PK vLñBH mimetypetext/x-wxmathmlPK vLöżo÷ o÷ content.xml
Boost Converter, esr
|
state 1 matrices
|
A1: matrix([0, 0], [0, 0]);
|
B1: matrix([1/L, 0], [0, -1/c]);
|
C1: matrix([0, 1]);
|
D1: matrix([0, -R]);
|
state 2 matrices
|
A2: matrix([-R/L, -1/L], [1/c, 0]);
|
B2: matrix([1/L, R/L], [0, -1/c]);
|
C2: matrix([R, 1]);
|
D2: matrix([0, -R]);
|
state variables, dc
|
X0: matrix([Il], [Vc]);
|
input variables, dc
|
U0: matrix([Vin], [Iout]);
|
basic computation; keep it as it is
|
A: D0 * A1 + (1 - D0) * A2;
|
A: ratsimp(A);
|
B: D0 * B1 + (1 - D0) * B2;
|
B: ratsimp(B);
|
C: D0 * C1 + (1 - D0) * C2;
|
C: ratsimp(C);
|
D: D0 * D1 + (1 - D0) * D2;
|
D: ratsimp(D);
|
dc computation, still without d hat, keep it as it is
|
iA: invert(A);
|
iA: ratsimp(iA);
|
x0: -iA . B . U0;
|
x0: ratsimp(x0);
|
y0: (D - C . iA . B) . U0;
|
y0: ratsimp(y0);
|
ac computation, keep it as it is
|
E: (A1 - A2) . X0 + (B1 - B2) . U0;
|
E: ratsimp(E);
|
F: (C1 - C2) . X0 + (D1 - D2) . U0;
|
F: matrix([ratsimp(F)]);
|
merging E and F; keep it as it is
|
B: addcol(B, E);
|
D: addcol(D, F);
|
computing transfer functions; keep it as it is
|
S0: s * diagmatrix(2, 1) - A;
|
S: invert(S0);
|
âD0â1c*s*
sâD0â1
*RL
+D0â1
2c*LsâD0â1
*RLs*sâD0â1
*RL
+D0â1
2c*L
S: ratsimp(S);
|
S: facsum(S, s);
|
tox: S . B;
|
tox: ratsimp(tox);
|
tox: facsum(tox, s);
|
tox: ev(tox, Il = x0[1, 1], Vc = x0[2, 1]);
|
tox: ratsimp(tox);
|
tox: facsum(tox, s);
|
toy: C . S . B + D;
|
toy: ratsimp(toy);
|
toy: facsum(toy, s);
|
toy: ev(toy, Il = x0[1, 1], Vc = x0[2, 1]);
|
toy: ratsimp(toy);
|
toy: facsum(toy, s);
|
substituting values
|
tox0: ev(tox, R = 0);
|
tox0: facsum(tox0, s);
|
toy0: ev(toy, R = 0);
|
toy0: facsum(toy0, s);
|
tox1: ev(tox, D0 = 0.5, Vin = 10, Iout = 0.5, L = 50e-6, c = 0.5e-3, R = 0);
|
tox2: ev(tox, D0 = 0.5, Vin = 10, Iout = 0.5, L = 50e-6, c = 0.5e-3, R = 0.1);
|
toy1: ev(toy, D0 = 0.5, Vin = 10, Iout = 0.5, L = 50e-6, c = 0.5e-3, R = 0);
|
factor(toy1);
|
toy2: ev(toy, D0 = 0.5, Vin = 10, Iout = 0.5, L = 50e-6, c = 0.5e-3, R = 0.1);
|
factor(toy2);
|
PK vLñBH mimetypePK vLöżo÷ o÷ 5 content.xmlPK o Í÷