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Навороченная схема системы автоматического управления

На рис. 1 представлена достаточно сложная для САУ схема. Смысла в этой схеме никакого нет, это просто демонстрация работы программы с разнородными блоками.

Рис. 1. Схема САУ

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>    restart:with(MSpice):ESolve(P,`CMOSOP-PSpiceFiles/SCHEMATIC1/SCHEMATIC1.net`);

`DC1 линейная модель ОУ`

`Cистема Кирхгофа (физика)`

-M/R4+(Gin-M)*beta1/`Rэб1`-(M-Gin)/`Rэб1` = 0

(F-P)/R2-(P-F)*s*C2-(P-Uin)/R3 = 0

Y = X2*H2

X2 = X3+X1

X3 = F*H0

(P-F)*s*C2-(F-V10)/R7-F/R6-(F-P)/R2 = 0

V10 = -A1*P

(Y-E)/R1-E*s*C1 = 0

X1 = T*K2*K3/(1+s*tau2)/(1+s*tau3)

T = Z*H1

Z = M-E

{E, P, T, Z, F, V10, Y, X2, X3, X1, M}

MSpice v8.95:   http://pspicelib.narod.ru

Заданы источники: [VGin, VB1, VUin, Jэ1]

Заданы узлы: {U, VG, CC}

Получены решения:

V_NET:=[E, P, T, Z, F, V10, Y, X2, X3, X1, M]:

J_NET:=[JVUin, JRэб1, JVGin, JR7, JC2, JC1, JR6, JR2, JR3, JR4, JR5, JR1, JVB1]:


Найдем выходную функцию

>    beta1:=beta: Rbe1:=Rbe:  Y:=simplify(limit(Y,AU1=infinity),'size');

Y := (1+s*C1*R1)*H2*(C2*tau3*R6*H0*Uin*((1+beta)*R4+`Rэб1`)*tau2*R2*R7*s^3+R6*H0*Uin*((1+beta)*R4+`Rэб1`)*((C2*(tau2+tau3)*R7-A1*tau2*tau3)*R2+tau2*tau3*R7)*s^2+((((H1*C2*Gin*K2*K3*(1+A1)*R3+C2*(Gin*H1...
Y := (1+s*C1*R1)*H2*(C2*tau3*R6*H0*Uin*((1+beta)*R4+`Rэб1`)*tau2*R2*R7*s^3+R6*H0*Uin*((1+beta)*R4+`Rэб1`)*((C2*(tau2+tau3)*R7-A1*tau2*tau3)*R2+tau2*tau3*R7)*s^2+((((H1*C2*Gin*K2*K3*(1+A1)*R3+C2*(Gin*H1...
Y := (1+s*C1*R1)*H2*(C2*tau3*R6*H0*Uin*((1+beta)*R4+`Rэб1`)*tau2*R2*R7*s^3+R6*H0*Uin*((1+beta)*R4+`Rэб1`)*((C2*(tau2+tau3)*R7-A1*tau2*tau3)*R2+tau2*tau3*R7)*s^2+((((H1*C2*Gin*K2*K3*(1+A1)*R3+C2*(Gin*H1...
Y := (1+s*C1*R1)*H2*(C2*tau3*R6*H0*Uin*((1+beta)*R4+`Rэб1`)*tau2*R2*R7*s^3+R6*H0*Uin*((1+beta)*R4+`Rэб1`)*((C2*(tau2+tau3)*R7-A1*tau2*tau3)*R2+tau2*tau3*R7)*s^2+((((H1*C2*Gin*K2*K3*(1+A1)*R3+C2*(Gin*H1...
Y := (1+s*C1*R1)*H2*(C2*tau3*R6*H0*Uin*((1+beta)*R4+`Rэб1`)*tau2*R2*R7*s^3+R6*H0*Uin*((1+beta)*R4+`Rэб1`)*((C2*(tau2+tau3)*R7-A1*tau2*tau3)*R2+tau2*tau3*R7)*s^2+((((H1*C2*Gin*K2*K3*(1+A1)*R3+C2*(Gin*H1...
Y := (1+s*C1*R1)*H2*(C2*tau3*R6*H0*Uin*((1+beta)*R4+`Rэб1`)*tau2*R2*R7*s^3+R6*H0*Uin*((1+beta)*R4+`Rэб1`)*((C2*(tau2+tau3)*R7-A1*tau2*tau3)*R2+tau2*tau3*R7)*s^2+((((H1*C2*Gin*K2*K3*(1+A1)*R3+C2*(Gin*H1...

>    H0:=1/(1+s); H1:=1/(1+s+2*s^2); H2:=s/(1+s);  

H0 := 1/(1+s)

H1 := 1/(1+s+2*s^2)

H2 := s/(1+s)

>    Y:=collect((Y),s);

Y := (1+s*C1*R1)*s/(1+s)*(C2*tau3*R6/(1+s)*Uin*((1+beta)*R4+`Rэб1`)*tau2*R2*R7*s^3+R6/(1+s)*Uin*((1+beta)*R4+`Rэб1`)*((C2*(tau2+tau3)*R7-A1*tau2*tau3)*R2+tau2*tau3*R7)*s^2+((((1/(1+s+2*s^2)*C2*Gin*K2*K...
Y := (1+s*C1*R1)*s/(1+s)*(C2*tau3*R6/(1+s)*Uin*((1+beta)*R4+`Rэб1`)*tau2*R2*R7*s^3+R6/(1+s)*Uin*((1+beta)*R4+`Rэб1`)*((C2*(tau2+tau3)*R7-A1*tau2*tau3)*R2+tau2*tau3*R7)*s^2+((((1/(1+s+2*s^2)*C2*Gin*K2*K...
Y := (1+s*C1*R1)*s/(1+s)*(C2*tau3*R6/(1+s)*Uin*((1+beta)*R4+`Rэб1`)*tau2*R2*R7*s^3+R6/(1+s)*Uin*((1+beta)*R4+`Rэб1`)*((C2*(tau2+tau3)*R7-A1*tau2*tau3)*R2+tau2*tau3*R7)*s^2+((((1/(1+s+2*s^2)*C2*Gin*K2*K...
Y := (1+s*C1*R1)*s/(1+s)*(C2*tau3*R6/(1+s)*Uin*((1+beta)*R4+`Rэб1`)*tau2*R2*R7*s^3+R6/(1+s)*Uin*((1+beta)*R4+`Rэб1`)*((C2*(tau2+tau3)*R7-A1*tau2*tau3)*R2+tau2*tau3*R7)*s^2+((((1/(1+s+2*s^2)*C2*Gin*K2*K...
Y := (1+s*C1*R1)*s/(1+s)*(C2*tau3*R6/(1+s)*Uin*((1+beta)*R4+`Rэб1`)*tau2*R2*R7*s^3+R6/(1+s)*Uin*((1+beta)*R4+`Rэб1`)*((C2*(tau2+tau3)*R7-A1*tau2*tau3)*R2+tau2*tau3*R7)*s^2+((((1/(1+s+2*s^2)*C2*Gin*K2*K...

>    Values(DC,RLCVI,[]):

Номиналы компонентов:   

R7:=WR:

C2:=C:

C1:=C:

R6:=1e3:  [1k]

R1:=R:

R2:=R2GAIN:

R3:=W:

R4:=1e3:  [1k]

R5:=1e3:  [1k]

A1:=1e6:  [1e6]

beta1:=100:  [100]

Jэ1:=1e-3:

Rэб1:=(k*Tkelvin/e*(1+beta1)/Jэ1):

e:=.1602176462e-18:

k:=.1380650277e-22:

Tkelvin:=300:  [300]

DC источник: VB1:=12:

DC источник: VGin:=1:

DC источник: VUin:=1:

>    Y:=collect((Y),s);

Y := (1+s*C*R)*s/(1+s)*(.1e4*C*tau3/(1+s)*Uin*(3611.054673+.1e4*beta)*tau2*R2GAIN*WR*s^3+.1e4/(1+s)*Uin*(3611.054673+.1e4*beta)*((C*(tau2+tau3)*WR-.1e7*tau2*tau3)*R2GAIN+tau2*tau3*WR)*s^2+(.1e7*((10000...
Y := (1+s*C*R)*s/(1+s)*(.1e4*C*tau3/(1+s)*Uin*(3611.054673+.1e4*beta)*tau2*R2GAIN*WR*s^3+.1e4/(1+s)*Uin*(3611.054673+.1e4*beta)*((C*(tau2+tau3)*WR-.1e7*tau2*tau3)*R2GAIN+tau2*tau3*WR)*s^2+(.1e7*((10000...
Y := (1+s*C*R)*s/(1+s)*(.1e4*C*tau3/(1+s)*Uin*(3611.054673+.1e4*beta)*tau2*R2GAIN*WR*s^3+.1e4/(1+s)*Uin*(3611.054673+.1e4*beta)*((C*(tau2+tau3)*WR-.1e7*tau2*tau3)*R2GAIN+tau2*tau3*WR)*s^2+(.1e7*((10000...
Y := (1+s*C*R)*s/(1+s)*(.1e4*C*tau3/(1+s)*Uin*(3611.054673+.1e4*beta)*tau2*R2GAIN*WR*s^3+.1e4/(1+s)*Uin*(3611.054673+.1e4*beta)*((C*(tau2+tau3)*WR-.1e7*tau2*tau3)*R2GAIN+tau2*tau3*WR)*s^2+(.1e7*((10000...
Y := (1+s*C*R)*s/(1+s)*(.1e4*C*tau3/(1+s)*Uin*(3611.054673+.1e4*beta)*tau2*R2GAIN*WR*s^3+.1e4/(1+s)*Uin*(3611.054673+.1e4*beta)*((C*(tau2+tau3)*WR-.1e7*tau2*tau3)*R2GAIN+tau2*tau3*WR)*s^2+(.1e7*((10000...
Y := (1+s*C*R)*s/(1+s)*(.1e4*C*tau3/(1+s)*Uin*(3611.054673+.1e4*beta)*tau2*R2GAIN*WR*s^3+.1e4/(1+s)*Uin*(3611.054673+.1e4*beta)*((C*(tau2+tau3)*WR-.1e7*tau2*tau3)*R2GAIN+tau2*tau3*WR)*s^2+(.1e7*((10000...
Y := (1+s*C*R)*s/(1+s)*(.1e4*C*tau3/(1+s)*Uin*(3611.054673+.1e4*beta)*tau2*R2GAIN*WR*s^3+.1e4/(1+s)*Uin*(3611.054673+.1e4*beta)*((C*(tau2+tau3)*WR-.1e7*tau2*tau3)*R2GAIN+tau2*tau3*WR)*s^2+(.1e7*((10000...

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