
Дана структурная схема
Ку Ка /(ТаS+1) Kk /(T2kS2+2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">x
TkS+1) Y1)Рассчитать диапазон измерения Ку, вкотором САУ устойчива.
2)Показать характер распределения корнейхарактеристического уравнения замкнутой системы и характер переходной функциисистемы по управляемой переменной (у) на границах устойчивости и вблизи них.
3)Промоделировать САУ (наблюдать процессы награницах вблизи них, сравнить результаты расчета и результаты моделирования.)Сделать выводы.
4)Оформить результаты расчета и результатымоделирования.
Критерий Найквиста.
W(S)=KyK1 / (T1 j<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
+1)*K2 / (T2(j<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w)2+2<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">xT1j<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w+1) K1=2K2=1,5
W(S)=Ky*2*1,5/(0,01j<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
+1)(-0,022<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w2+0,04*0,2j<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w+1)= T1=0,01T2=0,02
=3Ky/(-(0,02)2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
2+0,008j<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w+1-0,04*10-4j<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w3-<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w20,08*10-3+0,01j<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w)= <span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">x=0,2
=3Ky/((-(0,02)2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
2+1-0,08*10-3<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w2)+j(0,018<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w-0,04*10-4<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w3))c d
Kd=0 3Ky(0,018<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
-0,04*10-4<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w3)=0<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">Þ
K/c=-1 3ky/(-(0,02)2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
2+1-0,08*10-3<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w2)=-13Ky(0,018<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">w
-0,04*10-4<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w3)=01)<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-char-type:symbol;mso-symbol-font-family:Symbol">w
=02)0.018=0,04*10-4<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
2=4500Ky1=-(-(0,02)2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
2+1-0,08*10-3<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w2)/3=-1/3 (<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">w=0)Ky2=-(-(0,02)2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
2+1-0,08*10-3<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w2)/3=-(-(0,02)2*4500-0,08*10-3*4500+1)/3=0,3866<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">»0,387МАИ
кафедра 301
Лабораторная работа №3
по курсу
“Основы теорииавтоматического управления”
Выделение областейустойчивости в плоскости
двух параметров системы.
группа 03-302 Домнинский М.А.
М.1995
Задание.
Дана структурная схема САУ
Ку Ка /(ТаS+1) Kk /(T2kS2+2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">x
TkS+1) Y1)Исследовать влияние коэффициента передачи Куи Т1 на устойчивость методом D-разбиения.
2)Объяснить, почему при Т1<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">®
0 и Т1<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">®<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">¥система допускает неограниченоувеличить Ку без потери устойчивости.3)Промоделировать САУ и найти экспериментальнозначения Ку по крайней мере для 3 значений Т1 (устойчив.)
4)Сделать выводы.
1)W(S)=KyK1K2/(T1S+1)(T22S2+2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">x
T2S+1)A(S)= KyK1K2+(T1S+1)(T22S2+2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">x
T2S+1)= KyK1K2+T1(T2S2+2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">xT2S+1)+T2S2+2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">xT2S+1S=j<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
Ky(K1-K2)+T1(T1S3+2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">x
T2S2+S)+T2S2+2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">xT2S+1P(S) Q(S) S(S)
P(j<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
)=P1(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w)+jP2(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w)Q(j<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
)=Q1(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w)+jQ2(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w)S(j<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
)=S1(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w)+jS2(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w)P1=K1K2 P2=0 Q2=-T1<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
3+<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w Q1=-2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">xT2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w2 S1=-T2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w2+1 S2=2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">xT2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">wP1(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
) Q1(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w)<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">D
(<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">w)=P2(<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">w
) Q2(<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">w)
-S1(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
) Q1(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w)<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">D
<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">m(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w)=-S2(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
) Q2(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w)P1(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
)-S1(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w)<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">D
<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">n(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w)=P2(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
)-S2(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w)<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">D
(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w)=K1K2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w(-T22<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w2+1)<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">¹01) 0<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol"><
<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">w<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol"><1/T2 <span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">D<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">>01/T2<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-char-type:symbol;mso-symbol-font-family:Symbol"><
<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol"><<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">¥ <span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">D<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol"><0
KyK1K2+T1(-2<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-char-type:symbol;mso-symbol-font-family:Symbol">x
T2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w2‑)-T2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w2+1=0T1(-T2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
3+<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w)+2<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">xT2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w=0KyK1K2-T1T22<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">x
<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">w2 — T2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w2+1=0-T1T2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w
3+T1<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w=-2<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">xT2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">wT1=-2<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">x
<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">T2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w/(-T2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w3+<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w)=2<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">xT2/(T2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w2-1) , <span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">w<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">¹0Ky=(T1T22<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">x
<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">w2+T2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w2-1)/K1K2=(2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">xT2/(T2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w2-1)*T22<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">x<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">w2+T2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">w2-1)/K1K2Асимптоты:
y=ax+b a=K1K2T2/2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">x
2=0.15b= -T2<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-char-type:symbol;mso-symbol-font-family:Symbol">x
2=4*10-3y=0.15x-4*10-3 — наклонная асимптота
Т1=0 -горизонтальна яасимптота
<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">w
<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">=<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">0 , Ку=1/3Определение устойчивости :
В области IY кол-во корней 2-3, а т.к. система 3-гопорядка <span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-char-type:symbol;mso-symbol-font-family:Symbol">Þ
в этой обласи 0 корней<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">Þ r=3 <span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">Þ области I и YII — устойчивы2)при Т1<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-char-type:symbol;mso-symbol-font-family:Symbol">®
0 и Т1<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol;mso-symbol-font-family: Symbol">®<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">¥ при любом Ку система находится взоне устойчивости.3) Т1=8*10-3 Ку1=0.71
Т2=16*10-3 Ку2=0.39
Т3=24*10-3 Ку3=0.37
Вывод. Найденные примоделировании коэффициенты Ку согласуются с теоретическими расчетами.