| 1 | function pmsm_ildp4
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| 2 | %verze ildp algoritmu s uvazovanim P (v logaritmu) pro PMSM motor
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| 3 | %rozsirena verze o diag P v pi aproximaci u
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| 4 | tic
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| 5 |
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| 6 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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| 7 | %pocatecni konstanty
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| 8 |
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| 9 | Iterace = 20; %iterace
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| 10 | K = 20; %casy
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| 11 | N = 100; %vzorky
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| 12 |
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| 13 | %konstanty motoru
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| 14 | %Rs = 0.28;
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| 15 | %Ls = 0.003465;
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| 16 | %PSIpm = 0.1989;
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| 17 | %kp = 1.5;
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| 18 | %p = 4.0;
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| 19 | %J = 0.04;
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| 20 | DELTAt = 0.000125;
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| 21 |
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| 22 | %upravene konstanty
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| 23 | Ca = 0.9898;
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| 24 | Cb = 0.0072;
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| 25 | Cc = 0.0361;
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| 26 | Cd = 1.0;
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| 27 | Ce = 0.0149;
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| 28 |
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| 29 | %omezeni rizeni
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| 30 | cC1 = 100;
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| 31 | % cLb = -50;
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| 32 | % cUb = 50;
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| 33 |
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| 34 | %presnost mereni proudu
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| 35 | deltaI = 0.085;
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| 36 |
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| 37 | %matice
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| 38 | %kovariancni matice Q a R
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| 39 | mQ = diag([0.0013 0.0013 5.0e-6 1.0e-10]);
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| 40 | mR = diag([0.0006 0.0006]);
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| 41 |
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| 42 | %matice pro vypocet
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| 43 | %matice A zavisla na parametrech
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| 44 | mA = zeros(4);
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| 45 | mA(1,1) = Ca;
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| 46 | mA(2,2) = Ca;
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| 47 | mA(3,3) = Cd;
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| 48 | mA(4,4) = 1;
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| 49 | mA(4,3) = DELTAt;
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| 50 |
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| 51 | %macite C konstantni
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| 52 | mC = [ 1 0 0 0; 0 1 0 0];
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| 53 |
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| 54 | %pozadovana hodnota otacek
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| 55 | omega_t_stripe = 1.0015;
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| 56 |
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| 57 | %penalizace za vstupy
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| 58 | cPenPsi = 0;%0.000009;
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| 59 |
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| 60 | %pocatecni hodnoty
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| 61 | X0 = [0; 0; 1; pi/2];
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| 62 | Y0 = [0; 0];
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| 63 | P0 = diag([0.01 0.01 0.01 0.01]);
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| 64 |
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| 65 | h_bel = 0;
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| 66 | h_beldx = [0; 0; 0; 0;];
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| 67 | h_beldxdx = zeros(4);
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| 68 |
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| 69 | %velikost okoli pro lokalni metodu
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| 70 | % rhoi = 0.0001;
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| 71 | % rhoo = 0.00015;
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| 72 | % rhot = 0.00005;
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| 73 | % rhop = 0.0001;
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| 74 | rhoi = sqrt(mQ(1,1));
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| 75 | rhoo = sqrt(mQ(3,3));
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| 76 | rhot = sqrt(mQ(4,4));
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| 77 | rhop = 0.001;
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| 78 |
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| 79 | %zvetseni hamiltonianu pro minimalizace
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| 80 | % mag = 1000;
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| 81 | mag = 1;
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| 82 |
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| 83 | %prepinac sumu on/off
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| 84 | noise = 0;
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| 85 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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| 86 | %globalni promenne
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| 87 |
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| 88 | Kpi_alfa = -0.3*ones(1, K); %konstanty aproximace slozky rizeni u_alfa
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| 89 | Kpi_beta = 0.01*ones(1, K); %konstanty aproximace slozky rizeni u_beta
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| 90 | % Kpi_alfa = ones(1, K); %konstanty aproximace slozky rizeni u_alfa
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| 91 | % Kpi_beta = ones(1, K); %konstanty aproximace slozky rizeni u_beta
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| 92 | % Kpi_alfa = zeros(4, K); %konstanty aproximace slozky rizeni u_alfa
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| 93 | % Kpi_alfa(1, :) = 1000*Cc*Ce*ones(1, K);
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| 94 | % Kpi_alfa(2, :) = 1000*Cc*Ce*ones(1, K);
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| 95 | %
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| 96 | % Kpi_beta = zeros(4, K); %konstanty aproximace slozky rizeni u_beta
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| 97 | % Kpi_beta(1, :) = Cc*Ce*ones(1, K);
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| 98 | % Kpi_beta(2, :) = Cc*Ce*ones(1, K);
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| 99 | Kpi = ones(9, K);
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| 100 |
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| 101 |
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| 102 | Wv = zeros(6, K); %konstanty aproximace Bellmanovy fce
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| 103 |
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| 104 | Xkn = zeros(4, K, N); % X = [i_alfa, i_beta, omega, theta]
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| 105 | Ykn = zeros(2, K, N); % Y = [i_alfa, i_beta]
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| 106 | Pkn = zeros(4, 4, K, N); % P = N vzorku posloupnosti K matic 4x4
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| 107 |
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| 108 | mKy = zeros(4, 2); % K = pomocna matice pro vypocet
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| 109 | mRy = zeros(2, 2); % R = pomocna matice pro vypocet
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| 110 |
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| 111 | Xstripe = zeros(4, K);
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| 112 | Pstripe = zeros(4, 4, K);
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| 113 |
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| 114 | Epsilon = zeros(6, N); %globalni promena pro vypocet Bellmanovy fce z odchylek (X - Xprum)
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| 115 |
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| 116 | gka = 0; %globalni promenna pro prenos casu k
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| 117 | gnu = 0; %globalni promenna pro prenos vzorku n
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| 118 |
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| 119 | Uopt2 = zeros(2, N);
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| 120 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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| 121 | %hlavni iteracni smycka
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| 122 | for i = 1:Iterace,
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| 123 |
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| 124 | disp(['Iterace: ', num2str(i)]);
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| 125 | %generovani stavu
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| 126 | for n = 1:N,
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| 127 | Xkn(:, 1, n) = X0;
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| 128 | Ykn(:, 1, n) = Y0;
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| 129 | Pkn(:, :, 1, n) = P0;
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| 130 |
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| 131 | for k = 1:K-1,
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| 132 | Uk = uPi(k, Xkn(:, k, n), Pkn(:, :, k, n));
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| 133 |
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| 134 | mRy = mC * Pkn(:, :, k, n) * mC' + mR;
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| 135 | mKy = Pkn(:, :, k, n) * mC' / mRy;
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| 136 | Xkn(:, k+1, n) = fceG(Xkn(:, k, n), Uk) - mKy * (Ykn(:, k, n) - fceH(Xkn(:, k, n))) + noise * sqrtm(mQ) * randn(4, 1);%+gauss sum s rozptylem odmocnina mQ
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| 137 | Ykn(:, k+1, n) = round(Xkn(1:2, k+1, n) / deltaI) * deltaI; %X kopie do Y se vzorkovanim 0.085
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| 138 | mA(1, 3) = Cb * sin(Xkn(4, k, n));
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| 139 | mA(1, 4) = Cb * Xkn(3, k, n) * cos(Xkn(4, k, n));
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| 140 | mA(2, 3) = - Cb * cos(Xkn(4, k, n));
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| 141 | mA(2, 4) = Cb * Xkn(3, k, n) * sin(Xkn(4, k, n));
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| 142 | mA(3, 1) = - Ce * sin(Xkn(4, k, n));
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| 143 | mA(3, 2) = Ce * cos(Xkn(4, k, n));
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| 144 | mA(3, 4) = - Ce * (Xkn(2, k, n) * sin(Xkn(4, k, n)) + Xkn(1, k, n) * cos(Xkn(4, k, n)));
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| 145 | Pkn(:, :, k+1, n) = mA * (Pkn(:, :, k, n) - Pkn(:, :, k, n) * mC' * inv(mRy) * mC * Pkn(:, :, k, n)) * mA' + mQ;
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| 146 | end
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| 147 | end
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| 148 | Xstripe = mean(Xkn, 3);
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| 149 | Pstripe = mean(Pkn, 4);
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| 150 |
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| 151 | for k = K-1:-1:1,
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| 152 | gka = k;
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| 153 |
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| 154 | % 1]
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| 155 | for n = 1:N,
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| 156 | %krive okoli
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| 157 | Xkn(1, k, n) = Xstripe(1, k) + rhoi*randn();
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| 158 | Xkn(2, k, n) = Xstripe(2, k) + rhoi*randn();
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| 159 | Xkn(3, k, n) = Xstripe(3, k) + rhoo*randn();
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| 160 | Xkn(4, k, n) = Xstripe(4, k) + rhot*randn();
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| 161 |
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| 162 | Ykn(:, k, n) = round(Xkn(1:2, k, n) / deltaI) * deltaI;
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| 163 |
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| 164 | Pkn(:, :, k, n) = Pstripe(:, :, k) .* exp(rhop*randn(4));
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| 165 | end
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| 166 |
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| 167 | % 2]
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| 168 | for n = 1:N,
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| 169 | gnu = n;
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| 170 | % [Uopt2(:, n), Hmin(n)] = fmincon(@Hamilt, uPi(k, Xkn(:, k, n),Pkn(:, :, k, n)), [], [], [], [], [], [], @Cond2, optimset('GradConstr','on','Display','notify','Algorithm','active-set','TolFun',1e-20));
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| 171 | [Uopt2(:, n), Hmin(n)] = minimum(Xkn(:, k, n));
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| 172 | % Uopt2(1,n)=sin(2*pi/20*k);
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| 173 | % Z = zeros(101,101);
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| 174 | % ii = 0;
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| 175 | % jj = 0;
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| 176 | % for ii = -50:50,
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| 177 | % for jj = -50:50,
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| 178 | % Z(ii+51,jj+51) = Hamilt([ii,jj]);
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| 179 | % end
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| 180 | % end
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| 181 | % surf(Z);
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| 182 | end
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| 183 |
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| 184 | % 3]
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| 185 | for n = 1:N,
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| 186 | Vn(n) = DELTAt*Hmin(n)/mag + Vtilde(k+1, Xkn(:, k, n), Pkn(:, :, k, n));
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| 187 |
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| 188 | end
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| 189 |
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| 190 | % 4]
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| 191 | %urceni aproximace V Bellmanovy funkce
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| 192 | for n = 1:N,
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| 193 | Epsilon(1:4, n) = Xkn(1:4, k, n) - Xstripe(1:4, k);
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| 194 | tpdiag = diag(Pkn(:, :, k, n) ./ Pstripe(:, :, k));
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| 195 | Epsilon(5:6, n) = tpdiag(3:4);
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| 196 | end
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| 197 | mFi = matrixFi(Epsilon);
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| 198 | FiFiTInvFi = (mFi*mFi')\mFi;
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| 199 | Wv(:,k) = FiFiTInvFi * Vn';
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| 200 |
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| 201 | %urceni aproximace pi rizeni u
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| 202 | Kpi_alfa(k) = mean(Uopt2(1,:));
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| 203 | Kpi_beta(k) = mean(Uopt2(2,:));
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| 204 | % mPsi = ones(N,1);
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| 205 | % PsiPsiTInvPsi = (mPsi'*mPsi)\mPsi';
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| 206 | % Kpi_alfa(:, k) = PsiPsiTInvPsi * Uopt2(1,:)';
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| 207 | %
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| 208 | % mPsi = ones(N,1);
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| 209 | % PsiPsiTInvPsi = (mPsi'*mPsi)\mPsi';
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| 210 | % Kpi_beta(:, k) = PsiPsiTInvPsi * Uopt2(2,:)';
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| 211 | % mPsi = [sin(squeeze(Xkn(4, k, :))),...1
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| 212 | % cos(squeeze(Xkn(4, k, :))),...2
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| 213 | % (sin(squeeze(Xkn(4, k, :))).^2),...3
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| 214 | % (cos(squeeze(Xkn(4, k, :))).^2)];%4
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| 215 | % PsiPsiTInvPsi = (mPsi'*mPsi)\mPsi';
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| 216 | % Kpi_alfa(:, k) = PsiPsiTInvPsi * Uopt2(1,:)';
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| 217 | %
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| 218 | % mPsi = [sin(squeeze(Xkn(4, k, :))),...1
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| 219 | % cos(squeeze(Xkn(4, k, :))),...2
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| 220 | % (sin(squeeze(Xkn(4, k, :))).^2),...3
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| 221 | % (cos(squeeze(Xkn(4, k, :))).^2)];%4
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| 222 | % PsiPsiTInvPsi = (mPsi'*mPsi)\mPsi';
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| 223 | % Kpi_beta(:, k) = PsiPsiTInvPsi * Uopt2(2,:)';
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| 224 |
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| 225 | % tmpUfi = squeeze(Xkn(4, k, :) + DELTAt*Xkn(3, k, :));
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| 226 | % tmpUamp = sqrt(Uopt2(1,:).^2 + Uopt2(2,:).^2)';
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| 227 | % mPsi = [Cd*Cd*squeeze(Xkn(3, k, :)),...1
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| 228 | % Cd*Ce*squeeze(Xkn(2, k, :).*cos(Xkn(4, k, :))),...2
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| 229 | % - Cd*Ce*squeeze(Xkn(1, k, :).*sin(Xkn(4, k, :))),...3
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| 230 | % Ce*Ca*squeeze(Xkn(2, k, :)).*cos(tmpUfi),...4
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| 231 | % - Ce*Cb*squeeze(Xkn(3, k, :).*cos(Xkn(4, k, :))).*cos(tmpUfi),...5
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| 232 | % Ce*Ca*squeeze(Xkn(1, k, :)).*sin(tmpUfi),...6
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| 233 | % Ce*Cb*squeeze(Xkn(3, k, :).*sin(Xkn(4, k, :))).*sin(tmpUfi),...7
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| 234 | % Ce*Cc*squeeze( (cos(tmpUfi)).^2 - (sin(tmpUfi)).^2 ).*tmpUamp,...8
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| 235 | % tmpUamp];%9
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| 236 | % PsiPsiTInvPsi = (mPsi'*mPsi)\mPsi';
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| 237 | % Kpi(:, k) = PsiPsiTInvPsi * (omega_t_stripe*ones(N, 1));
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| 238 | end
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| 239 | end
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| 240 |
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| 241 | %%%%%%%%%%%
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| 242 | toc
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| 243 | % keyboard
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| 244 | Kpi
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| 245 | Kpi_alfa
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| 246 | Kpi_beta
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| 247 | %vykresleni grafu
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| 248 | clf
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| 249 | subplot(3,4,3);
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| 250 | plot(1:K,omega_t_stripe*ones(1,K));
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| 251 |
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| 252 | Ukn = zeros(2, K, N);
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| 253 | for n = 1:N,
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| 254 | Xkn(:, 1, n) = X0;
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| 255 | Ykn(:, 1, n) = Y0;
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| 256 | Pkn(:, :, 1, n) = P0;
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| 257 | for k = 1:K-1,
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| 258 | Ukn(:, k, n) = uPi(k, Xkn(:, k, n), Pkn(:, :, k, n));
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| 259 | mRy = mC * Pkn(:, :, k, n) * mC' + mR;
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| 260 | mKy = Pkn(:, :, k, n) * mC' / mRy;
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| 261 | Xkn(:, k+1, n) = fceG(Xkn(:, k, n), Ukn(:, k, n)) - mKy * (Ykn(:, k, n) - fceH(Xkn(:, k, n))) + noise * sqrtm(mQ) * randn(4, 1);%+gauss sum s rozptylem odmocnina mQ
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| 262 | Ykn(:, k+1, n) = round(Xkn(1:2, k+1, n) / deltaI) * deltaI; %X kopie do Y se vzorkovanim 0.085
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| 263 | mA(1, 3) = Cb * sin(Xkn(4, k, n));
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| 264 | mA(1, 4) = Cb * Xkn(3, k, n) * cos(Xkn(4, k, n));
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| 265 | mA(2, 3) = - Cb * cos(Xkn(4, k, n));
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| 266 | mA(2, 4) = Cb * Xkn(3, k, n) * sin(Xkn(4, k, n));
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| 267 | mA(3, 1) = - Ce * sin(Xkn(4, k, n));
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| 268 | mA(3, 2) = Ce * cos(Xkn(4, k, n));
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| 269 | mA(3, 4) = - Ce * (Xkn(2, k, n) * sin(Xkn(4, k, n)) + Xkn(1, k, n) * cos(Xkn(4, k, n)));
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| 270 | Pkn(:, :, k+1, n) = mA * (Pkn(:, :, k, n) - Pkn(:, :, k, n) * mC' * inv(mRy) * mC * Pkn(:, :, k, n)) * mA' + mQ;
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| 271 | end
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| 272 |
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| 273 | hold all
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| 274 | subplot(3,4,1);
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| 275 | title('X:i_{\alpha}')
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| 276 | plot(1:K,Xkn(1,:,n))
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| 277 |
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| 278 | hold all
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| 279 | subplot(3,4,2);
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| 280 | title('X:i_{\beta}')
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| 281 | plot(1:K,Xkn(2,:,n))
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| 282 |
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| 283 | hold all
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| 284 | subplot(3,4,3);
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| 285 | title('X:\omega')
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| 286 | plot(1:K,Xkn(3,:,n))
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| 287 |
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| 288 | hold all
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| 289 | subplot(3,4,4);
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| 290 | title('X:\theta')
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| 291 | plot(1:K,Xkn(4,:,n))
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| 292 |
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| 293 | hold all
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| 294 | subplot(3,4,5);
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| 295 | title('Y:i_{\alpha}')
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| 296 | plot(1:K,Ykn(1,:,n))
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| 297 |
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| 298 | hold all
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| 299 | subplot(3,4,6);
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| 300 | title('Y:i_{\beta}')
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| 301 | plot(1:K,Ykn(2,:,n))
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| 302 |
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| 303 | hold all
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| 304 | subplot(3,4,7);
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| 305 | title('u_{\alpha}')
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| 306 | plot(1:K,Ukn(1,:,n))
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| 307 |
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| 308 | hold all
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| 309 | subplot(3,4,8);
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| 310 | title('u_{\beta}')
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| 311 | plot(1:K,Ukn(2,:,n))
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| 312 |
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| 313 | hold all
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| 314 | subplot(3,4,9);
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| 315 | title('P(1, 1)')
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| 316 | plot(1:K,squeeze(Pkn(1, 1, :, n)))
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| 317 |
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| 318 | hold all
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| 319 | subplot(3,4,10);
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| 320 | title('P(2, 2)')
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| 321 | plot(1:K,squeeze(Pkn(2, 2, :, n)))
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| 322 |
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| 323 | hold all
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| 324 | subplot(3,4,11);
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| 325 | title('P(3, 3)')
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| 326 | plot(1:K,squeeze(Pkn(3, 3, :, n)))
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| 327 |
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| 328 | hold all
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| 329 | subplot(3,4,12);
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| 330 | title('P(4, 4)')
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|---|
| 331 | plot(1:K,squeeze(Pkn(4, 4, :, n)))
|
|---|
| 332 | end
|
|---|
| 333 |
|
|---|
| 334 | figure
|
|---|
| 335 |
|
|---|
| 336 | for n = 1:N,
|
|---|
| 337 | Xkn(:, 1, n) = X0;
|
|---|
| 338 | for k = 1:K-1,
|
|---|
| 339 | Ukn(:, k, n) = uPi(k, Xkn(:, k, n), zeros(4));
|
|---|
| 340 | Xkn(:, k+1, n) = fceG(Xkn(:, k, n), Ukn(:, k, n)) + noise * sqrtm(mQ) * randn(4, 1);
|
|---|
| 341 | end
|
|---|
| 342 |
|
|---|
| 343 | hold all
|
|---|
| 344 | subplot(2,3,1);
|
|---|
| 345 | title('X:i_{\alpha}')
|
|---|
| 346 | plot(1:K,Xkn(1,:,n))
|
|---|
| 347 |
|
|---|
| 348 | hold all
|
|---|
| 349 | subplot(2,3,2);
|
|---|
| 350 | title('X:i_{\beta}')
|
|---|
| 351 | plot(1:K,Xkn(2,:,n))
|
|---|
| 352 |
|
|---|
| 353 | hold all
|
|---|
| 354 | subplot(2,3,3);
|
|---|
| 355 | title('X:\omega')
|
|---|
| 356 | plot(1:K,Xkn(3,:,n))
|
|---|
| 357 |
|
|---|
| 358 | hold all
|
|---|
| 359 | subplot(2,3,4);
|
|---|
| 360 | title('X:\theta')
|
|---|
| 361 | plot(1:K,Xkn(4,:,n))
|
|---|
| 362 |
|
|---|
| 363 | hold all
|
|---|
| 364 | subplot(2,3,5);
|
|---|
| 365 | title('u_{\alpha}')
|
|---|
| 366 | plot(1:K,Ukn(1,:,n))
|
|---|
| 367 |
|
|---|
| 368 | hold all
|
|---|
| 369 | subplot(2,3,6);
|
|---|
| 370 | title('u_{\beta}')
|
|---|
| 371 | plot(1:K,Ukn(2,:,n))
|
|---|
| 372 |
|
|---|
| 373 | end
|
|---|
| 374 |
|
|---|
| 375 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|---|
| 376 | %pomocne funkce
|
|---|
| 377 |
|
|---|
| 378 | function [val_uPi] = uPi(k_uPi, x_uPi, p_uPi)
|
|---|
| 379 | val_uPi = zeros(2, 1);
|
|---|
| 380 | val_uPi(1) = Kpi_alfa(k_uPi);
|
|---|
| 381 | val_uPi(2) = Kpi_beta(k_uPi);
|
|---|
| 382 | % val_uPi(1) = Kpi_alfa(1, k_uPi)*sin(x_uPi(4)) + Kpi_alfa(2, k_uPi)*cos(x_uPi(4)) + Kpi_alfa(3, k_uPi)*(sin(x_uPi(4)))^2 + Kpi_alfa(4, k_uPi)*(cos(x_uPi(4)))^2;
|
|---|
| 383 | % val_uPi(2) = Kpi_beta(1, k_uPi)*sin(x_uPi(4)) + Kpi_beta(2, k_uPi)*cos(x_uPi(4)) + Kpi_beta(3, k_uPi)*(sin(x_uPi(4)))^2 + Kpi_beta(4, k_uPi)*(cos(x_uPi(4)))^2;
|
|---|
| 384 | % tmpfi = x_uPi(4) + DELTAt*x_uPi(3);
|
|---|
| 385 | % tmpw = ( omega_t_stripe - Cd*(Kpi(1, k_uPi)*Cd*x_uPi(3) + Kpi(2, k_uPi)*Ce*x_uPi(2)*cos(x_uPi(4)) - Kpi(3, k_uPi)*Ce*x_uPi(1)*sin(x_uPi(4)))...
|
|---|
| 386 | % - Ce*( (Kpi(4, k_uPi)*Ca*x_uPi(2) - Kpi(5, k_uPi)*Cb*x_uPi(3)*cos(x_uPi(4)))*cos(tmpfi)...
|
|---|
| 387 | % -(Kpi(6, k_uPi)*Ca*x_uPi(1) + Kpi(7, k_uPi)*Cb*x_uPi(3)*sin(x_uPi(4)))*sin(tmpfi) ) ) /...
|
|---|
| 388 | % (Kpi(8, k_uPi)*Ce*Cc*( (cos(tmpfi))^2 - (sin(tmpfi))^2 ) + Kpi(9, k_uPi));
|
|---|
| 389 | %
|
|---|
| 390 | % if(tmpw > cC1)
|
|---|
| 391 | % tmpw = cC1;
|
|---|
| 392 | % elseif(tmpw < - cC1)
|
|---|
| 393 | % tmpw = -cC1;
|
|---|
| 394 | % end
|
|---|
| 395 | % val_uPi(1) = tmpw*sin(tmpfi);
|
|---|
| 396 | % val_uPi(2) = tmpw*cos(tmpfi);
|
|---|
| 397 | end
|
|---|
| 398 |
|
|---|
| 399 | function [val_ham] = Hamilt(u_ham)
|
|---|
| 400 | mRy = mC * Pkn(:, :, gka, gnu) * mC' + mR;
|
|---|
| 401 | mKy = Pkn(:, :, gka, gnu) * mC' / mRy;
|
|---|
| 402 | tXkn = fceG(Xkn(:, gka, gnu), u_ham) - mKy * (Ykn(:, gka, gnu) - fceH(Xkn(:, gka, gnu)));
|
|---|
| 403 | mA(1, 3) = Cb * sin(Xkn(4, gka, gnu));
|
|---|
| 404 | mA(1, 4) = Cb * Xkn(3, gka, gnu) * cos(Xkn(4, gka, gnu));
|
|---|
| 405 | mA(2, 3) = - Cb * cos(Xkn(4, gka, gnu));
|
|---|
| 406 | mA(2, 4) = Cb * Xkn(3, gka, gnu) * sin(Xkn(4, gka, gnu));
|
|---|
| 407 | mA(3, 1) = - Ce * sin(Xkn(4, gka, gnu));
|
|---|
| 408 | mA(3, 2) = Ce * cos(Xkn(4, gka, gnu));
|
|---|
| 409 | mA(3, 4) = - Ce * (Xkn(2, gka, gnu) * sin(Xkn(4, gka, gnu)) + Xkn(1, gka, gnu) * cos(Xkn(4, gka, gnu)));
|
|---|
| 410 | tPkn = mA * (Pkn(:, :, gka, gnu) - Pkn(:, :, gka, gnu) * mC' * inv(mRy) * mC * Pkn(:, :, gka, gnu)) * mA' + mQ;
|
|---|
| 411 | tf = zeros(4,1);
|
|---|
| 412 | tf(1:2) = tXkn(3:4);
|
|---|
| 413 | tfpdiag = diag(tPkn);
|
|---|
| 414 | tf(3:4) = tfpdiag(3:4);
|
|---|
| 415 |
|
|---|
| 416 | % loss = (tXkn(3) - omega_t_stripe)^2;
|
|---|
| 417 | % loss = (Cd * Xkn(3, gka, gnu) + Ce * ((Ca * Xkn(2, gka, gnu) - Cb * Xkn(3, gka, gnu) * cos(Xkn(4, gka, gnu)) + Cc * u_ham(2)) * cos(Xkn(4, gka, gnu)) - (Ca * Xkn(1, gka, gnu) + Cb * Xkn(3, gka, gnu) * sin(Xkn(4, gka, gnu)) + Cc * u_ham(1)) * sin(Xkn(4, gka, gnu))) - omega_t_stripe)^2;
|
|---|
| 418 | % if(gka == 1)
|
|---|
| 419 | % loss = (tXkn(3) - omega_t_stripe)^2;
|
|---|
| 420 | % else
|
|---|
| 421 | % loss = (Cd * Xkn(3, gka, gnu) + Ce * ((Ca * Xkn(2, gka-1, gnu) - Cb * Xkn(3, gka-1, gnu) * cos(Xkn(4, gka-1, gnu)) + Cc * u_ham(2)) * cos(Xkn(4, gka, gnu)) - (Ca * Xkn(1, gka-1, gnu) + Cb * Xkn(3, gka-1, gnu) * sin(Xkn(4, gka-1, gnu)) + Cc * u_ham(1)) * sin(Xkn(4, gka, gnu))) - omega_t_stripe)^2;
|
|---|
| 422 | % end
|
|---|
| 423 | % loss = (Cd * tXkn(3) + Ce * ((Ca * Xkn(2, gka, gnu) - Cb * Xkn(3, gka, gnu) * cos(Xkn(4, gka, gnu)) + Cc * u_ham(2)) * cos(tXkn(4)) - (Ca * Xkn(1, gka, gnu) + Cb * Xkn(3, gka, gnu) * sin(Xkn(4, gka, gnu)) + Cc * u_ham(1)) * sin(tXkn(4))) - omega_t_stripe)^2;
|
|---|
| 424 |
|
|---|
| 425 |
|
|---|
| 426 | % loss = loss + cPenPsi*(u_ham(1)^2 + u_ham(2)^2);
|
|---|
| 427 | loss = ( Cd*(Cd*Xkn(3, gka, gnu)...
|
|---|
| 428 | + Ce*Xkn(2, gka, gnu)*cos(Xkn(4, gka, gnu))...
|
|---|
| 429 | - Ce*Xkn(1, gka, gnu)*sin(Xkn(4, gka, gnu)))...
|
|---|
| 430 | + Ce*( (Ca*Xkn(2, gka, gnu) - Cb*Xkn(3, gka, gnu)*cos(Xkn(4, gka, gnu)) )*cos(Xkn(4, gka, gnu)+DELTAt*Xkn(3, gka, gnu))...
|
|---|
| 431 | -(Ca*Xkn(1, gka, gnu) + Cb*Xkn(3, gka, gnu)*sin(Xkn(4, gka, gnu)) )*sin(Xkn(4, gka, gnu)+DELTAt*Xkn(3, gka, gnu)))...
|
|---|
| 432 | + Ce*Cc*u_ham(2)*cos(Xkn(4, gka, gnu)+DELTAt*Xkn(3, gka, gnu))...
|
|---|
| 433 | - Ce*Cc*u_ham(1)*sin(Xkn(4, gka, gnu)+DELTAt*Xkn(3, gka, gnu))...
|
|---|
| 434 | - omega_t_stripe )^2;
|
|---|
| 435 |
|
|---|
| 436 | val_ham = mag*(loss + tf' * Vtilde_dx(gka+1, Xkn(:, gka, gnu), Pkn(:, :, gka, gnu)) + 1/2 * trace(mQ * Vtilde_dx_dx(gka+1, Xkn(:, gka, gnu), Pkn(:, :, gka, gnu))));
|
|---|
| 437 |
|
|---|
| 438 | end
|
|---|
| 439 |
|
|---|
| 440 | function [val_Vt] = Vtilde(k_Vt, x_Vt, p_Vt)
|
|---|
| 441 | if(k_Vt == K)
|
|---|
| 442 | val_Vt = h_bel;
|
|---|
| 443 | else
|
|---|
| 444 | Epsl = zeros(6, 1);
|
|---|
| 445 | Epsl(1:4) = x_Vt(1:4) - Xstripe(1:4, k_Vt);
|
|---|
| 446 | tpdiag = diag(p_Vt ./ Pstripe(:, :, k));
|
|---|
| 447 | Epsl(5:6) = tpdiag(3:4);
|
|---|
| 448 |
|
|---|
| 449 | val_Vt = vectFi(Epsl)' * Wv(:,k_Vt);
|
|---|
| 450 | end
|
|---|
| 451 | end
|
|---|
| 452 |
|
|---|
| 453 | function [val_Vt] = Vtilde_dx(k_Vt, x_Vt, p_Vt)
|
|---|
| 454 | if(k_Vt == K)
|
|---|
| 455 | val_Vt = h_beldx;
|
|---|
| 456 | else
|
|---|
| 457 | Epsl = zeros(6, 1);
|
|---|
| 458 | Epsl(1:4) = x_Vt(1:4) - Xstripe(1:4, k_Vt);
|
|---|
| 459 | tpdiag = diag(p_Vt ./ Pstripe(:, :, k));
|
|---|
| 460 | Epsl(5:6) = tpdiag(3:4);
|
|---|
| 461 |
|
|---|
| 462 | val_Vt = difFi(Epsl)' * Wv(:,k_Vt);
|
|---|
| 463 | end
|
|---|
| 464 | end
|
|---|
| 465 |
|
|---|
| 466 | function [val_Fi] = vectFi(x_Fi)
|
|---|
| 467 | val_Fi = [ ...
|
|---|
| 468 | 1; ... %1
|
|---|
| 469 | x_Fi(3); ...
|
|---|
| 470 | % x_Fi(4); ...
|
|---|
| 471 | log(x_Fi(5)); ... %ln Xi pro 5-8 tj diagonala matice Pt 4x4
|
|---|
| 472 | % log(x_Fi(6)); ...
|
|---|
| 473 | x_Fi(3)^2; ...
|
|---|
| 474 | % x_Fi(3)*x_Fi(4); ...
|
|---|
| 475 | x_Fi(3)*log(x_Fi(5)); ...
|
|---|
| 476 | % x_Fi(3)*log(x_Fi(6)); ...
|
|---|
| 477 | % x_Fi(4)^2; ...
|
|---|
| 478 | % x_Fi(4)*log(x_Fi(5)); ...
|
|---|
| 479 | % x_Fi(4)*log(x_Fi(6)); ...
|
|---|
| 480 | log(x_Fi(5))^2;...
|
|---|
| 481 | % log(x_Fi(5))*log(x_Fi(6));...
|
|---|
| 482 | % log(x_Fi(6))^2
|
|---|
| 483 | ];
|
|---|
| 484 | end
|
|---|
| 485 |
|
|---|
| 486 | function [val_Fi] = matrixFi(x_Fi)
|
|---|
| 487 | val_Fi = [ ...
|
|---|
| 488 | ones(1, N); ... %1
|
|---|
| 489 | x_Fi(3, :); ...
|
|---|
| 490 | % x_Fi(4, :); ...
|
|---|
| 491 | log(x_Fi(5, :)); ... %ln Xi pro 5-8 tj diagonala matice Pt 4x4
|
|---|
| 492 | % log(x_Fi(6, :)); ...
|
|---|
| 493 | x_Fi(3, :).^2; ...
|
|---|
| 494 | % x_Fi(3, :).*x_Fi(4, :); ...
|
|---|
| 495 | x_Fi(3, :).*log(x_Fi(5, :)); ...
|
|---|
| 496 | % x_Fi(3, :).*log(x_Fi(6, :)); ...
|
|---|
| 497 | % x_Fi(4, :).^2; ...
|
|---|
| 498 | % x_Fi(4, :).*log(x_Fi(5, :)); ...
|
|---|
| 499 | % x_Fi(4, :).*log(x_Fi(6, :)); ...
|
|---|
| 500 | log(x_Fi(5, :)).^2;...
|
|---|
| 501 | % log(x_Fi(5, :)).*log(x_Fi(6, :));...
|
|---|
| 502 | % log(x_Fi(6, :)).^2
|
|---|
| 503 | ];
|
|---|
| 504 |
|
|---|
| 505 | end
|
|---|
| 506 |
|
|---|
| 507 | function [val_Fi] = difFi(x_Fi)
|
|---|
| 508 | val_Fi = [ ...
|
|---|
| 509 | 0 0 0 0; ... %1
|
|---|
| 510 | 1 0 0 0; ... %2
|
|---|
| 511 | % 0 1 0 0; ...%3
|
|---|
| 512 | 0 0 1/(x_Fi(5)) 0; ... %4 %ln Xi pro 5-8 tj diagonala matice Pt 4x4
|
|---|
| 513 | % 0 0 0 1/(x_Fi(6)); ... %5
|
|---|
| 514 | 2*x_Fi(3) 0 0 0; ...%6
|
|---|
| 515 | % x_Fi(4) x_Fi(3) 0 0; ...%7
|
|---|
| 516 | log(x_Fi(5)) 0 x_Fi(3)/(x_Fi(5)) 0; ...%8
|
|---|
| 517 | % log(x_Fi(6)) 0 0 x_Fi(3)/(x_Fi(6)); ... %9
|
|---|
| 518 | % 0 2*x_Fi(4) 0 0; ...%10
|
|---|
| 519 | % 0 log(x_Fi(5)) x_Fi(4)/(x_Fi(5)) 0; ...%11
|
|---|
| 520 | % 0 log(x_Fi(6)) 0 x_Fi(4)/(x_Fi(6)); ... %12
|
|---|
| 521 | 0 0 2*log(x_Fi(5))/(x_Fi(5)) 0;...%13
|
|---|
| 522 | % 0 0 log(x_Fi(6))/(x_Fi(5)) log(x_Fi(5))/(x_Fi(6));...%14
|
|---|
| 523 | % 0 0 0 2*log(x_Fi(6))/(x_Fi(6))
|
|---|
| 524 | ];%15
|
|---|
| 525 | end
|
|---|
| 526 |
|
|---|
| 527 | function [valvt] = Vtilde_dx_dx(kin, x_Vt, p_Vt)
|
|---|
| 528 | if(kin == K)
|
|---|
| 529 | valvt = h_beldxdx;
|
|---|
| 530 | else
|
|---|
| 531 | % valvt = Wv(4, kin)*diag([0 0 -1/(p_Vt(3,3)^2) 0]) +...
|
|---|
| 532 | % Wv(5, kin)*diag([0 0 0 -1/(p_Vt(4,4)^2)]) +...
|
|---|
| 533 | % Wv(6, kin)*diag([2 0 0 0]) +...
|
|---|
| 534 | % Wv(7, kin)*[0 1 0 0; 1 0 0 0; 0 0 0 0; 0 0 0 0] +...
|
|---|
| 535 | % Wv(8, kin)*[0 0 1/p_Vt(3,3) 0; 0 0 0 0; 1/p_Vt(3,3) 0 -x_Vt(3)/(p_Vt(3,3)^2) 0; 0 0 0 0] +...
|
|---|
| 536 | % Wv(9, kin)*[0 0 1/p_Vt(4,4) 0; 0 0 0 0; 0 0 0 0; 1/p_Vt(4,4) 0 0 -x_Vt(3)/(p_Vt(4,4)^2)] +...
|
|---|
| 537 | % Wv(10, kin)*diag([0 2 0 0]) +...
|
|---|
| 538 | % Wv(11, kin)*[0 0 0 0; 0 0 1/p_Vt(3,3) 0; 0 1/p_Vt(3,3) -x_Vt(4)/(p_Vt(3,3)^2) 0; 0 0 0 0] +...
|
|---|
| 539 | % Wv(12, kin)*[0 0 0 0; 0 0 0 1/p_Vt(4,4); 0 0 0 0; 0 1/p_Vt(4,4) 0 -x_Vt(4)/(p_Vt(4,4)^2)] +...
|
|---|
| 540 | % Wv(13, kin)*[0 0 0 0; 0 0 0 0; 0 0 2*(1-log(p_Vt(3,3)))/(p_Vt(3,3)^2) 0; 0 0 0 0] +...
|
|---|
| 541 | % Wv(14, kin)*[0 0 0 0; 0 0 0 0; 0 0 -log(p_Vt(4,4))/(p_Vt(3,3)^2) 1/(p_Vt(4,4))/(p_Vt(3,3)); 0 0 1/(p_Vt(4,4))/(p_Vt(3,3)) -log(p_Vt(3,3))/(p_Vt(4,4)^2)] +...
|
|---|
| 542 | % Wv(15, kin)*[0 0 0 0; 0 0 0 0; 0 0 0 0; 0 0 0 2*(1-log(p_Vt(4,4)))/(p_Vt(4,4)^2)];
|
|---|
| 543 | valvt = Wv(3, kin)*diag([0 0 0 -1/(p_Vt(3,3)^2)]) +...%
|
|---|
| 544 | Wv(4, kin)*diag([2 0 0 0]) +...
|
|---|
| 545 | Wv(5, kin)*[0 0 1/p_Vt(3,3) 0; 0 0 0 0; 1/p_Vt(3,3) 0 -x_Vt(3)/(p_Vt(3,3)^2) 0; 0 0 0 0] +...
|
|---|
| 546 | Wv(6, kin)*[0 0 0 0; 0 0 0 0; 0 0 2*(1-log(p_Vt(3,3)))/(p_Vt(3,3)^2) 0; 0 0 0 0];
|
|---|
| 547 | end
|
|---|
| 548 | end
|
|---|
| 549 |
|
|---|
| 550 | function [c, ceq, GC, GCeq] = Cond2(x)
|
|---|
| 551 | c = x(1)*x(1) + x(2)*x(2) - cC1^2;
|
|---|
| 552 | ceq = [];
|
|---|
| 553 | GC = [2*x(1); 2*x(2)];
|
|---|
| 554 | GCeq = [];
|
|---|
| 555 | end
|
|---|
| 556 |
|
|---|
| 557 | function [x_ret] = fceG(x_in, u_in)
|
|---|
| 558 | x_ret = zeros(4, 1);
|
|---|
| 559 | x_ret(1) = Ca * x_in(1) + Cb * x_in(3) * sin(x_in(4)) + Cc * u_in(1);
|
|---|
| 560 | x_ret(2) = Ca * x_in(2) - Cb * x_in(3) * cos(x_in(4)) + Cc * u_in(2);
|
|---|
| 561 | x_ret(3) = Cd * x_in(3) + Ce * (x_in(2) * cos(x_in(4)) - x_in(1) * sin(x_in(4)));
|
|---|
| 562 | x_ret(4) = x_in(4) + x_in(3) * DELTAt;
|
|---|
| 563 | end
|
|---|
| 564 |
|
|---|
| 565 | function [y_ret] = fceH(x_in)
|
|---|
| 566 | y_ret = zeros(2, 1);
|
|---|
| 567 | y_ret(1) = x_in(1);
|
|---|
| 568 | y_ret(2) = x_in(2);
|
|---|
| 569 | end
|
|---|
| 570 |
|
|---|
| 571 | function [Uopt_ret, Hmin_ret] = minimum(xin)
|
|---|
| 572 | w = (Cd*(Cd*xin(3) + Ce*(xin(2)*cos(xin(4) - xin(1)*sin(xin(4))))) - omega_t_stripe +...
|
|---|
| 573 | Ce*((Ca*xin(2)-Cb*xin(3)*cos(xin(4)))*cos(xin(4)+DELTAt*xin(3))-(Ca*xin(1)+Cb*xin(3)*sin(xin(4)))*sin(xin(4)+DELTAt*xin(3)))) / ...
|
|---|
| 574 | (Ce*Cc*(sin(xin(4)*sin(xin(4)+DELTAt*xin(3))) - cos(xin(4)*cos(xin(4)+DELTAt*xin(3)))));
|
|---|
| 575 | if(w > cC1)
|
|---|
| 576 | w = cC1;
|
|---|
| 577 | elseif(w < - cC1)
|
|---|
| 578 | w = -cC1;
|
|---|
| 579 | end
|
|---|
| 580 | Uopt_ret(1) = w*sin(xin(4));
|
|---|
| 581 | Uopt_ret(2) = w*cos(xin(4));
|
|---|
| 582 | Hmin_ret = Hamilt(Uopt_ret);
|
|---|
| 583 | end
|
|---|
| 584 |
|
|---|
| 585 | end
|
|---|
