PK ¶v‰LñB–H mimetypetext/x-wxmathmlPK ¶v‰LÀÓQÙ’ Ù’ content.xml
Buck Converter, esr
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state 1 matrices
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A1: matrix([-R/L, -1/L], [1/c, 0]);
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B1: matrix([1/L, R/L], [0, -1/c]);
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C1: matrix([R, 1]);
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D1: matrix([0, -R]);
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state 2 matrices
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A2: matrix([-R/L, -1/L], [1/c, 0]);
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B2: matrix([0, R/L], [0, -1/c]);
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C2: matrix([R, 1]);
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D2: matrix([0, -R]);
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state variables, dc
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X0: matrix([Il], [Vc]);
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input variables, dc
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U0: matrix([Vin], [Iout]);
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basic computation; keep it as it is
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A: D0 * A1 + (1 - D0) * A2;
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A: ratsimp(A);
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B: D0 * B1 + (1 - D0) * B2;
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B: ratsimp(B);
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C: D0 * C1 + (1 - D0) * C2;
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C: ratsimp(C);
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D: D0 * D1 + (1 - D0) * D2;
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D: ratsimp(D);
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dc computation, still without d hat, keep it as it is
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iA: invert(A);
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iA: ratsimp(iA);
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x0: -iA . B . U0;
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x0: ratsimp(x0);
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y0: (D - C . iA . B) . U0;
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y0: ratsimp(y0);
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ac computation, keep it as it is
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E: (A1 - A2) . X0 + (B1 - B2) . U0;
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E: ratsimp(E);
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F: (C1 - C2) . X0 + (D1 - D2) . U0;
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F: matrix([ratsimp(F)]);
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merging E and F; keep it as it is
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B: addcol(B, E);
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D: addcol(D, F);
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computing transfer functions; keep it as it is
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S0: s * diagmatrix(2, 1) - A;
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S: invert(S0);
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1c*s*
s+RL
+1c*Ls+RLs*s+RL
+1c*L
S: ratsimp(S);
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S: facsum(S, s);
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tox: S . B;
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tox: ratsimp(tox);
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tox: facsum(tox, s);
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tox: ev(tox, Il = x0[1, 1], Vc = x0[2, 1]);
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tox: ratsimp(tox);
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tox: facsum(tox, s);
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toy: C . S . B + D;
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toy: ratsimp(toy);
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toy: facsum(toy, s);
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toy: ev(toy, Il = x0[1, 1], Vc = x0[2, 1]);
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toy: ratsimp(toy);
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toy: facsum(toy, s);
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substituting values
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tox0: ev(tox, R = 0);
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tox0: ratsimp(tox0);
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toy0: subst(0, R, toy);
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toy0: ratsimp(toy0);
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tox1: ev(tox, D0 = 0.5, Vin = 20, Iout = 1, L = 50e-6, c = 0.5e-3, R = 0);
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tox2: ev(tox, D0 = 0.5, Vin = 20, Iout = 1, L = 50e-6, c = 0.5e-3, R = 0.1);
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toy1: ev(toy, D0 = 0.5, Vin = 20, Iout = 1, L = 50e-6, c = 0.5e-3, R = 0);
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toy2: ev(toy, D0 = 0.5, Vin = 20, Iout = 1, L = 50e-6, c = 0.5e-3, R = 0.1);
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PK ¶v‰LñB–H mimetypePK ¶v‰LÀÓQÙ’ Ù’ 5 content.xmlPK o 7“