[1416] | 1 | %simulator PMSM pro PCRB s lepsi ocekavanou hodnotou E |
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| 2 | % zatim zaver: |
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| 3 | % |
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| 4 | clear all; |
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| 5 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 6 | % parametry stroje |
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| 7 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 8 | Rs = 0.28; |
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| 9 | Ls = 0.003465; |
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| 10 | psipm = 0.1989; |
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| 11 | B = 0; |
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| 12 | TL = 0; |
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| 13 | kp = 1.5; |
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| 14 | pp = 4.0; |
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| 15 | J = 0.04; |
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| 16 | dt = 0.000125; |
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| 17 | |
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| 18 | a = 0.9898; |
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| 19 | b = 0.0072; |
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| 20 | c = 0.0361; |
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| 21 | d = 1.0; |
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| 22 | e = 0.0149; |
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| 23 | |
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| 24 | Lq = 1.0*Ls; |
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| 25 | Ld = 0.9*Ls; |
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| 26 | |
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| 27 | Q = diag([0.0013 0.0013 5.0e-6 1.0e-10]); |
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| 28 | R = diag([0.0006 0.0006]); |
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| 29 | |
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| 30 | |
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| 31 | T = 120000; %horizont |
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| 32 | |
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| 33 | ref_ome = zeros(1, T); %referencni signal |
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| 34 | % ref_profile = [1, 10, 50, 200, 200, 30, 0, 0, -1, -10, -50, -200, -200, -30, 0]; |
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| 35 | ref_profile = [0, -1, 3, 6, 9, 6, 3, 0, 0, 0, 0, 0,0,-3, -6, -3]; |
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| 36 | % ref_profile = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; |
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| 37 | |
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| 38 | for k = 1:T, |
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| 39 | index = floor(k*dt); |
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| 40 | if(index>0) |
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| 41 | lower = ref_profile(index); |
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| 42 | else |
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| 43 | lower = 0; |
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| 44 | end |
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| 45 | if(index<T*dt) |
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| 46 | upper = ref_profile(index+1); |
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| 47 | else |
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| 48 | upper = 0; |
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| 49 | end |
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| 50 | ref_ome(k) = lower + (upper-lower)*dt*(k-index/dt); |
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| 51 | end |
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| 52 | |
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| 53 | |
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| 54 | |
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| 55 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 56 | % promenne stavu systemu |
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| 57 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 58 | |
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| 59 | x_sys = zeros(4, T); %vnitrni stav systemu |
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| 60 | u_ab = zeros(2, T); %rizeni systemu v alfa-beta |
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| 61 | |
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| 62 | iJn = zeros(4,4,T); |
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| 63 | iJn2 = zeros(4,4,T); |
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| 64 | iJn3 = zeros(4,4,T); |
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| 65 | iJn4 = zeros(4,4,T); |
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| 66 | iJn5 = zeros(4,4,T); |
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| 67 | Jj = inv(Q); |
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| 68 | Jj2 = inv(Q); |
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| 69 | Jj3 = inv(Q); |
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| 70 | Jj4 = inv(Q); |
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| 71 | Jj5 = inv(Q); |
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| 72 | |
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| 73 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 74 | % promenne rizeni |
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| 75 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 76 | |
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| 77 | u_dq = zeros(2, T); |
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| 78 | |
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| 79 | %PI vektorove |
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| 80 | % kon_pi = 3.0; |
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| 81 | % kon_ii = 0.00375; |
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| 82 | % kon_pu = 20.0; |
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| 83 | % kon_iu = 0.05; |
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| 84 | sum_iq = 0; |
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| 85 | sum_ud = 0; |
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| 86 | sum_uq = 0; |
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| 87 | |
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| 88 | kon_pi = 30.0; |
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| 89 | kon_ii = 0.0; |
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| 90 | kon_pu = 20.0; |
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| 91 | kon_iu = 0.0; |
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| 92 | |
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| 93 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 94 | % inicializace |
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| 95 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 96 | |
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| 97 | %alpha-beta, equal Ls |
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| 98 | DF = zeros(4); |
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| 99 | DF(1,1) = a; |
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| 100 | DF(2,2) = a; |
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| 101 | DF(3,3) = d; |
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| 102 | DF(4,3) = dt; |
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| 103 | DF(4,4) = 1.0; |
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| 104 | DH = zeros(2,4); |
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| 105 | DH(1,1) = 1.0; |
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| 106 | DH(2,2) = 1.0; |
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| 107 | |
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| 108 | %d-q red, equal Ls |
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| 109 | DF2 = zeros(4); |
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| 110 | DF2(1,1) = a; |
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| 111 | DF2(2,2) = a; |
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| 112 | DF2(2,3) = -b; |
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| 113 | DF2(3,2) = e; |
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| 114 | DF2(3,3) = d; |
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| 115 | DF2(4,3) = dt; |
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| 116 | DF2(4,4) = 1.0; |
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| 117 | DH2 = DH; |
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| 118 | |
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| 119 | %d-q full, equal Ls |
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| 120 | DF3 = DF2; |
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| 121 | |
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| 122 | %d-q, not equal Ld, Lq |
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| 123 | DF4 = zeros(4); |
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| 124 | DF4(1,1) = 1.0 - Rs*dt/Ld; |
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| 125 | DF4(2,2) = 1.0 - Rs*dt/Lq; |
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| 126 | DF4(3,3) = 1-B*dt/J; |
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| 127 | DF4(4,3) = dt; |
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| 128 | DF4(4,4) = 1.0; |
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| 129 | |
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| 130 | %alpha-beta, not equal Ld, Lq |
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| 131 | DF5 = zeros(4); |
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| 132 | |
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| 133 | % figure; |
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| 134 | |
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| 135 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 136 | % hlavni smycka |
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| 137 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 138 | |
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| 139 | for t = 1:T-1, |
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| 140 | |
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| 141 | |
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| 142 | %%%%% rizeni %%%% (estxt -> ut) |
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| 143 | ial = x_sys(1, t); |
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| 144 | ibe = x_sys(2, t); |
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| 145 | ome = x_sys(3, t); |
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| 146 | the = x_sys(4, t); |
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| 147 | |
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| 148 | id = ial*cos(the) + ibe*sin(the); |
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| 149 | iq = ibe*cos(the) - ial*sin(the); |
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| 150 | |
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| 151 | %%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 152 | |
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| 153 | %alpha-beta, equal Ls |
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| 154 | % DF(1,3) = b*sin(the); |
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| 155 | % DF(1,4) = b*ome*cos(the); |
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| 156 | % DF(2,3) = -b*cos(the); |
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| 157 | % DF(2,4) = b*ome*sin(the); |
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| 158 | % DF(3,1) = -e*sin(the); |
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| 159 | % DF(3,2) = e*cos(the); |
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| 160 | % DF(3,4) = -e*(ial*cos(the)+ibe*sin(the)); |
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| 161 | % |
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| 162 | % D11 = DF'*inv(Q)*DF; |
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| 163 | % D12 = -DF'*inv(Q); |
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| 164 | % D21 = D12'; |
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| 165 | % D22 = inv(Q) + DH'*inv(R)*DH; |
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| 166 | % |
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| 167 | % Jj = D22 - D21*inv(Jj + D11)*D12; |
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| 168 | % |
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| 169 | % iJn(:,:,t) = inv(Jj); |
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| 170 | |
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| 171 | %d-q red, equal Ls ... DF-OK |
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| 172 | % DH2(1,1) = cos(the); |
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| 173 | % DH2(1,2) = -sin(the); |
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| 174 | % DH2(1,4) = -id*ome*sin(the)-iq*ome*cos(the); |
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| 175 | % DH2(2,1) = sin(the); |
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| 176 | % DH2(2,2) = cos(the); |
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| 177 | % DH2(2,4) = id*ome*cos(the)-iq*ome*sin(the); |
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| 178 | % D11 = DF2'*inv(Q)*DF2; |
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| 179 | % D12 = -DF2'*inv(Q); |
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| 180 | % D21 = D12'; |
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| 181 | % % D22 = inv(Q) + DH'*inv(R)*DH; |
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| 182 | % D22 = inv(Q) + DH2'*inv(R)*DH2; |
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| 183 | % |
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| 184 | % Jj2 = D22 - D21*inv(Jj2 + D11)*D12; |
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| 185 | % |
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| 186 | % iJn2(:,:,t) = inv(Jj2); |
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| 187 | |
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| 188 | %d-q full, equal Ls |
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| 189 | % DF3(1,2) = dt*ome; |
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| 190 | % DF3(1,3) = dt*iq; |
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| 191 | % DF3(2,1) = -dt*ome; |
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| 192 | % DF3(2,3) = -dt*id-b; |
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| 193 | % D11 = DF3'*inv(Q)*DF3; !!!!!!!!!!!!!!!!!BAD |
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| 194 | iQ = inv(Q); |
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| 195 | q11 = iQ(1,1); |
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| 196 | q12 = iQ(1,2); |
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| 197 | q13 = iQ(1,3); |
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| 198 | q14 = iQ(1,4); |
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| 199 | q21 = iQ(2,1); |
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| 200 | q22 = iQ(2,2); |
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| 201 | q23 = iQ(2,3); |
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| 202 | q24 = iQ(2,4); |
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| 203 | q31 = iQ(3,1); |
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| 204 | q32 = iQ(3,2); |
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| 205 | q33 = iQ(3,3); |
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| 206 | q34 = iQ(3,4); |
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| 207 | q41 = iQ(4,1); |
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| 208 | q42 = iQ(4,2); |
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| 209 | q43 = iQ(4,3); |
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| 210 | q44 = iQ(4,4); |
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| 211 | om = ome; |
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| 212 | D11 = [[a*(a*iQ(1,1) - dt*om*iQ(2,1)) - dt*om*a*iQ(1,2) + dt^2*Q(3,3)*iQ(2,2), a*(a*iQ(1,2) - dt*om*iQ(2,2)) + e*(a*iQ(1,3) - dt*om*iQ(2,3)) + dt*om*a*iQ(1,1) - dt^2*Q(3,3)*iQ(2,1), d*(a*iQ(1,3) - dt*om*iQ(2,3)) - (a*iQ(1,2) - dt*om*iQ(2,2))*b - a*iQ(1,2)*dt*id - dt^2*Q(1,3)*iQ(2,2) + dt*(a*q14 - dt*om*q24) + dt*iq*a*q11 - dt^2*Q(2,3)*q21, a*q14 - dt*om*q24];... |
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| 213 | [ a*(a*q21 + e*q31 + dt*om*q11) - dt*om*(a*q22 + e*q32) - dt^2*Q(3,3)*q12, a*(a*q22 + e*q32 + dt*om*q12) + e*(a*q23 + e*q33 + dt*om*q13) + dt*om*(a*q21 + e*q31) + dt^2*Q(3,3)*q11, d*(a*q23 + e*q33 + dt*om*q13) + dt*(a*q24 + e*q34 + dt*om*q14) - b*(a*q22 + e*q32 + dt*om*q12) - dt*id*(a*q22 + e*q32) - dt^2*Q(1,3)*q12 + dt*iq*(a*q21 + e*q31) + dt^2*Q(2,3)*q11,a*q24 + e*q34 + dt*om*q14];... |
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| 214 | [ a*(d*q31 + dt*q41 - q21*(b + dt*id) + dt*iq*q11) - dt*om*(d*q32 + dt*q42 - q22*b) + dt*q22*(dt*Q(1,3)) - dt^2*Q(2,3)*q12, a*(d*q32 + dt*q42 - q22*(b + dt*id) + dt*iq*q12) + e*(d*q33 + dt*q43 - q23*(b + dt*id) + dt*iq*q13) + dt*om*(d*q31 + dt*q41 - q21*b) - q21*dt^2*Q(1,3) + dt^2*Q(2,3)*q11, d*(d*q33 + dt*q43 - q23*(b + dt*id) + dt*iq*q13) - (b + dt*id)*(d*q32 + dt*q42 - q22*b) + b*(q22*dt*id - dt*iq*q12) + dt*(q22*dt*Q(1,1) - dt*Q(1,2)*q12) + dt*(d*q34 + dt*q44 - q24*(b + dt*id) + dt*iq*q14) + dt*iq*(d*q31 + dt*q41 - q21*b) + dt*(- q21*dt*Q(1,2) + dt*Q(2,2)*q11), d*q34 + dt*q44 - q24*(b + dt*id) + dt*iq*q14];... |
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| 215 | [ a*q41 - dt*om*q42, a*q42 + e*q43 + dt*om*q41, d*q43 + dt*q44 - q42*(b + dt*id) + dt*iq*q41, q44]]; |
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| 216 | |
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| 217 | D12 = -DF3'*iQ; |
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| 218 | D21 = D12'; |
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| 219 | % % D22 = inv(Q) + DH'*inv(R)*DH; |
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| 220 | D22 = inv(Q) + DH2'*inv(R)*DH2; |
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| 221 | |
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| 222 | Jj3 = D22 - D21*inv(Jj3 + D11)*D12; |
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| 223 | |
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| 224 | iJn3(:,:,t) = inv(Jj3); |
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| 225 | |
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| 226 | %d-q, not equal Ld, Lq |
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| 227 | % DF4(1,2) = Lq*dt/Ld*ome; |
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| 228 | % DF4(1,3) = Lq*dt/Ld*iq; |
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| 229 | % DF4(2,1) = -Ld*dt/Lq*ome; |
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| 230 | % DF4(2,3) = -Ld*dt/Lq*id-psipm*dt/Lq; |
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| 231 | % DF4(3,1) = kp*pp*pp*dt*(Ld-Lq)/J*iq; |
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| 232 | % DF4(3,2) = kp*pp*pp*dt/J*((Ld-Lq)*id+psipm); |
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| 233 | % D11 = DF4'*inv(Q)*DF4; |
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| 234 | % D12 = -DF4'*inv(Q); |
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| 235 | % D21 = D12'; |
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| 236 | % D22 = inv(Q) + DH'*inv(R)*DH; |
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| 237 | % % D22 = inv(Q) + DH2'*inv(R)*DH2; |
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| 238 | % |
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| 239 | % Jj4 = D22 - D21*inv(Jj4 + D11)*D12; |
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| 240 | % |
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| 241 | % iJn4(:,:,t) = inv(Jj4); |
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| 242 | |
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| 243 | %alpha-beta, not equal Ld, Lq |
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| 244 | % ia = ial; |
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| 245 | % ib = ibe; |
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| 246 | % psi = psipm; |
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| 247 | % kppj = kp*pp*pp/J; |
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| 248 | % DF5 = [[ (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)];... |
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| 249 | % [ (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)];... |
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| 250 | % [ -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)];... |
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| 251 | % [ 0.0, 0.0, dt, 1.0]]; |
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| 252 | % D11 = DF5'*inv(Q)*DF5; |
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| 253 | % D12 = -DF5'*inv(Q); |
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| 254 | % D21 = D12'; |
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| 255 | % D22 = inv(Q) + DH'*inv(R)*DH; |
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| 256 | % |
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| 257 | % Jj5 = D22 - D21*inv(Jj5 + D11)*D12; |
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| 258 | % |
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| 259 | % iJn5(:,:,t) = inv(Jj5); |
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| 260 | |
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| 261 | |
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| 262 | %%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 263 | |
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| 264 | |
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| 265 | sum_iq = sum_iq + ref_ome(t) - ome; |
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| 266 | ref_iq = kon_pi*(ref_ome(t) - ome) + kon_ii*sum_iq; |
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| 267 | sum_ud = sum_ud - id; |
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| 268 | u_dq(1, t) = kon_pu*(-id) + kon_iu*sum_ud; |
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| 269 | sum_uq = sum_uq + ref_iq - iq; |
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| 270 | u_dq(2, t) = kon_pu*(ref_iq - iq) + kon_iu*sum_uq; |
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| 271 | u_dq(1, t) = u_dq(1, t) - Ls*ome*ref_iq; |
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| 272 | u_dq(2, t) = u_dq(2, t) + psipm*ome; |
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| 273 | |
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| 274 | |
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| 275 | % u_dq(2,t) = u_dq(2,t) + 10.0*cos(100*dt*t); |
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| 276 | |
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| 277 | % ual = u_dq(1,t)*cos(the) - u_dq(2,t)*sin(the); |
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| 278 | % ube = u_dq(1,t)*sin(the) + u_dq(2,t)*cos(the); |
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| 279 | % |
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| 280 | % % ual = ual + 10.0*cos(100*dt*t); |
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| 281 | % % ube = ube + 10.0*sin(100*dt*t); |
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| 282 | % |
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| 283 | % % duab = sign(rand(2,1)-0.5)*10; |
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| 284 | % % ual = ual + duab(1); |
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| 285 | % % ube = ube + duab(2); |
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| 286 | % |
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| 287 | % ud = ual*cos(the) + ube*sin(the); |
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| 288 | % uq = ube*cos(the) - ual*sin(the); |
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| 289 | |
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| 290 | % u_dq(1,t) = 0.1*Ld/dt - (1.0*Ld/dt - Rs)*id - Lq*ome*iq; |
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| 291 | |
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| 292 | %%%% simulace %%% (xt + ut -> xt+1; xt+1 -> yt+1) |
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| 293 | idpl = (1.0 - Rs*dt/Ld)*id + Lq*dt/Ld*ome*iq + dt/Ld*u_dq(1,t); |
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| 294 | iqpl = (1.0 - Rs*dt/Lq)*iq - psipm*dt/Lq*ome - Ld*dt/Lq*ome*id + dt/Lq*u_dq(2,t); |
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| 295 | |
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| 296 | x_sys(1, t+1) = idpl*cos(the) - iqpl*sin(the); |
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| 297 | x_sys(2, t+1) = idpl*sin(the) + iqpl*cos(the); |
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| 298 | |
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| 299 | x_sys(3, t+1) = ref_ome(t);%(1.0-B*dt/J)*ome + kp*pp*pp*dt/J*((Ld-Lq)*id*iq + psipm*iq); |
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| 300 | x_sys(4, t+1) = the + dt*ome; |
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| 301 | |
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| 302 | end |
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| 303 | |
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| 304 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 305 | % zaznam vysledku |
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| 306 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 307 | |
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| 308 | xax = 1:T-1; |
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| 309 | timex = (xax)*dt; |
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| 310 | |
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| 311 | % subplot(2, 2, 1); |
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| 312 | % plot(timex, x_sys(1, xax)); |
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| 313 | % subplot(2, 2, 2); |
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| 314 | % plot(timex, x_sys(2, xax)); |
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| 315 | % subplot(2, 2, 3); |
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| 316 | % plot(timex, x_sys(3, xax), timex, ref_ome(xax)); |
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| 317 | % subplot(2, 2, 4); |
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| 318 | % plot(timex, atan2(sin(x_sys(4, xax)),cos(x_sys(4, xax)))); |
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| 319 | |
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| 320 | % subplot(2,1,1); |
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| 321 | % plot(timex, x_sys(3, xax), timex, ref_ome(xax)); |
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| 322 | % subplot(2,1,2); |
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| 323 | hold on; |
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| 324 | plot(timex, squeeze(iJn3(4,4,xax)),'r');%,timex, squeeze(iJn5(4,4,xax)),timex, squeeze(iJn4(4,4,xax))); |
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| 325 | |
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| 326 | % figure; |
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| 327 | % plot(timex, x_sys(3, xax)-ref_ome(xax)); |
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