[1436] | 1 | function [A_k, C_k, pre_k, A_l] = assembDeriv(ksi, iab, ksi0, Q, R, ref_ome, inddq) |
---|
[1435] | 2 | a = 0.9898; |
---|
| 3 | b = 0.0072; |
---|
| 4 | c = 0.0361; |
---|
| 5 | d = 1.0; |
---|
| 6 | e = 0.0149; |
---|
| 7 | dt = 0.000125; |
---|
[1436] | 8 | |
---|
| 9 | Rs = 0.28; |
---|
| 10 | Ls = 0.003465; |
---|
| 11 | psi = 0.1989; |
---|
| 12 | B = 0; |
---|
| 13 | kp = 1.5; |
---|
| 14 | pp = 4.0; |
---|
| 15 | J = 0.04; |
---|
| 16 | Lq = 1.0*Ls; |
---|
| 17 | Ld = 0.9*Ls; |
---|
| 18 | kpp = kp*pp*pp; |
---|
| 19 | kppj = kpp/J; |
---|
[1435] | 20 | |
---|
| 21 | ome = ksi(1); |
---|
| 22 | the = ksi(2); |
---|
| 23 | P = [ksi(3), ksi(4); ksi(4), ksi(5)]; |
---|
| 24 | ia = iab(1); |
---|
| 25 | ib = iab(2); |
---|
| 26 | A_k = zeros(5); |
---|
| 27 | A_l = zeros(6); |
---|
| 28 | |
---|
| 29 | |
---|
| 30 | %puvodni matice derivaci |
---|
[1436] | 31 | if(inddq == 0) |
---|
| 32 | %stejne indukcnosti |
---|
| 33 | A = [d, -e*(ia*cos(the)+ib*sin(the)); dt, 1.0]; |
---|
| 34 | else |
---|
| 35 | %ruzne indukcnosti |
---|
| 36 | A = [d, -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); dt, 1.0]; |
---|
| 37 | end |
---|
[1435] | 38 | C = [b*sin(the), b*ome*cos(the); -b*cos(the), b*ome*sin(the)]; |
---|
| 39 | |
---|
| 40 | %dalsi matice EKF |
---|
| 41 | Pp = A*P*A' + Q; |
---|
| 42 | S = C*Pp*C' + R; |
---|
| 43 | K = Pp*C'/S; |
---|
| 44 | Pnew = (eye(2) - K*C)*Pp; |
---|
| 45 | |
---|
| 46 | %derivace zakladnich matic EKF stavu |
---|
| 47 | % dAdom = zeros(4); |
---|
| 48 | dAdth = [0, e*(ia*sin(the)-ib*cos(the)); 0, 0]; |
---|
| 49 | % dAdP = zeros(4); |
---|
| 50 | dCdom = [0, b*cos(the); 0, b*sin(the)]; |
---|
| 51 | dCdth = [b*cos(the), -b*ome*sin(the); b*sin(the), b*ome*cos(the)]; |
---|
| 52 | % dCdP = zeros(4); |
---|
| 53 | % dPdomth = zeros(4); |
---|
| 54 | dPdPo = [1, 0; 0, 0]; |
---|
| 55 | dPdPot = [0, 1; 1, 0]; |
---|
| 56 | dPdPt = [0, 0; 0, 1]; |
---|
| 57 | |
---|
| 58 | %derivace dalsich matic EKF stavu |
---|
| 59 | % dPpdom = zeros(4); |
---|
| 60 | dPpdth = dAdth*P*A' + A*P*dAdth'; |
---|
| 61 | dPpdPo = A*dPdPo*A'; |
---|
| 62 | dPpdPot = A*dPdPot*A'; |
---|
| 63 | dPpdPt = A*dPdPt*A'; |
---|
| 64 | |
---|
| 65 | dSdom = dCdom*Pp*C' + C*Pp*dCdom'; |
---|
| 66 | dSdth = dCdth*Pp*C' + C*dPpdth*C' + C*Pp*dCdth'; |
---|
| 67 | dSdPo = C*dPpdPo*C'; |
---|
| 68 | dSdPot = C*dPpdPot*C'; |
---|
| 69 | dSdPt = C*dPpdPt*C'; |
---|
| 70 | |
---|
| 71 | dKdom = Pp*dCdom'/S - Pp*C'/S*dSdom/S; |
---|
| 72 | dKdth = dPpdth*C'/S + Pp*dCdth'/S - Pp*C'/S*dSdth/S; |
---|
| 73 | dKdPo = dPpdPo*C'/S - Pp*C'/S*dSdPo/S; |
---|
| 74 | dKdPot = dPpdPot*C'/S - Pp*C'/S*dSdPot/S; |
---|
| 75 | dKdPt = dPpdPt*C'/S - Pp*C'/S*dSdPt/S; |
---|
| 76 | |
---|
| 77 | dPnewdom = - dKdom*C*Pp - K*dCdom*Pp; |
---|
| 78 | dPnewdth = dPpdth - dKdth*C*Pp - K*dCdth*Pp - K*C*dPpdth; |
---|
| 79 | dPnewdPo = dPpdPo - dKdPo*C*Pp - K*C*dPpdPo; |
---|
| 80 | dPnewdPot = dPpdPot - dKdPot*C*Pp - K*C*dPpdPot; |
---|
| 81 | dPnewdPt = dPpdPt - dKdPt*C*Pp - K*C*dPpdPt; |
---|
| 82 | |
---|
| 83 | A_k(1,1) = d; |
---|
| 84 | A_k(1,2) = -e*(ia*cos(the)+ib*sin(the)); |
---|
| 85 | % A_k(1,3) = 0; |
---|
| 86 | % A_k(1,4) = 0; |
---|
| 87 | % A_k(1,5) = 0; |
---|
| 88 | |
---|
| 89 | A_k(2,1) = dt; |
---|
| 90 | A_k(2,2) = 1.0; |
---|
| 91 | % A_k(2,3) = 0; |
---|
| 92 | % A_k(2,4) = 0; |
---|
| 93 | % A_k(2,5) = 0; |
---|
| 94 | |
---|
| 95 | A_k(3,1) = dPnewdom(1,1); |
---|
| 96 | A_k(3,2) = dPnewdth(1,1); |
---|
| 97 | A_k(3,3) = dPnewdPo(1,1); |
---|
| 98 | A_k(3,4) = dPnewdPot(1,1); |
---|
| 99 | A_k(3,5) = dPnewdPt(1,1); |
---|
| 100 | |
---|
| 101 | A_k(4,1) = dPnewdom(1,2); |
---|
| 102 | A_k(4,2) = dPnewdth(1,2); |
---|
| 103 | A_k(4,3) = dPnewdPo(1,2); |
---|
| 104 | A_k(4,4) = dPnewdPot(1,2); |
---|
| 105 | A_k(4,5) = dPnewdPt(1,2); |
---|
| 106 | |
---|
| 107 | A_k(5,1) = dPnewdom(2,2); |
---|
| 108 | A_k(5,2) = dPnewdth(2,2); |
---|
| 109 | A_k(5,3) = dPnewdPo(2,2); |
---|
| 110 | A_k(5,4) = dPnewdPot(2,2); |
---|
| 111 | A_k(5,5) = dPnewdPt(2,2); |
---|
| 112 | |
---|
| 113 | phi = zeros(5,1); |
---|
| 114 | phi(1) = d*ksi0(1) + e*(ib*cos(ksi0(2)) - ia*sin(ksi0(2))); |
---|
| 115 | phi(2) = ksi0(2) + dt*ksi0(1); |
---|
| 116 | phi(3) = Pnew(1,1); |
---|
| 117 | phi(4) = Pnew(1,2); |
---|
| 118 | phi(5) = Pnew(2,2); |
---|
| 119 | |
---|
| 120 | A_l(1:5,1:5) = A_k; |
---|
| 121 | A_l(1:5,6) = phi - A_k*ksi0; |
---|
| 122 | A_l(6,6) = 1.0; |
---|
| 123 | |
---|
| 124 | %%% |
---|
| 125 | A_l(1,2) = 0; %maze clen e*(...), ktery se prevede do B |
---|
| 126 | A_l(1:2,6) = [0;dt*ref_ome]; %zmena korekce, protoze je to tam uz linearni, ale posun |
---|
| 127 | %%% |
---|
| 128 | |
---|
| 129 | C_k = zeros(2,5); |
---|
| 130 | C_k(1:2,1:2) = C; |
---|
| 131 | |
---|
| 132 | pre_k = zeros(3,1); |
---|
| 133 | pre_k(1) = Pnew(1,1); |
---|
| 134 | pre_k(2) = Pnew(1,2); |
---|
[1436] | 135 | pre_k(3) = Pnew(2,2); |
---|
| 136 | %max x(5) = pi^2/3 ... variance of uniform -pi,pi |
---|
| 137 | if(pre_k(3) > pi^2/3) |
---|
| 138 | pre_k(3) = pi^2/3; |
---|
| 139 | end |
---|
[1435] | 140 | end |
---|