clear
variables
syms
L1 L12 L2 R T Ug
assume(0 < R & 0 < L1 & 0 < L12 & 0 < L2 & Ug ~= 0 & 0 < T)
Jednacine
syms
I1 I2 U1 U2 k s
jednacine = subs([Ug == R*I1 + U1, U1 == L1*s*I1 + L12*s*I2, U2 == L12*s*I1 + L2*s*I2, I2 == 0], L12, k*sqrt(L1*L2))
jednacine =
syms
L U t
zamena = subs([L1 == L, L2 == 4*L, k == 1/2, Ug == laplace(U*(heaviside(t) - heaviside(t - T)), t, s)], L, R*T)
zamena =
odziv = solve(jednacine, [I1, I2, U1, U2])
odziv =
struct with fields:
I1: Ug/(R + L1*s) I2: 0 U1: (L1*Ug*s)/(R + L1*s) U2: (L1^(1/2)*L2^(1/2)*Ug*k*s)/(R + L1*s)
U2_zamena = simplify(subs(odziv.U2, lhs(zamena), rhs(zamena)))
U2_zamena =
Inverzna Laplasova tranformacija
syms
u2(t)
u2(t) = ilaplace(U2_zamena, s, t)
u2(t) =
vrednosti = unique([U == 1, T == 1])
vrednosti =
u2_num(t) = subs(u2(t), lhs(vrednosti), rhs(vrednosti))
u2_num(t) =
Crtanje grafika
fplot(t, u2_num(t), [0, 7])
ylim([-0.8, 1.2]);
grid
on
;
xlabel(
't'
)
ylabel(
'u2(t)'
)