How to Solve with subs

I am trying to first solve for Tau first, and then plug the known value back in and solve for y(t) @ 1.5 seconds.

it is given that @ y(1.2)=80.

clear;clc;

syms T %Tau

syms yt

t=1.2;

y0=0;

KA=100; %steady response

U_t=(y0-KA)*exp(-t/T); %transient response

y_t=80; %given that y(t), if y(1.2)=80

eq3_5a=y_t==KA+U_t

Tau=vpasolve(eq3_5a,T)

subs(U_t,T,Tau)

eq3_5b=yt==KA+U_t

solve(eq3_5b,yt)

Answer 1

[VBBV]

clear;clc;
syms T yt
t=1.2;
y0=0;
KA=100; %steady response
U_t=(y0-KA)*exp(-t/T) %transient response

U_t = 

y_t=80; %given that y(t), if y(1.2)=80
eq3_5a=y_t==KA+U_t

eq3_5a = 

Tau=vpasolve(eq3_5a,T)

Tau = 

0.74560192147153417284863926581669

subs(U_t,T,Tau)

ans = 

eq3_5b=yt==KA+U_t

eq3_5b = 

Yt = solve(eq3_5b,yt)

Yt = 

vpa(subs(Yt,T,1.5),4)

ans = 

55.07

[Kyle Langford]

Close, but I need to sub T=0.7456 %Tau, and t =1.5 %time, then solve for Yt.

[VBBV]

clear;clc;
syms T yt
t=1.5;  % change here 
y0=0;
KA=100; %steady response
U_t=(y0-KA)*exp(-t/T) %transient response

U_t = 

y_t=80; %given that y(t), if y(1.2)=80
eq3_5a=y_t==KA+U_t

eq3_5a = 

Tau=vpasolve(eq3_5a,T)

Tau = 

0.93200240183941771606079908227086

subs(U_t,T,Tau)

ans = 

eq3_5b=yt==KA+U_t

eq3_5b = 

Yt = solve(eq3_5b,yt)

Yt = 

vpa(subs(Yt,T,0.7456),4)

ans = 

86.63

[Kyle Langford]

But now your Tau value is 0.93200xxxxx, I want to solve for Tau first, then plug it back into the equation and solve for y_t, when t=1.5.

I was able to do it by basically just clearing everything and restarting all over in the second half.

Is there no way to subs() 2 variables?

If in the first solution you gave me, if we could vpa(subs(Yt,T,Tau),subs(t,1.2,1.5)) that would be perfect, but it won't let me.

Maybe I am just not setting up my initial conditions correctly.

[VBBV]

clear;clc;
syms T yt t
% t=1.2;
y0=0;
KA=100; %steady response
U_t= (y0-KA)*exp(-t/T) %transient response

U_t = 

y_t=80; %given that y(t), if y(1.2)=80
eq3_5a=y_t==KA+U_t;
Tau=vpasolve(subs(eq3_5a,t,1.2),T)

Tau = 

0.74560192147153417284863926581669

subs(U_t,T,Tau);
eq3_5b=yt==KA+U_t

eq3_5b = 

Yt = solve(eq3_5b,yt);
vpa(subs(Yt,[T t],[Tau 1.5]),4)

ans = 

86.63

Ok, It is possible to Subs 2 variables like above

[Kyle Langford]

Sweet. Thanks! I tried to do something similar using {} but it didn't work. I see i was using the wrong characters.