| 1 | function pmsm_ildp2
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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 = 2; %iterace
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| 10 | K = 20; %casy
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| 11 | N = 50; %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*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 | %matice
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| 35 | %kovariancni matice Q a R
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| 36 | mQ = diag([0.0013 0.0013 5.0e-6 1.0e-10]);
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| 37 | mR = diag([0.0006 0.0006]);
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| 38 |
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| 39 | mSigma = mR*mR';
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| 40 |
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| 41 | %matice pro vypocet
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| 42 | %matice A zavisla na parametrech
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| 43 | mA = zeros(4);
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| 44 | mA(1,1) = Ca;
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| 45 | mA(2,2) = Ca;
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| 46 | mA(3,3) = Cd;
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| 47 | mA(4,4) = 1;
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| 48 | mA(4,3) = DELTAt;
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| 49 |
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| 50 | %macite C konstantni
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| 51 | mC = [ 1 0 0 0; 0 1 0 0];
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| 52 |
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| 53 | %pozadovana hodnota otacek
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| 54 | omega_t_stripe = 1.0015;
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| 55 |
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| 56 | %pocatecni hodnoty
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| 57 | X0 = [0; 0; 1; pi/2];
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| 58 | Y0 = [0; 0];
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| 59 | P0 = diag([0.01 0.01 0.01 0.01]);
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| 60 |
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| 61 | h_bel = 0;
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| 62 | h_beldx = [0; 0; 0; 0; 0; 0; 0; 0];
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| 63 |
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| 64 | %velikost okoli pro lokalni metodu
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| 65 | rho = 0.01;
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| 66 |
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| 67 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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| 68 | %globalni promenne
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| 69 |
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| 70 | % Kpi_alfa = ones(12, K); %konstanty aproximace slozky rizeni u_alfa
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| 71 | Kpi_alfa = ones(11, K); %konstanty aproximace slozky rizeni u_alfa
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| 72 | Kpi_alfa(1, :) = (Cd - Cb*Ce)*ones(1, K);
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| 73 | Kpi_alfa(2, :) = Ca*Ce*ones(1, K);
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| 74 | Kpi_alfa(3, :) = Ca*Ce*ones(1, K);
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| 75 | Kpi_alfa(4, :) = Cc*Ce*ones(1, K);
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| 76 | % Kpi_alfa(5, :) = zeros(1, K);
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| 77 | % Kpi_beta = ones(12, K); %konstanty aproximace slozky rizeni u_beta
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| 78 | Kpi_beta = ones(11, K); %konstanty aproximace slozky rizeni u_beta
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| 79 | Kpi_beta(1, :) = (Cd - Cb*Ce)*ones(1, K);
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| 80 | Kpi_beta(2, :) = Ca*Ce*ones(1, K);
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| 81 | Kpi_beta(3, :) = Ca*Ce*ones(1, K);
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| 82 | Kpi_beta(4, :) = Cc*Ce*ones(1, K);
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| 83 | % Kpi_beta(5, :) = zeros(1, K);
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| 84 |
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| 85 | Wv = zeros(35, K); %konstanty aproximace Bellmanovy fce
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| 86 |
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| 87 | Xkn = zeros(4, K, N); % X = [i_alfa, i_beta, omega, theta]
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| 88 | Ykn = zeros(2, K, N); % Y = [i_alfa, i_beta]
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| 89 | Pkn = zeros(4, 4, K, N); % P = N vzorku posloupnosti K matic 4x4
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| 90 |
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| 91 | mKy = zeros(4, 2); % K = pomocna matice pro vypocet
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| 92 | mRy = zeros(2, 2); % R = pomocna matice pro vypocet
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| 93 |
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| 94 | Xstripe = zeros(4, K);
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| 95 | Ystripe = zeros(4, K);
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| 96 | Pstripe = zeros(4, 4, K);
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| 97 |
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| 98 | Epsilon = zeros(20, N); %globalni promena pro vypocet Bellmanovy fce z odchylek (X - Xprum)
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| 99 |
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| 100 | gka = 0; %globalni promenna pro prenos casu k
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| 101 | gnu = 0; %globalni promenna pro prenos vzorku n
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| 102 |
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| 103 | Uopt2 = zeros(2, N);
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| 104 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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| 105 | %hlavni iteracni smycka
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| 106 | for i = 1:Iterace,
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| 107 |
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| 108 | %generovani stavu
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| 109 | for n = 1:N,
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| 110 | Xkn(:, 1, n) = X0;
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| 111 | Ykn(:, 1, n) = Y0 + mR * [randn(); randn()];
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| 112 | Pkn(:, :, 1, n) = P0;
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| 113 |
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| 114 | for k = 1:K-1,
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| 115 | Uk = uPi(k, Xkn(:, k, n), Pkn(:, :, k, n));
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| 116 |
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| 117 | mRy = mC * Pkn(:, :, k, n) * mC' + mR;
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| 118 | mKy = Pkn(:, :, k, n) * mC' / mRy;
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| 119 | Xkn(:, k+1, n) = fceG(Xkn(:, k, n), Uk) - mKy * (Ykn(:, k, n) - fceH(Xkn(:, k, n)));
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| 120 | Ykn(:, k+1, n) = Xkn(1:2, k+1, n) + mR * [randn(); randn()]; %X kopie do Y + sum
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| 121 | mA(1, 3) = Cb * sin(Xkn(4, k, n));
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| 122 | mA(1, 4) = Cb * Xkn(3, k, n) * cos(Xkn(4, k, n));
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| 123 | mA(2, 3) = - Cb * cos(Xkn(4, k, n));
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| 124 | mA(2, 4) = Cb * Xkn(3, k, n) * sin(Xkn(4, k, n));
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| 125 | mA(3, 1) = - Ce * sin(Xkn(4, k, n));
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| 126 | mA(3, 2) = Ce * cos(Xkn(4, k, n));
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| 127 | 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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| 128 | Pkn(:, :, k+1, n) = mA * (Pkn(:, :, k, n) - Pkn(:, :, k, n) * mC' * inv(mRy) * mC * Pkn(:, :, k, n)) * mA + mQ;
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| 129 | end
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| 130 | end
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| 131 | Xstripe = mean(Xkn, 3);
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| 132 | Ystripe = mean(Ykn, 3);
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| 133 | Pstripe = mean(Pkn, 4);
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| 134 |
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| 135 | for k = K-1:-1:1,
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| 136 | gka = k;
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| 137 |
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| 138 | % 1]
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| 139 | for n = 1:N,
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| 140 | %krive okoli
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| 141 | Ykn(1, k, n) = Ykn(1, k, n) - Xkn(1, k, n);
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| 142 | Ykn(2, k, n) = Ykn(2, k, n) - Xkn(2, k, n);
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| 143 |
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| 144 | Xkn(1, k, n) = Xstripe(1, k) + rho*randn();
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| 145 | Xkn(2, k, n) = Xstripe(2, k) + rho*randn();
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| 146 | Xkn(3, k, n) = Xstripe(3, k) + rho*randn();
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| 147 | Xkn(4, k, n) = Xstripe(4, k) + rho*randn();
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| 148 |
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| 149 | Ykn(1, k, n) = Ykn(1, k, n) + Xkn(1, k, n);
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| 150 | Ykn(2, k, n) = Ykn(2, k, n) + Xkn(2, k, n);
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| 151 |
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| 152 | Pkn(:, :, k, n) = Pstripe(:, :, k) .* exp(rho*randn(4));
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| 153 | end
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| 154 |
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| 155 | % 2]
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| 156 | for n = 1:N,
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| 157 | gnu = n;
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| 158 | [Uopt2(:, n), Hmin(n)] = fmincon(@Hamilt, uPi(k, Xkn(:, k, n),Pkn(:, :, k, n)), [], [], [], [], cLb, cUb, @Cond2, optimset('GradConstr','on','Display','notify','Algorithm','active-set'));
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| 159 | end
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| 160 |
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| 161 | % 3]
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| 162 | for n = 1:N,
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| 163 | Vn(n) = DELTAt*Hmin(n) + Vtilde(k+1, Xkn(:, k, n), Pkn(:, :, k, n));
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| 164 | end
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| 165 |
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| 166 | % 4]
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| 167 | Epsilon = zeros(8, N);
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| 168 | for n = 1:N,
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| 169 | Epsilon(1:4, n) = Xkn(1:4, k, n) - Xstripe(1:4, k);
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| 170 | Epsilon(5:8, n) = diag(Pkn(:, :, k, n) ./ Pstripe(:, :, k));
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| 171 | end
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| 172 | mFi = matrixFi(Epsilon);
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| 173 | FiFiTInvFi = (mFi*mFi')\mFi;
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| 174 | Wv(:,k) = FiFiTInvFi * Vn';
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| 175 |
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| 176 | for n = 1:N,
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| 177 | tialfa(n) = Xkn(1, k, n);
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| 178 | tibeta(n) = Xkn(2, k, n);
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| 179 | tomega(n) = Xkn(3, k, n);
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| 180 | ttheta(n) = Xkn(4, k, n);
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| 181 | tp1(n) = Pkn(1, 1, k, n);
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| 182 | tp2(n) = Pkn(2, 2, k, n);
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| 183 | tp3(n) = Pkn(3, 3, k, n);
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| 184 | tp4(n) = Pkn(4, 4, k, n);
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| 185 | end
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| 186 | % mPsi = [tomega',...1
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| 187 | % -tialfa'.*sin(ttheta)',...2
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| 188 | % tibeta'.*cos(ttheta)',...3
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| 189 | % -Uopt2(1,:)'.*sin(ttheta)',...4
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| 190 | % ones(N,1),...5
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| 191 | % log(tp3)',...6
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| 192 | % -tialfa'.*log(tp4)',...7
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| 193 | % -log(tp1)'.*sin(ttheta)',...8
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| 194 | % tibeta'.*log(tp4)',...9
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| 195 | % log(tp2)'.*cos(ttheta)',...10
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| 196 | % -Uopt2(1,:)'.*log(tp4)',...11
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| 197 | % -Uopt2(1,:)'];%12
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| 198 | mPsi = [tomega',...1
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| 199 | -tialfa'.*sin(ttheta)',...2
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| 200 | tibeta'.*cos(ttheta)',...3
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| 201 | -Uopt2(1,:)'.*sin(ttheta)',...4
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| 202 | log(tp3)',...6
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| 203 | -tialfa'.*log(tp4)',...7
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| 204 | -log(tp1)'.*sin(ttheta)',...8
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| 205 | tibeta'.*log(tp4)',...9
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| 206 | log(tp2)'.*cos(ttheta)',...10
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| 207 | -Uopt2(1,:)'.*log(tp4)',...11
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| 208 | -Uopt2(1,:)'];%12
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| 209 | PsiPsiTInvPsi = (mPsi'*mPsi)\mPsi';
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| 210 | Kpi_alfa(:, k) = PsiPsiTInvPsi * (omega_t_stripe * ones(N, 1));
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| 211 |
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| 212 | % mPsi = [tomega',...1
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| 213 | % -tialfa'.*sin(ttheta)',...2
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| 214 | % tibeta'.*cos(ttheta)',...3
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| 215 | % Uopt2(2,:)'.*cos(ttheta)',...4
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| 216 | % ones(N,1),...5
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| 217 | % -log(tp3)',...6
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| 218 | % tialfa'.*log(tp4)',...7
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| 219 | % log(tp1)'.*sin(ttheta)',...8
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| 220 | % -tibeta'.*log(tp4)',...9
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| 221 | % -log(tp2)'.*cos(ttheta)',...10
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| 222 | % Uopt2(2,:)'.*log(tp4)',...11
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| 223 | % Uopt2(2,:)'];%12
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| 224 | mPsi = [tomega',...1
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| 225 | -tialfa'.*sin(ttheta)',...2
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| 226 | tibeta'.*cos(ttheta)',...3
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| 227 | Uopt2(2,:)'.*cos(ttheta)',...4
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| 228 | -log(tp3)',...6
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| 229 | tialfa'.*log(tp4)',...7
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| 230 | log(tp1)'.*sin(ttheta)',...8
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| 231 | -tibeta'.*log(tp4)',...9
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| 232 | -log(tp2)'.*cos(ttheta)',...10
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| 233 | Uopt2(2,:)'.*log(tp4)',...11
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| 234 | Uopt2(2,:)'];%12
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| 235 | PsiPsiTInvPsi = (mPsi'*mPsi)\mPsi';
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| 236 | Kpi_beta(:, k) = PsiPsiTInvPsi * (omega_t_stripe * ones(N, 1));
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| 237 | end
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| 238 | end
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| 239 |
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| 240 | %%%%%%%%%%%
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| 241 | toc
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| 242 | % keyboard
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| 243 | Kpi_alfa
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| 244 | Kpi_beta
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| 245 | %vykresleni grafu
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| 246 | clf
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| 247 | subplot(3,4,3);
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| 248 | plot(1:K,omega_t_stripe*ones(1,K));
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| 249 |
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| 250 | Ukn = zeros(2, K, N);
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| 251 | for n = 1:N,
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| 252 | Xkn(:, 1, n) = X0;
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| 253 | Ykn(:, 1, n) = Y0 + mR * [randn(); randn()];
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| 254 | Pkn(:, :, 1, n) = P0;
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| 255 | for k = 1:K-1,
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| 256 | Ukn(:, k, n) = uPi(k, Xkn(:, k, n), Pkn(:, :, k, n));
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| 257 | mRy = mC * Pkn(:, :, k, n) * mC' + mR;
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| 258 | mKy = Pkn(:, :, k, n) * mC' / mRy;
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| 259 | Xkn(:, k+1, n) = fceG(Xkn(:, k, n), Ukn(:, k, n)) - mKy * (Ykn(:, k, n) - fceH(Xkn(:, k, n)));
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| 260 | Ykn(:, k+1, n) = Xkn(1:2, k+1, n) + mR * [randn(); randn()]; %X kopie do Y + sum
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| 261 | mA(1, 3) = Cb * sin(Xkn(4, k, n));
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| 262 | mA(1, 4) = Cb * Xkn(3, k, n) * cos(Xkn(4, k, n));
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| 263 | mA(2, 3) = - Cb * cos(Xkn(4, k, n));
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| 264 | mA(2, 4) = Cb * Xkn(3, k, n) * sin(Xkn(4, k, n));
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| 265 | mA(3, 1) = - Ce * sin(Xkn(4, k, n));
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| 266 | mA(3, 2) = Ce * cos(Xkn(4, k, n));
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| 267 | 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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| 268 | Pkn(:, :, k+1, n) = mA * (Pkn(:, :, k, n) - Pkn(:, :, k, n) * mC' * inv(mRy) * mC * Pkn(:, :, k, n)) * mA + mQ;
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| 269 | end
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| 270 |
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| 271 | hold all
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| 272 | subplot(3,4,1);
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| 273 | title('X:i_{\alpha}')
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| 274 | plot(1:K,Xkn(1,:,n))
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| 275 |
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| 276 | hold all
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| 277 | subplot(3,4,2);
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| 278 | title('X:i_{\beta}')
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| 279 | plot(1:K,Xkn(2,:,n))
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| 280 |
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| 281 | hold all
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| 282 | subplot(3,4,3);
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| 283 | title('X:\omega')
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| 284 | plot(1:K,Xkn(3,:,n))
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| 285 |
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| 286 | hold all
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| 287 | subplot(3,4,4);
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| 288 | title('X:\theta')
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| 289 | plot(1:K,Xkn(4,:,n))
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| 290 |
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| 291 | hold all
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| 292 | subplot(3,4,5);
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| 293 | title('Y:i_{\alpha}')
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| 294 | plot(1:K,Ykn(1,:,n))
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| 295 |
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| 296 | hold all
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| 297 | subplot(3,4,6);
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| 298 | title('Y:i_{\beta}')
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| 299 | plot(1:K,Ykn(2,:,n))
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| 300 |
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| 301 | hold all
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| 302 | subplot(3,4,7);
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| 303 | title('u_{\alpha}')
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| 304 | plot(1:K,Ukn(1,:,n))
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| 305 |
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| 306 | hold all
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| 307 | subplot(3,4,8);
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| 308 | title('u_{\beta}')
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| 309 | plot(1:K,Ukn(2,:,n))
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| 310 |
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| 311 | hold all
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| 312 | subplot(3,4,9);
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| 313 | title('P(1, 1)')
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| 314 | plot(1:K,squeeze(Pkn(1, 1, :, n)))
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| 315 |
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| 316 | hold all
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| 317 | subplot(3,4,10);
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| 318 | title('P(2, 2)')
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| 319 | plot(1:K,squeeze(Pkn(2, 2, :, n)))
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| 320 |
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| 321 | hold all
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| 322 | subplot(3,4,11);
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| 323 | title('P(3, 3)')
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| 324 | plot(1:K,squeeze(Pkn(3, 3, :, n)))
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| 325 |
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| 326 | hold all
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| 327 | subplot(3,4,12);
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| 328 | title('P(4, 4)')
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| 329 | plot(1:K,squeeze(Pkn(4, 4, :, n)))
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| 330 | end
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| 331 |
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| 332 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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| 333 | %pomocne funkce
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| 334 |
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| 335 | function [val_uPi] = uPi(k_uPi, x_uPi, p_uPi)
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| 336 | val_uPi = zeros(2, 1);
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| 337 | % val_uPi(1) = (-omega_t_stripe + Kpi_alfa(1, k_uPi)*x_uPi(3)+Kpi_alfa(6, k_uPi)*log(p_uPi(3,3)) - Kpi_alfa(2, k_uPi)*x_uPi(1)*sin(x_uPi(4))-Kpi_alfa(7, k_uPi)*x_uPi(1)*log(p_uPi(4,4))-Kpi_alfa(8, k_uPi)*log(p_uPi(1,1))*sin(x_uPi(4)) + Kpi_alfa(3, k_uPi)*x_uPi(2)*cos(x_uPi(4))+Kpi_alfa(9, k_uPi)*x_uPi(2)*log(p_uPi(4,4))+Kpi_alfa(10, k_uPi)*log(p_uPi(2,2))*cos(x_uPi(4)) + Kpi_alfa(5)) / (Kpi_alfa(4)*sin(x_uPi(4))+Kpi_alfa(11)*log(p_uPi(4,4))+Kpi_alfa(12));
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| 338 | % val_uPi(2) = ( omega_t_stripe - Kpi_beta(1, k_uPi)*x_uPi(3)-Kpi_beta(6, k_uPi)*log(p_uPi(3,3)) + Kpi_beta(2, k_uPi)*x_uPi(1)*sin(x_uPi(4))+Kpi_beta(7, k_uPi)*x_uPi(1)*log(p_uPi(4,4))+Kpi_beta(8, k_uPi)*log(p_uPi(1,1))*sin(x_uPi(4)) - Kpi_beta(3, k_uPi)*x_uPi(2)*cos(x_uPi(4))-Kpi_beta(9, k_uPi)*x_uPi(2)*log(p_uPi(4,4))-Kpi_beta(10, k_uPi)*log(p_uPi(2,2))*cos(x_uPi(4)) - Kpi_beta(5)) / (Kpi_beta(4)*cos(x_uPi(4))+Kpi_beta(11)*log(p_uPi(4,4))+Kpi_beta(12));
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|---|
| 339 | val_uPi(1) = (-omega_t_stripe + Kpi_alfa(1, k_uPi)*x_uPi(3)+Kpi_alfa(5, k_uPi)*log(p_uPi(3,3)) - Kpi_alfa(2, k_uPi)*x_uPi(1)*sin(x_uPi(4))-Kpi_alfa(6, k_uPi)*x_uPi(1)*log(p_uPi(4,4))-Kpi_alfa(7, k_uPi)*log(p_uPi(1,1))*sin(x_uPi(4)) + Kpi_alfa(3, k_uPi)*x_uPi(2)*cos(x_uPi(4))+Kpi_alfa(8, k_uPi)*x_uPi(2)*log(p_uPi(4,4))+Kpi_alfa(9, k_uPi)*log(p_uPi(2,2))*cos(x_uPi(4)) + Kpi_alfa(5)) / (Kpi_alfa(4)*sin(x_uPi(4))+Kpi_alfa(10)*log(p_uPi(4,4))+Kpi_alfa(11));
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| 340 | val_uPi(2) = ( omega_t_stripe - Kpi_beta(1, k_uPi)*x_uPi(3)-Kpi_beta(5, k_uPi)*log(p_uPi(3,3)) + Kpi_beta(2, k_uPi)*x_uPi(1)*sin(x_uPi(4))+Kpi_beta(6, k_uPi)*x_uPi(1)*log(p_uPi(4,4))+Kpi_beta(7, k_uPi)*log(p_uPi(1,1))*sin(x_uPi(4)) - Kpi_beta(3, k_uPi)*x_uPi(2)*cos(x_uPi(4))-Kpi_beta(8, k_uPi)*x_uPi(2)*log(p_uPi(4,4))-Kpi_beta(9, k_uPi)*log(p_uPi(2,2))*cos(x_uPi(4)) - Kpi_beta(5)) / (Kpi_beta(4)*cos(x_uPi(4))+Kpi_beta(10)*log(p_uPi(4,4))+Kpi_beta(11));
|
|---|
| 341 |
|
|---|
| 342 | if (val_uPi(1)<cLb)
|
|---|
| 343 | val_uPi(1) = cLb;
|
|---|
| 344 | end
|
|---|
| 345 | if (val_uPi(1)>cUb)
|
|---|
| 346 | val_uPi(1) = cUb;
|
|---|
| 347 | end
|
|---|
| 348 | if (val_uPi(2)<cLb)
|
|---|
| 349 | val_uPi(2) = cLb;
|
|---|
| 350 | end
|
|---|
| 351 | if (val_uPi(2)>cUb)
|
|---|
| 352 | val_uPi(2) = cUb;
|
|---|
| 353 | end
|
|---|
| 354 | end
|
|---|
| 355 |
|
|---|
| 356 | function [val_ham] = Hamilt(u_ham)
|
|---|
| 357 | mRy = mC * Pkn(:, :, gka, gnu) * mC' + mR;
|
|---|
| 358 | mKy = Pkn(:, :, gka, gnu) * mC' / mRy;
|
|---|
| 359 | tXkn = fceG(Xkn(:, gka, gnu), u_ham) - mKy * (Ykn(:, gka, gnu) - fceH(Xkn(:, gka, gnu)));
|
|---|
| 360 | mA(1, 3) = Cb * sin(Xkn(4, gka, gnu));
|
|---|
| 361 | mA(1, 4) = Cb * Xkn(3, gka, gnu) * cos(Xkn(4, gka, gnu));
|
|---|
| 362 | mA(2, 3) = - Cb * cos(Xkn(4, gka, gnu));
|
|---|
| 363 | mA(2, 4) = Cb * Xkn(3, gka, gnu) * sin(Xkn(4, gka, gnu));
|
|---|
| 364 | mA(3, 1) = - Ce * sin(Xkn(4, gka, gnu));
|
|---|
| 365 | mA(3, 2) = Ce * cos(Xkn(4, gka, gnu));
|
|---|
| 366 | mA(3, 4) = - Ce * (Xkn(2, gka, gnu) * sin(Xkn(4, gka, gnu)) + Xkn(1, gka, gnu) * cos(Xkn(4, gka, gnu)));
|
|---|
| 367 | tPkn = mA * (Pkn(:, :, gka, gnu) - Pkn(:, :, gka, gnu) * mC' * inv(mRy) * mC * Pkn(:, :, gka, gnu)) * mA + mQ;
|
|---|
| 368 | tf = zeros(8,1);
|
|---|
| 369 | tf(1:4) = tXkn;
|
|---|
| 370 | tf(5:8) = diag(tPkn);
|
|---|
| 371 |
|
|---|
| 372 | loss = (tXkn(3) - omega_t_stripe)^2;
|
|---|
| 373 |
|
|---|
| 374 | val_ham = loss + tf' * Vtilde_dx(gka+1, Xkn(:, gka, gnu), Pkn(:, :, gka, gnu)) + 1/2 * trace(mSigma * ( Wv(10, gka+1)*[2 0; 0 0] + Wv(18, gka+1)*[0 0; 0 2] ));
|
|---|
| 375 |
|
|---|
| 376 | end
|
|---|
| 377 |
|
|---|
| 378 | function [val_Vt] = Vtilde(k_Vt, x_Vt, p_Vt)
|
|---|
| 379 | if(k_Vt == K)
|
|---|
| 380 | val_Vt = h_bel;
|
|---|
| 381 | else
|
|---|
| 382 | Epsl = zeros(8, 1);
|
|---|
| 383 | Epsl(1:4) = x_Vt(1:4) - Xstripe(1:4, k_Vt);
|
|---|
| 384 | Epsl(5:8) = diag(p_Vt ./ Pstripe(:, :, k));
|
|---|
| 385 |
|
|---|
| 386 | val_Vt = vectFi(Epsl)' * Wv(:,k_Vt);
|
|---|
| 387 | end
|
|---|
| 388 | end
|
|---|
| 389 |
|
|---|
| 390 | function [val_Vt] = Vtilde_dx(k_Vt, x_Vt, p_Vt)
|
|---|
| 391 | if(k_Vt == K)
|
|---|
| 392 | val_Vt = h_beldx;
|
|---|
| 393 | else
|
|---|
| 394 | Epsl = zeros(8, 1);
|
|---|
| 395 | Epsl(1:4) = x_Vt(1:4) - Xstripe(1:4, k_Vt);
|
|---|
| 396 | Epsl(5:8) = diag(p_Vt ./ Pstripe(:, :, k));
|
|---|
| 397 |
|
|---|
| 398 | val_Vt = difFi(Epsl)' * Wv(:,k_Vt);
|
|---|
| 399 | end
|
|---|
| 400 | end
|
|---|
| 401 |
|
|---|
| 402 | function [val_Fi] = vectFi(x_Fi)
|
|---|
| 403 | val_Fi = [ ...
|
|---|
| 404 | 1; ... %1
|
|---|
| 405 | x_Fi(1); ... %Xi pro 1-4
|
|---|
| 406 | x_Fi(2); ...
|
|---|
| 407 | x_Fi(3); ...
|
|---|
| 408 | x_Fi(4); ...
|
|---|
| 409 | log(x_Fi(5)); ... %ln Xi pro 5-8 tj diagonala matice Pt 4x4
|
|---|
| 410 | log(x_Fi(6)); ...
|
|---|
| 411 | log(x_Fi(7)); ...
|
|---|
| 412 | log(x_Fi(8)); ...
|
|---|
| 413 | x_Fi(1)^2; ... %kvadraticke cleny jen v Xi 1-4 a kombinovane
|
|---|
| 414 | x_Fi(1)*x_Fi(2); ...
|
|---|
| 415 | x_Fi(1)*x_Fi(3); ...
|
|---|
| 416 | x_Fi(1)*x_Fi(4); ...
|
|---|
| 417 | x_Fi(1)*log(x_Fi(5)); ...
|
|---|
| 418 | x_Fi(1)*log(x_Fi(6)); ...
|
|---|
| 419 | x_Fi(1)*log(x_Fi(7)); ...
|
|---|
| 420 | x_Fi(1)*log(x_Fi(8)); ...
|
|---|
| 421 | x_Fi(2)^2; ...
|
|---|
| 422 | x_Fi(2)*x_Fi(3); ...
|
|---|
| 423 | x_Fi(2)*x_Fi(4); ...
|
|---|
| 424 | x_Fi(2)*log(x_Fi(5)); ...
|
|---|
| 425 | x_Fi(2)*log(x_Fi(6)); ...
|
|---|
| 426 | x_Fi(2)*log(x_Fi(7)); ...
|
|---|
| 427 | x_Fi(2)*log(x_Fi(8)); ...
|
|---|
| 428 | x_Fi(3)^2; ...
|
|---|
| 429 | x_Fi(3)*x_Fi(4); ...
|
|---|
| 430 | x_Fi(3)*log(x_Fi(5)); ...
|
|---|
| 431 | x_Fi(3)*log(x_Fi(6)); ...
|
|---|
| 432 | x_Fi(3)*log(x_Fi(7)); ...
|
|---|
| 433 | x_Fi(3)*log(x_Fi(8)); ...
|
|---|
| 434 | x_Fi(4)^2; ...
|
|---|
| 435 | x_Fi(4)*log(x_Fi(5)); ...
|
|---|
| 436 | x_Fi(4)*log(x_Fi(6)); ...
|
|---|
| 437 | x_Fi(4)*log(x_Fi(7)); ...
|
|---|
| 438 | x_Fi(4)*log(x_Fi(8)); ...
|
|---|
| 439 | ];
|
|---|
| 440 | end
|
|---|
| 441 |
|
|---|
| 442 | function [val_Fi] = matrixFi(x_Fi)
|
|---|
| 443 | val_Fi = [ ...
|
|---|
| 444 | ones(1, N); ... %1
|
|---|
| 445 | x_Fi(1, :); ... %Xi pro 1-4
|
|---|
| 446 | x_Fi(2, :); ...
|
|---|
| 447 | x_Fi(3, :); ...
|
|---|
| 448 | x_Fi(4, :); ...
|
|---|
| 449 | log(x_Fi(5, :)); ... %ln Xi pro 5-8 tj diagonala matice Pt 4x4
|
|---|
| 450 | log(x_Fi(6, :)); ...
|
|---|
| 451 | log(x_Fi(7, :)); ...
|
|---|
| 452 | log(x_Fi(8, :)); ...
|
|---|
| 453 | x_Fi(1, :).^2; ... %kvadraticke cleny jen v Xi 1-4 a kombinovane
|
|---|
| 454 | x_Fi(1, :).*x_Fi(2, :); ...
|
|---|
| 455 | x_Fi(1, :).*x_Fi(3, :); ...
|
|---|
| 456 | x_Fi(1, :).*x_Fi(4, :); ...
|
|---|
| 457 | x_Fi(1, :).*log(x_Fi(5, :)); ...
|
|---|
| 458 | x_Fi(1, :).*log(x_Fi(6, :)); ...
|
|---|
| 459 | x_Fi(1, :).*log(x_Fi(7, :)); ...
|
|---|
| 460 | x_Fi(1, :).*log(x_Fi(8, :)); ...
|
|---|
| 461 | x_Fi(2, :).^2; ...
|
|---|
| 462 | x_Fi(2, :).*x_Fi(3, :); ...
|
|---|
| 463 | x_Fi(2, :).*x_Fi(4, :); ...
|
|---|
| 464 | x_Fi(2, :).*log(x_Fi(5, :)); ...
|
|---|
| 465 | x_Fi(2, :).*log(x_Fi(6, :)); ...
|
|---|
| 466 | x_Fi(2, :).*log(x_Fi(7, :)); ...
|
|---|
| 467 | x_Fi(2, :).*log(x_Fi(8, :)); ...
|
|---|
| 468 | x_Fi(3, :).^2; ...
|
|---|
| 469 | x_Fi(3, :).*x_Fi(4, :); ...
|
|---|
| 470 | x_Fi(3, :).*log(x_Fi(5, :)); ...
|
|---|
| 471 | x_Fi(3, :).*log(x_Fi(6, :)); ...
|
|---|
| 472 | x_Fi(3, :).*log(x_Fi(7, :)); ...
|
|---|
| 473 | x_Fi(3, :).*log(x_Fi(8, :)); ...
|
|---|
| 474 | x_Fi(4, :).^2; ...
|
|---|
| 475 | x_Fi(4, :).*log(x_Fi(5, :)); ...
|
|---|
| 476 | x_Fi(4, :).*log(x_Fi(6, :)); ...
|
|---|
| 477 | x_Fi(4, :).*log(x_Fi(7, :)); ...
|
|---|
| 478 | x_Fi(4, :).*log(x_Fi(8, :)); ...
|
|---|
| 479 | ];
|
|---|
| 480 |
|
|---|
| 481 | end
|
|---|
| 482 |
|
|---|
| 483 | function [val_Fi] = difFi(x_Fi)
|
|---|
| 484 | val_Fi = [ ...
|
|---|
| 485 | 0 0 0 0 0 0 0 0; ...
|
|---|
| 486 | 1 0 0 0 0 0 0 0; ...
|
|---|
| 487 | 0 1 0 0 0 0 0 0; ...
|
|---|
| 488 | 0 0 1 0 0 0 0 0; ...
|
|---|
| 489 | 0 0 0 1 0 0 0 0; ...
|
|---|
| 490 | 0 0 0 0 1/x_Fi(5) 0 0 0; ...
|
|---|
| 491 | 0 0 0 0 0 1/x_Fi(6) 0 0; ...
|
|---|
| 492 | 0 0 0 0 0 0 1/x_Fi(7) 0; ...
|
|---|
| 493 | 0 0 0 0 0 0 0 1/x_Fi(8); ...
|
|---|
| 494 | 2*x_Fi(1) 0 0 0 0 0 0 0; ...
|
|---|
| 495 | x_Fi(2) x_Fi(1) 0 0 0 0 0 0; ...
|
|---|
| 496 | x_Fi(3) 0 x_Fi(1) 0 0 0 0 0; ...
|
|---|
| 497 | x_Fi(4) 0 0 x_Fi(1) 0 0 0 0; ...
|
|---|
| 498 | log(x_Fi(5)) 0 0 0 x_Fi(1)/x_Fi(5) 0 0 0; ...
|
|---|
| 499 | log(x_Fi(6)) 0 0 0 0 x_Fi(1)/x_Fi(6) 0 0; ...
|
|---|
| 500 | log(x_Fi(7)) 0 0 0 0 0 x_Fi(1)/x_Fi(7) 0; ...
|
|---|
| 501 | log(x_Fi(8)) 0 0 0 0 0 0 x_Fi(1)/x_Fi(8); ...
|
|---|
| 502 | 0 2*x_Fi(2) 0 0 0 0 0 0; ...
|
|---|
| 503 | 0 x_Fi(3) x_Fi(2) 0 0 0 0 0; ...
|
|---|
| 504 | 0 x_Fi(4) 0 x_Fi(2) 0 0 0 0; ...
|
|---|
| 505 | 0 log(x_Fi(5)) 0 0 x_Fi(2)/x_Fi(5) 0 0 0; ...
|
|---|
| 506 | 0 log(x_Fi(6)) 0 0 0 x_Fi(2)/x_Fi(6) 0 0; ...
|
|---|
| 507 | 0 log(x_Fi(7)) 0 0 0 0 x_Fi(2)/x_Fi(7) 0; ...
|
|---|
| 508 | 0 log(x_Fi(8)) 0 0 0 0 0 x_Fi(2)/x_Fi(8); ...
|
|---|
| 509 | 0 0 2*x_Fi(3) 0 0 0 0 0; ...
|
|---|
| 510 | 0 0 x_Fi(4) x_Fi(3) 0 0 0 0; ...
|
|---|
| 511 | 0 0 log(x_Fi(5)) 0 x_Fi(3)/x_Fi(5) 0 0 0; ...
|
|---|
| 512 | 0 0 log(x_Fi(6)) 0 0 x_Fi(3)/x_Fi(6) 0 0; ...
|
|---|
| 513 | 0 0 log(x_Fi(7)) 0 0 0 x_Fi(3)/x_Fi(7) 0; ...
|
|---|
| 514 | 0 0 log(x_Fi(8)) 0 0 0 0 x_Fi(3)/x_Fi(8); ...
|
|---|
| 515 | 0 0 0 2*x_Fi(4) 0 0 0 0; ...
|
|---|
| 516 | 0 0 0 log(x_Fi(5)) x_Fi(4)/x_Fi(5) 0 0 0; ...
|
|---|
| 517 | 0 0 0 log(x_Fi(6)) 0 x_Fi(4)/x_Fi(6) 0 0; ...
|
|---|
| 518 | 0 0 0 log(x_Fi(7)) 0 0 x_Fi(4)/x_Fi(7) 0; ...
|
|---|
| 519 | 0 0 0 log(x_Fi(8)) 0 0 0 x_Fi(4)/x_Fi(8); ...
|
|---|
| 520 | ];
|
|---|
| 521 | end
|
|---|
| 522 |
|
|---|
| 523 | function [c, ceq, GC, GCeq] = Cond2(x)
|
|---|
| 524 | c = x(1)*x(1) + x(2)*x(2) - cC1;
|
|---|
| 525 | ceq = [];
|
|---|
| 526 | GC = [2*x(1); 2*x(2)];
|
|---|
| 527 | GCeq = [];
|
|---|
| 528 | end
|
|---|
| 529 |
|
|---|
| 530 | function [x_ret] = fceG(x_in, u_in)
|
|---|
| 531 | x_ret = zeros(4, 1);
|
|---|
| 532 | x_ret(1) = Ca * x_in(1) + Cb * x_in(3) * sin(x_in(4)) + Cc * u_in(1);
|
|---|
| 533 | x_ret(2) = Ca * x_in(2) - Cb * x_in(3) * cos(x_in(4)) + Cc * u_in(2);
|
|---|
| 534 | x_ret(3) = Cd * x_in(3) + Ce * (x_in(2) * cos(x_in(4)) - x_in(1) * sin(x_in(4)));
|
|---|
| 535 | x_ret(4) = x_in(4) + x_in(3) * DELTAt;
|
|---|
| 536 | end
|
|---|
| 537 |
|
|---|
| 538 | function [x_ret] = fceG_du(x_in, u_in)
|
|---|
| 539 | x_ret = zeros(4, 2);
|
|---|
| 540 | x_ret(1, 1) = Cc;
|
|---|
| 541 | x_ret(2, 2) = Cc;
|
|---|
| 542 | end
|
|---|
| 543 |
|
|---|
| 544 | function [y_ret] = fceH(x_in)
|
|---|
| 545 | y_ret = zeros(2, 1);
|
|---|
| 546 | y_ret(1) = x_in(1);
|
|---|
| 547 | y_ret(2) = x_in(2);
|
|---|
| 548 | end
|
|---|
| 549 |
|
|---|
| 550 | end
|
|---|
