function [A_k, C_k, pre_k, A_l] = assembDeriv4(ksi, uab, ksi0, Q, R, ref_ome, inddq) a = 0.9898; b = 0.0072; c = 0.0361; d = 1.0; e = 0.0149; dt = 0.000125; Rs = 0.28; Ls = 0.003465; psi = 0.1989; B = 0; kp = 1.5; pp = 4.0; J = 0.04; Lq = 1.0*Ls; Ld = 0.9*Ls; kpp = kp*pp*pp; kppj = kpp/J; ia = ksi(1); ib = ksi(2); ome = ksi(3); the = ksi(4); P = [ksi(5), ksi(6), ksi(8), ksi(11);... ksi(6), ksi(7), ksi(9), ksi(12);... ksi(8), ksi(9), ksi(10), ksi(13);... ksi(11), ksi(12), ksi(13), ksi(14)]; A_k = zeros(14); A_l = zeros(15); %puvodni matice derivaci if(inddq == 0) %stejne indukcnosti A = [a, 0, b*sin(the), b*ome*cos(the);... 0, a, -b*cos(the), b*ome*sin(the);... -e*sin(the), e*cos(the), d, -e*(ib*sin(the)+ia*cos(the));... 0, 0, dt, 1.0]; else %ruzne indukcnosti A = [[ (Lq - Rs*dt*sin(the)^2)/Lq - (dt*ome*sin(the)*Lq^2*cos(the) + Rs*dt*Lq*cos(the)^2)/(Ld*Lq) + (Ld*dt*ome*cos(the)*sin(the))/Lq, (dt*(Ld - Lq)*(- Lq*ome*cos(the)^2 + Rs*cos(the)*sin(the) + Ld*ome*sin(the)^2))/(Ld*Lq), dt*cos(the)*(ia*sin(the) - ib*cos(the) + (Lq*(ib*cos(the) - ia*sin(the)))/Ld) + dt*sin(the)*(psi/Lq - ia*cos(the) - ib*sin(the) + (Ld*(ia*cos(the) + ib*sin(the)))/Lq), (dt*(ome*psi*cos(the) + Rs*ib*cos(2*the) - Rs*ia*sin(2*the)))/Lq + (Ld*dt*(ia*ome*cos(2*the) + ib*ome*sin(2*the)))/Lq - (dt*(Lq^2*ia*ome*cos(2*the) + Lq^2*ib*ome*sin(2*the) + Lq*Rs*ib*cos(2*the) - Lq*Rs*ia*sin(2*the)))/(Ld*Lq)];... [ (dt*(Ld - Lq)*(- Ld*ome*cos(the)^2 + Rs*cos(the)*sin(the) + Lq*ome*sin(the)^2))/(Ld*Lq), (Lq - Rs*dt*cos(the)^2)/Lq - (Lq*Rs*dt*sin(the)^2 - Lq^2*dt*ome*cos(the)*sin(the))/(Ld*Lq) - (Ld*dt*ome*cos(the)*sin(the))/Lq, (dt*(Lq*ia - psi*cos(the)))/Lq + (dt*((Lq^2*ia*cos(2*the))/2 - (Lq^2*ia)/2 + (Lq^2*ib*sin(2*the))/2))/(Ld*Lq) - (Ld*dt*(ia/2 + (ia*cos(2*the))/2 + (ib*sin(2*the))/2))/Lq, (dt*ome*psi*sin(the) - Rs*dt*ia*(2*sin(the)^2 - 1) + Rs*dt*ib*sin(2*the))/Lq + (Ld*(dt*ib*ome*(2*sin(the)^2 - 1) + dt*ia*ome*sin(2*the)))/Lq - (Lq*Rs*dt*ib*sin(2*the) + Lq^2*dt*ib*ome*(2*sin(the)^2 - 1) + Lq^2*dt*ia*ome*sin(2*the) - Lq*Rs*dt*ia*(2*sin(the)^2 - 1))/(Ld*Lq)];... [ -dt*kppj*(psi*sin(the) - cos(the)*(Ld - Lq)*(ib*cos(the) - ia*sin(the)) + sin(the)*(Ld - Lq)*(ia*cos(the) + ib*sin(the))), dt*kppj*(psi*cos(the) + cos(the)*(Ld - Lq)*(ia*cos(the) + ib*sin(the)) + sin(the)*(Ld - Lq)*(ib*cos(the) - ia*sin(the))), 1.0, -dt*kppj*(psi*(ia*cos(the) + ib*sin(the)) + (Ld - Lq)*(ia*cos(the) + ib*sin(the))^2 - (Ld - Lq)*(ib*cos(the) - ia*sin(the))^2)];... [ 0.0, 0.0, dt, 1.0]]; end C = [1, 0, 0, 0;... 0, 1, 0, 0]; %dalsi matice EKF Pp = A*P*A' + Q; S = C*Pp*C' + R; K = Pp*C'/S; Pnew = (eye(4) - K*C)*Pp; %derivace zakladnich matic EKF stavu dAdia = [0, 0, 0, 0;... 0, 0, 0, 0;... 0, 0, 0, -e*cos(the);... 0, 0, 0, 0]; dAdib = [0, 0, 0, 0;... 0, 0, 0, 0;... 0, 0, 0, -e*sin(the);... 0, 0, 0, 0]; dAdom = [0, 0, 0, b*cos(the);... 0, 0, 0, b*sin(the);... 0, 0, 0, 0;... 0, 0, 0, 0]; dAdth = [0, 0, b*cos(the), -b*ome*sin(the);... 0, 0, b*sin(the), b*ome*cos(the);... -e*cos(the), -e*sin(the), 0, -e*(ib*cos(the)-ia*sin(the));... 0, 0, 0, 0]; % dAdP = zeros(4); % dCdiaibomth = zeros(2,4); % dCdP = zeros(2,4); % dPdiaibomth = zeros(4); dPdP5 = zeros(4); dPdP5(1,1) = 1; dPdP6 = zeros(4); dPdP6(1,2) = 1; dPdP6(2,1) = 1; dPdP7 = zeros(4); dPdP7(2,2) = 1; dPdP8 = zeros(4); dPdP8(1,3) = 1; dPdP8(3,1) = 1; dPdP9 = zeros(4); dPdP9(2,3) = 1; dPdP9(3,2) = 1; dPdP10 = zeros(4); dPdP10(3,3) = 1; dPdP11 = zeros(4); dPdP11(1,4) = 1; dPdP11(4,1) = 1; dPdP12 = zeros(4); dPdP12(2,4) = 1; dPdP12(4,2) = 1; dPdP13 = zeros(4); dPdP13(3,4) = 1; dPdP13(4,3) = 1; dPdP14 = zeros(4); dPdP14(4,4) = 1; %derivace dalsich matic EKF stavu dPpdia = dAdia*P*A' + A*P*dAdia'; dPpdib = dAdib*P*A' + A*P*dAdib'; dPpdom = dAdom*P*A' + A*P*dAdom'; dPpdth = dAdth*P*A' + A*P*dAdth'; dPpdP5 = A*dPdP5*A'; dPpdP6 = A*dPdP6*A'; dPpdP7 = A*dPdP7*A'; dPpdP8 = A*dPdP8*A'; dPpdP9 = A*dPdP9*A'; dPpdP10 = A*dPdP10*A'; dPpdP11 = A*dPdP11*A'; dPpdP12 = A*dPdP12*A'; dPpdP13 = A*dPdP13*A'; dPpdP14 = A*dPdP14*A'; dSdia = C*dPpdia*C'; dSdib = C*dPpdib*C'; dSdom = C*dPpdom*C'; dSdth = C*dPpdth*C'; dSdP5 = C*dPpdP5*C'; dSdP6 = C*dPpdP6*C'; dSdP7 = C*dPpdP7*C'; dSdP8 = C*dPpdP8*C'; dSdP9 = C*dPpdP9*C'; dSdP10 = C*dPpdP10*C'; dSdP11 = C*dPpdP11*C'; dSdP12 = C*dPpdP12*C'; dSdP13 = C*dPpdP13*C'; dSdP14 = C*dPpdP14*C'; dKdia = dPpdia*C'/S - Pp*C'/S*dSdia/S; dKdib = dPpdib*C'/S - Pp*C'/S*dSdib/S; dKdom = dPpdom*C'/S - Pp*C'/S*dSdom/S; dKdth = dPpdth*C'/S - Pp*C'/S*dSdth/S; dKdP5 = dPpdP5*C'/S - Pp*C'/S*dSdP5/S; dKdP6 = dPpdP6*C'/S - Pp*C'/S*dSdP6/S; dKdP7 = dPpdP7*C'/S - Pp*C'/S*dSdP7/S; dKdP8 = dPpdP8*C'/S - Pp*C'/S*dSdP8/S; dKdP9 = dPpdP9*C'/S - Pp*C'/S*dSdP9/S; dKdP10 = dPpdP10*C'/S - Pp*C'/S*dSdP10/S; dKdP11 = dPpdP11*C'/S - Pp*C'/S*dSdP11/S; dKdP12 = dPpdP12*C'/S - Pp*C'/S*dSdP12/S; dKdP13 = dPpdP13*C'/S - Pp*C'/S*dSdP13/S; dKdP14 = dPpdP14*C'/S - Pp*C'/S*dSdP14/S; dPnewdia = dPpdia - dKdia*C*Pp - K*C*dPpdia; dPnewdib = dPpdib - dKdib*C*Pp - K*C*dPpdib; dPnewdom = dPpdom - dKdom*C*Pp - K*C*dPpdom; dPnewdth = dPpdth - dKdth*C*Pp - K*C*dPpdth; dPnewdP5 = dPpdP5 - dKdP5*C*Pp - K*C*dPpdP5; dPnewdP6 = dPpdP6 - dKdP6*C*Pp - K*C*dPpdP6; dPnewdP7 = dPpdP7 - dKdP7*C*Pp - K*C*dPpdP7; dPnewdP8 = dPpdP8 - dKdP8*C*Pp - K*C*dPpdP8; dPnewdP9 = dPpdP9 - dKdP9*C*Pp - K*C*dPpdP9; dPnewdP10 = dPpdP10 - dKdP10*C*Pp - K*C*dPpdP10; dPnewdP11 = dPpdP11 - dKdP11*C*Pp - K*C*dPpdP11; dPnewdP12 = dPpdP12 - dKdP12*C*Pp - K*C*dPpdP12; dPnewdP13 = dPpdP13 - dKdP13*C*Pp - K*C*dPpdP13; dPnewdP14 = dPpdP14 - dKdP14*C*Pp - K*C*dPpdP14; A_k(1:4,1:4) = A; %A_k(1:4,5:14) = zeros(4,10); pttrn = [1 5 6 9 10 11 13 14 15 16]'; %pattern for selecting proper elements from P matrices A_k(5:14,1) = dPnewdia(pttrn); A_k(5:14,2) = dPnewdib(pttrn); A_k(5:14,3) = dPnewdom(pttrn); A_k(5:14,4) = dPnewdth(pttrn); A_k(5:14,5) = dPnewdP5(pttrn); A_k(5:14,6) = dPnewdP6(pttrn); A_k(5:14,7) = dPnewdP7(pttrn); A_k(5:14,8) = dPnewdP8(pttrn); A_k(5:14,9) = dPnewdP9(pttrn); A_k(5:14,10) = dPnewdP10(pttrn); A_k(5:14,11) = dPnewdP11(pttrn); A_k(5:14,12) = dPnewdP12(pttrn); A_k(5:14,13) = dPnewdP13(pttrn); A_k(5:14,14) = dPnewdP14(pttrn); phi = zeros(14,1); phi(1) = a*ksi0(1) + b*ksi0(3)*sin(ksi0(4)) + c*uab(1); phi(2) = a*ksi0(2) - b*ksi0(3)*cos(ksi0(4)) + c*uab(2); phi(3) = d*ksi0(3) + e*(ksi0(2)*cos(ksi0(4)) - ksi0(1)*sin(ksi0(4))); phi(4) = ksi0(4) + dt*ksi0(3); phi(5:14) = Pnew(pttrn); A_l(1:14,1:14) = A_k; A_l(1:14,15) = phi - A_k*ksi0; A_l(15,15) = 1.0; C_k = zeros(2,14); C_k(1:2,1:4) = C; pre_k = Pnew(pttrn); %max x(14) = pi^2/3 ... variance of uniform -pi,pi if(pre_k(10) > pi^2/3) pre_k(10) = pi^2/3; end end