| 1 | function pmsm_ildp3
|
|---|
| 2 | %verze ildp algoritmu s uvazovanim P (v logaritmu) pro PMSM motor
|
|---|
| 3 | %rozsirena verze o diag P v pi aproximaci u
|
|---|
| 4 | tic
|
|---|
| 5 |
|
|---|
| 6 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|---|
| 7 | %pocatecni konstanty
|
|---|
| 8 |
|
|---|
| 9 | Iterace = 5; %iterace
|
|---|
| 10 | K = 5; %casy
|
|---|
| 11 | N = 50; %vzorky
|
|---|
| 12 |
|
|---|
| 13 | %konstanty motoru
|
|---|
| 14 | %Rs = 0.28;
|
|---|
| 15 | %Ls = 0.003465;
|
|---|
| 16 | %PSIpm = 0.1989;
|
|---|
| 17 | %kp = 1.5;
|
|---|
| 18 | %p = 4.0;
|
|---|
| 19 | %J = 0.04;
|
|---|
| 20 | DELTAt = 0.000125;
|
|---|
| 21 |
|
|---|
| 22 | %upravene konstanty
|
|---|
| 23 | Ca = 0.9898;
|
|---|
| 24 | Cb = 0.0072;
|
|---|
| 25 | Cc = 0.0361;
|
|---|
| 26 | Cd = 1.0;
|
|---|
| 27 | Ce = 0.0149;
|
|---|
| 28 |
|
|---|
| 29 | %omezeni rizeni
|
|---|
| 30 | cC1 = 100;
|
|---|
| 31 | % cLb = -50;
|
|---|
| 32 | % cUb = 50;
|
|---|
| 33 |
|
|---|
| 34 | %presnost mereni proudu
|
|---|
| 35 | deltaI = 0.085;
|
|---|
| 36 |
|
|---|
| 37 | %matice
|
|---|
| 38 | %kovariancni matice Q a R
|
|---|
| 39 | mQ = diag([0.0013 0.0013 5.0e-6 1.0e-10]);
|
|---|
| 40 | mR = diag([0.0006 0.0006]);
|
|---|
| 41 |
|
|---|
| 42 | %matice pro vypocet
|
|---|
| 43 | %matice A zavisla na parametrech
|
|---|
| 44 | mA = zeros(4);
|
|---|
| 45 | mA(1,1) = Ca;
|
|---|
| 46 | mA(2,2) = Ca;
|
|---|
| 47 | mA(3,3) = Cd;
|
|---|
| 48 | mA(4,4) = 1;
|
|---|
| 49 | mA(4,3) = DELTAt;
|
|---|
| 50 |
|
|---|
| 51 | %macite C konstantni
|
|---|
| 52 | mC = [ 1 0 0 0; 0 1 0 0];
|
|---|
| 53 |
|
|---|
| 54 | %pozadovana hodnota otacek
|
|---|
| 55 | omega_t_stripe = 1.0015;
|
|---|
| 56 |
|
|---|
| 57 | %penalizace za vstupy
|
|---|
| 58 | cPenPsi = 0;%0.000009;
|
|---|
| 59 |
|
|---|
| 60 | %pocatecni hodnoty
|
|---|
| 61 | X0 = [0; 0; 1; pi/2];
|
|---|
| 62 | Y0 = [0; 0];
|
|---|
| 63 | P0 = diag([0.01 0.01 0.01 0.01]);
|
|---|
| 64 |
|
|---|
| 65 | h_bel = 0;
|
|---|
| 66 | h_beldx = [0; 0; 0; 0; 0; 0];
|
|---|
| 67 | h_beldxdx = zeros(4);
|
|---|
| 68 |
|
|---|
| 69 | %velikost okoli pro lokalni metodu
|
|---|
| 70 | % rhoi = 0.0001;
|
|---|
| 71 | % rhoo = 0.00015;
|
|---|
| 72 | % rhot = 0.00005;
|
|---|
| 73 | % rhop = 0.0001;
|
|---|
| 74 | rhoi = sqrt(mQ(1,1)); %1.5;
|
|---|
| 75 | rhoo = sqrt(mQ(3,3));%1.5;
|
|---|
| 76 | rhot = sqrt(mQ(4,4));%1.5;
|
|---|
| 77 | rhop = 0.001;
|
|---|
| 78 |
|
|---|
| 79 | %zvetseni hamiltonianu pro minimalizace
|
|---|
| 80 | % mag = 1000;
|
|---|
| 81 | mag = 1;
|
|---|
| 82 |
|
|---|
| 83 | %prepinac sumu on/off
|
|---|
| 84 | noise = 0;
|
|---|
| 85 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|---|
| 86 | %globalni promenne
|
|---|
| 87 |
|
|---|
| 88 | Kpi_alfa = -0.2*ones(1, K); %konstanty aproximace slozky rizeni u_alfa
|
|---|
| 89 | Kpi_beta = 0.01*ones(1, K); %konstanty aproximace slozky rizeni u_beta
|
|---|
| 90 | % Kpi_alfa = ones(1, K); %konstanty aproximace slozky rizeni u_alfa
|
|---|
| 91 | % Kpi_beta = ones(1, K); %konstanty aproximace slozky rizeni u_beta
|
|---|
| 92 | % Kpi_alfa = zeros(4, K); %konstanty aproximace slozky rizeni u_alfa
|
|---|
| 93 | % Kpi_alfa(1, :) = 1000*Cc*Ce*ones(1, K);
|
|---|
| 94 | % Kpi_alfa(2, :) = 1000*Cc*Ce*ones(1, K);
|
|---|
| 95 | %
|
|---|
| 96 | % Kpi_beta = zeros(4, K); %konstanty aproximace slozky rizeni u_beta
|
|---|
| 97 | % Kpi_beta(1, :) = Cc*Ce*ones(1, K);
|
|---|
| 98 | % Kpi_beta(2, :) = Cc*Ce*ones(1, K);
|
|---|
| 99 | Kpi = ones(9, K);
|
|---|
| 100 |
|
|---|
| 101 |
|
|---|
| 102 | Wv = zeros(25, K); %konstanty aproximace Bellmanovy fce
|
|---|
| 103 |
|
|---|
| 104 | Xkn = zeros(4, K, N); % X = [i_alfa, i_beta, omega, theta]
|
|---|
| 105 | Ykn = zeros(2, K, N); % Y = [i_alfa, i_beta]
|
|---|
| 106 | Pkn = zeros(4, 4, K, N); % P = N vzorku posloupnosti K matic 4x4
|
|---|
| 107 |
|
|---|
| 108 | mKy = zeros(4, 2); % K = pomocna matice pro vypocet
|
|---|
| 109 | mRy = zeros(2, 2); % R = pomocna matice pro vypocet
|
|---|
| 110 |
|
|---|
| 111 | Xstripe = zeros(4, K);
|
|---|
| 112 | Pstripe = zeros(4, 4, K);
|
|---|
| 113 |
|
|---|
| 114 | Epsilon = zeros(6, N); %globalni promena pro vypocet Bellmanovy fce z odchylek (X - Xprum)
|
|---|
| 115 |
|
|---|
| 116 | gka = 0; %globalni promenna pro prenos casu k
|
|---|
| 117 | gnu = 0; %globalni promenna pro prenos vzorku n
|
|---|
| 118 |
|
|---|
| 119 | Uopt2 = zeros(2, N);
|
|---|
| 120 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|---|
| 121 | %hlavni iteracni smycka
|
|---|
| 122 | for i = 1:Iterace,
|
|---|
| 123 |
|
|---|
| 124 | disp(['Iterace: ', num2str(i)]);
|
|---|
| 125 | %generovani stavu
|
|---|
| 126 | for n = 1:N,
|
|---|
| 127 | Xkn(:, 1, n) = X0;
|
|---|
| 128 | Ykn(:, 1, n) = Y0;
|
|---|
| 129 | Pkn(:, :, 1, n) = P0;
|
|---|
| 130 |
|
|---|
| 131 | for k = 1:K-1,
|
|---|
| 132 | Uk = uPi(k, Xkn(:, k, n), Pkn(:, :, k, n));
|
|---|
| 133 |
|
|---|
| 134 | mRy = mC * Pkn(:, :, k, n) * mC' + mR;
|
|---|
| 135 | mKy = Pkn(:, :, k, n) * mC' / mRy;
|
|---|
| 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
|
|---|
| 137 | Ykn(:, k+1, n) = round(Xkn(1:2, k+1, n) / deltaI) * deltaI; %X kopie do Y se vzorkovanim 0.085
|
|---|
| 138 | mA(1, 3) = Cb * sin(Xkn(4, k, n));
|
|---|
| 139 | mA(1, 4) = Cb * Xkn(3, k, n) * cos(Xkn(4, k, n));
|
|---|
| 140 | mA(2, 3) = - Cb * cos(Xkn(4, k, n));
|
|---|
| 141 | mA(2, 4) = Cb * Xkn(3, k, n) * sin(Xkn(4, k, n));
|
|---|
| 142 | mA(3, 1) = - Ce * sin(Xkn(4, k, n));
|
|---|
| 143 | mA(3, 2) = Ce * cos(Xkn(4, k, n));
|
|---|
| 144 | mA(3, 4) = - Ce * (Xkn(2, k, n) * sin(Xkn(4, k, n)) + Xkn(1, k, n) * cos(Xkn(4, k, n)));
|
|---|
| 145 | Pkn(:, :, k+1, n) = mA * (Pkn(:, :, k, n) - Pkn(:, :, k, n) * mC' * inv(mRy) * mC * Pkn(:, :, k, n)) * mA' + mQ;
|
|---|
| 146 | end
|
|---|
| 147 | end
|
|---|
| 148 | Xstripe = mean(Xkn, 3);
|
|---|
| 149 | Pstripe = mean(Pkn, 4);
|
|---|
| 150 |
|
|---|
| 151 | for k = K-1:-1:1,
|
|---|
| 152 | gka = k;
|
|---|
| 153 |
|
|---|
| 154 | % 1]
|
|---|
| 155 | for n = 1:N,
|
|---|
| 156 | %krive okoli
|
|---|
| 157 | Xkn(1, k, n) = Xstripe(1, k) + rhoi*randn();
|
|---|
| 158 | Xkn(2, k, n) = Xstripe(2, k) + rhoi*randn();
|
|---|
| 159 | Xkn(3, k, n) = Xstripe(3, k) + rhoo*randn();
|
|---|
| 160 | Xkn(4, k, n) = Xstripe(4, k) + rhot*randn();
|
|---|
| 161 |
|
|---|
| 162 | Ykn(:, k, n) = round(Xkn(1:2, k, n) / deltaI) * deltaI;
|
|---|
| 163 |
|
|---|
| 164 | Pkn(:, :, k, n) = Pstripe(:, :, k) .* exp(rhop*randn(4));
|
|---|
| 165 | end
|
|---|
| 166 |
|
|---|
| 167 | % 2]
|
|---|
| 168 | for n = 1:N,
|
|---|
| 169 | gnu = n;
|
|---|
| 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-12));
|
|---|
| 171 | % Uopt2(1,n)=sin(2*pi/20*k);
|
|---|
| 172 | % Z = zeros(101,101);
|
|---|
| 173 | % ii = 0;
|
|---|
| 174 | % jj = 0;
|
|---|
| 175 | % for ii = -50:50,
|
|---|
| 176 | % for jj = -50:50,
|
|---|
| 177 | % Z(ii+51,jj+51) = Hamilt([ii,jj]);
|
|---|
| 178 | % end
|
|---|
| 179 | % end
|
|---|
| 180 | % surf(Z);
|
|---|
| 181 | end
|
|---|
| 182 |
|
|---|
| 183 | % 3]
|
|---|
| 184 | for n = 1:N,
|
|---|
| 185 | Vn(n) = DELTAt*Hmin(n)/mag + Vtilde(k+1, Xkn(:, k, n), Pkn(:, :, k, n));
|
|---|
| 186 |
|
|---|
| 187 | end
|
|---|
| 188 |
|
|---|
| 189 | % 4]
|
|---|
| 190 | %urceni aproximace V Bellmanovy funkce
|
|---|
| 191 | for n = 1:N,
|
|---|
| 192 | Epsilon(1:4, n) = Xkn(1:4, k, n) - Xstripe(1:4, k);
|
|---|
| 193 | tpdiag = diag(Pkn(:, :, k, n) ./ Pstripe(:, :, k));
|
|---|
| 194 | Epsilon(5:6, n) = tpdiag(3:4);
|
|---|
| 195 | end
|
|---|
| 196 | mFi = matrixFi(Epsilon);
|
|---|
| 197 | FiFiTInvFi = inv(mFi*mFi'+1e-5*eye(25))*mFi;
|
|---|
| 198 | Wv(:,k) = FiFiTInvFi * Vn';
|
|---|
| 199 |
|
|---|
| 200 | %urceni aproximace pi rizeni u
|
|---|
| 201 | Kpi_alfa(k) = mean(Uopt2(1,:));
|
|---|
| 202 | Kpi_beta(k) = mean(Uopt2(2,:));
|
|---|
| 203 | % mPsi = ones(N,1);
|
|---|
| 204 | % PsiPsiTInvPsi = (mPsi'*mPsi)\mPsi';
|
|---|
| 205 | % Kpi_alfa(:, k) = PsiPsiTInvPsi * Uopt2(1,:)';
|
|---|
| 206 | %
|
|---|
| 207 | % mPsi = ones(N,1);
|
|---|
| 208 | % PsiPsiTInvPsi = (mPsi'*mPsi)\mPsi';
|
|---|
| 209 | % Kpi_beta(:, k) = PsiPsiTInvPsi * Uopt2(2,:)';
|
|---|
| 210 | % mPsi = [sin(squeeze(Xkn(4, k, :))),...1
|
|---|
| 211 | % cos(squeeze(Xkn(4, k, :))),...2
|
|---|
| 212 | % (sin(squeeze(Xkn(4, k, :))).^2),...3
|
|---|
| 213 | % (cos(squeeze(Xkn(4, k, :))).^2)];%4
|
|---|
| 214 | % PsiPsiTInvPsi = (mPsi'*mPsi)\mPsi';
|
|---|
| 215 | % Kpi_alfa(:, k) = PsiPsiTInvPsi * Uopt2(1,:)';
|
|---|
| 216 | %
|
|---|
| 217 | % mPsi = [sin(squeeze(Xkn(4, k, :))),...1
|
|---|
| 218 | % cos(squeeze(Xkn(4, k, :))),...2
|
|---|
| 219 | % (sin(squeeze(Xkn(4, k, :))).^2),...3
|
|---|
| 220 | % (cos(squeeze(Xkn(4, k, :))).^2)];%4
|
|---|
| 221 | % PsiPsiTInvPsi = (mPsi'*mPsi)\mPsi';
|
|---|
| 222 | % Kpi_beta(:, k) = PsiPsiTInvPsi * Uopt2(2,:)';
|
|---|
| 223 | % tmpUfi = squeeze(Xkn(4, k, :) + DELTAt*Xkn(3, k, :));
|
|---|
| 224 | % tmpUamp = sqrt(Uopt2(1,:).^2 + Uopt2(2,:).^2)';
|
|---|
| 225 | % mPsi = [Cd*Cd*squeeze(Xkn(3, k, :)),...1
|
|---|
| 226 | % Cd*Ce*squeeze(Xkn(2, k, :).*cos(Xkn(4, k, :))),...2
|
|---|
| 227 | % - Cd*Ce*squeeze(Xkn(1, k, :).*sin(Xkn(4, k, :))),...3
|
|---|
| 228 | % Ce*Ca*squeeze(Xkn(2, k, :)).*cos(tmpUfi),...4
|
|---|
| 229 | % - Ce*Cb*squeeze(Xkn(3, k, :).*cos(Xkn(4, k, :))).*cos(tmpUfi),...5
|
|---|
| 230 | % Ce*Ca*squeeze(Xkn(1, k, :)).*sin(tmpUfi),...6
|
|---|
| 231 | % Ce*Cb*squeeze(Xkn(3, k, :).*sin(Xkn(4, k, :))).*sin(tmpUfi),...7
|
|---|
| 232 | % Ce*Cc*squeeze( (cos(tmpUfi)).^2 - (sin(tmpUfi)).^2 ).*tmpUamp,...8
|
|---|
| 233 | % tmpUamp];%9
|
|---|
| 234 | % PsiPsiTInvPsi = (mPsi'*mPsi)\mPsi';
|
|---|
| 235 | % Kpi(:, k) = PsiPsiTInvPsi * (omega_t_stripe*ones(N, 1));
|
|---|
| 236 | end
|
|---|
| 237 | end
|
|---|
| 238 |
|
|---|
| 239 | %%%%%%%%%%%
|
|---|
| 240 | toc
|
|---|
| 241 | % keyboard
|
|---|
| 242 | Kpi_alfa
|
|---|
| 243 | Kpi_beta
|
|---|
| 244 | %vykresleni grafu
|
|---|
| 245 | clf
|
|---|
| 246 | subplot(3,4,3);
|
|---|
| 247 | plot(1:K,omega_t_stripe*ones(1,K));
|
|---|
| 248 |
|
|---|
| 249 | Ukn = zeros(2, K, N);
|
|---|
| 250 | for n = 1:N,
|
|---|
| 251 | Xkn(:, 1, n) = X0;
|
|---|
| 252 | Ykn(:, 1, n) = Y0;
|
|---|
| 253 | Pkn(:, :, 1, n) = P0;
|
|---|
| 254 | for k = 1:K-1,
|
|---|
| 255 | Ukn(:, k, n) = uPi(k, Xkn(:, k, n), Pkn(:, :, k, n));
|
|---|
| 256 | mRy = mC * Pkn(:, :, k, n) * mC' + mR;
|
|---|
| 257 | mKy = Pkn(:, :, k, n) * mC' / mRy;
|
|---|
| 258 | 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
|
|---|
| 259 | Ykn(:, k+1, n) = round(Xkn(1:2, k+1, n) / deltaI) * deltaI; %X kopie do Y se vzorkovanim 0.085
|
|---|
| 260 | mA(1, 3) = Cb * sin(Xkn(4, k, n));
|
|---|
| 261 | mA(1, 4) = Cb * Xkn(3, k, n) * cos(Xkn(4, k, n));
|
|---|
| 262 | mA(2, 3) = - Cb * cos(Xkn(4, k, n));
|
|---|
| 263 | mA(2, 4) = Cb * Xkn(3, k, n) * sin(Xkn(4, k, n));
|
|---|
| 264 | mA(3, 1) = - Ce * sin(Xkn(4, k, n));
|
|---|
| 265 | mA(3, 2) = Ce * cos(Xkn(4, k, n));
|
|---|
| 266 | mA(3, 4) = - Ce * (Xkn(2, k, n) * sin(Xkn(4, k, n)) + Xkn(1, k, n) * cos(Xkn(4, k, n)));
|
|---|
| 267 | Pkn(:, :, k+1, n) = mA * (Pkn(:, :, k, n) - Pkn(:, :, k, n) * mC' * inv(mRy) * mC * Pkn(:, :, k, n)) * mA' + mQ;
|
|---|
| 268 | end
|
|---|
| 269 |
|
|---|
| 270 | hold all
|
|---|
| 271 | subplot(3,4,1);
|
|---|
| 272 | title('X:i_{\alpha}')
|
|---|
| 273 | plot(1:K,Xkn(1,:,n))
|
|---|
| 274 |
|
|---|
| 275 | hold all
|
|---|
| 276 | subplot(3,4,2);
|
|---|
| 277 | title('X:i_{\beta}')
|
|---|
| 278 | plot(1:K,Xkn(2,:,n))
|
|---|
| 279 |
|
|---|
| 280 | hold all
|
|---|
| 281 | subplot(3,4,3);
|
|---|
| 282 | title('X:\omega')
|
|---|
| 283 | plot(1:K,Xkn(3,:,n))
|
|---|
| 284 |
|
|---|
| 285 | hold all
|
|---|
| 286 | subplot(3,4,4);
|
|---|
| 287 | title('X:\theta')
|
|---|
| 288 | plot(1:K,Xkn(4,:,n))
|
|---|
| 289 |
|
|---|
| 290 | hold all
|
|---|
| 291 | subplot(3,4,5);
|
|---|
| 292 | title('Y:i_{\alpha}')
|
|---|
| 293 | plot(1:K,Ykn(1,:,n))
|
|---|
| 294 |
|
|---|
| 295 | hold all
|
|---|
| 296 | subplot(3,4,6);
|
|---|
| 297 | title('Y:i_{\beta}')
|
|---|
| 298 | plot(1:K,Ykn(2,:,n))
|
|---|
| 299 |
|
|---|
| 300 | hold all
|
|---|
| 301 | subplot(3,4,7);
|
|---|
| 302 | title('u_{\alpha}')
|
|---|
| 303 | plot(1:K,Ukn(1,:,n))
|
|---|
| 304 |
|
|---|
| 305 | hold all
|
|---|
| 306 | subplot(3,4,8);
|
|---|
| 307 | title('u_{\beta}')
|
|---|
| 308 | plot(1:K,Ukn(2,:,n))
|
|---|
| 309 |
|
|---|
| 310 | hold all
|
|---|
| 311 | subplot(3,4,9);
|
|---|
| 312 | title('P(1, 1)')
|
|---|
| 313 | plot(1:K,squeeze(Pkn(1, 1, :, n)))
|
|---|
| 314 |
|
|---|
| 315 | hold all
|
|---|
| 316 | subplot(3,4,10);
|
|---|
| 317 | title('P(2, 2)')
|
|---|
| 318 | plot(1:K,squeeze(Pkn(2, 2, :, n)))
|
|---|
| 319 |
|
|---|
| 320 | hold all
|
|---|
| 321 | subplot(3,4,11);
|
|---|
| 322 | title('P(3, 3)')
|
|---|
| 323 | plot(1:K,squeeze(Pkn(3, 3, :, n)))
|
|---|
| 324 |
|
|---|
| 325 | hold all
|
|---|
| 326 | subplot(3,4,12);
|
|---|
| 327 | title('P(4, 4)')
|
|---|
| 328 | plot(1:K,squeeze(Pkn(4, 4, :, n)))
|
|---|
| 329 | end
|
|---|
| 330 |
|
|---|
| 331 | figure
|
|---|
| 332 |
|
|---|
| 333 | for n = 1:N,
|
|---|
| 334 | Xkn(:, 1, n) = X0;
|
|---|
| 335 | for k = 1:K-1,
|
|---|
| 336 | Ukn(:, k, n) = uPi(k, Xkn(:, k, n), zeros(4));
|
|---|
| 337 | Xkn(:, k+1, n) = fceG(Xkn(:, k, n), Ukn(:, k, n)) + noise * sqrtm(mQ) * randn(4, 1);
|
|---|
| 338 | end
|
|---|
| 339 |
|
|---|
| 340 | hold all
|
|---|
| 341 | subplot(2,3,1);
|
|---|
| 342 | title('X:i_{\alpha}')
|
|---|
| 343 | plot(1:K,Xkn(1,:,n))
|
|---|
| 344 |
|
|---|
| 345 | hold all
|
|---|
| 346 | subplot(2,3,2);
|
|---|
| 347 | title('X:i_{\beta}')
|
|---|
| 348 | plot(1:K,Xkn(2,:,n))
|
|---|
| 349 |
|
|---|
| 350 | hold all
|
|---|
| 351 | subplot(2,3,3);
|
|---|
| 352 | title('X:\omega')
|
|---|
| 353 | plot(1:K,Xkn(3,:,n))
|
|---|
| 354 |
|
|---|
| 355 | hold all
|
|---|
| 356 | subplot(2,3,4);
|
|---|
| 357 | title('X:\theta')
|
|---|
| 358 | plot(1:K,Xkn(4,:,n))
|
|---|
| 359 |
|
|---|
| 360 | hold all
|
|---|
| 361 | subplot(2,3,5);
|
|---|
| 362 | title('u_{\alpha}')
|
|---|
| 363 | plot(1:K,Ukn(1,:,n))
|
|---|
| 364 |
|
|---|
| 365 | hold all
|
|---|
| 366 | subplot(2,3,6);
|
|---|
| 367 | title('u_{\beta}')
|
|---|
| 368 | plot(1:K,Ukn(2,:,n))
|
|---|
| 369 |
|
|---|
| 370 | end
|
|---|
| 371 |
|
|---|
| 372 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|---|
| 373 | %pomocne funkce
|
|---|
| 374 |
|
|---|
| 375 | function [val_uPi] = uPi(k_uPi, x_uPi, p_uPi)
|
|---|
| 376 | val_uPi = zeros(2, 1);
|
|---|
| 377 | val_uPi(1) = Kpi_alfa(k_uPi);
|
|---|
| 378 | val_uPi(2) = Kpi_beta(k_uPi);
|
|---|
| 379 | % 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;
|
|---|
| 380 | % 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;
|
|---|
| 381 | % tmpfi = x_uPi(4) + DELTAt*x_uPi(3);
|
|---|
| 382 | % 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)))...
|
|---|
| 383 | % - Ce*( (Kpi(4, k_uPi)*Ca*x_uPi(2) - Kpi(5, k_uPi)*Cb*x_uPi(3)*cos(x_uPi(4)))*cos(tmpfi)...
|
|---|
| 384 | % -(Kpi(6, k_uPi)*Ca*x_uPi(1) + Kpi(7, k_uPi)*Cb*x_uPi(3)*sin(x_uPi(4)))*sin(tmpfi) ) ) /...
|
|---|
| 385 | % (Kpi(8, k_uPi)*Ce*Cc*( (cos(tmpfi))^2 - (sin(tmpfi))^2 ) + Kpi(9, k_uPi));
|
|---|
| 386 | %
|
|---|
| 387 | % if(tmpw > cC1)
|
|---|
| 388 | % tmpw = cC1;
|
|---|
| 389 | % elseif(tmpw < - cC1)
|
|---|
| 390 | % tmpw = -cC1;
|
|---|
| 391 | % end
|
|---|
| 392 | % val_uPi(1) = tmpw*sin(tmpfi);
|
|---|
| 393 | % val_uPi(2) = tmpw*cos(tmpfi);
|
|---|
| 394 | end
|
|---|
| 395 |
|
|---|
| 396 | function [val_ham] = Hamilt(u_ham)
|
|---|
| 397 | mRy = mC * Pkn(:, :, gka, gnu) * mC' + mR;
|
|---|
| 398 | mKy = Pkn(:, :, gka, gnu) * mC' / mRy;
|
|---|
| 399 | tXkn = fceG(Xkn(:, gka, gnu), u_ham) - mKy * (Ykn(:, gka, gnu) - fceH(Xkn(:, gka, gnu)));
|
|---|
| 400 | mA(1, 3) = Cb * sin(Xkn(4, gka, gnu));
|
|---|
| 401 | mA(1, 4) = Cb * Xkn(3, gka, gnu) * cos(Xkn(4, gka, gnu));
|
|---|
| 402 | mA(2, 3) = - Cb * cos(Xkn(4, gka, gnu));
|
|---|
| 403 | mA(2, 4) = Cb * Xkn(3, gka, gnu) * sin(Xkn(4, gka, gnu));
|
|---|
| 404 | mA(3, 1) = - Ce * sin(Xkn(4, gka, gnu));
|
|---|
| 405 | mA(3, 2) = Ce * cos(Xkn(4, gka, gnu));
|
|---|
| 406 | mA(3, 4) = - Ce * (Xkn(2, gka, gnu) * sin(Xkn(4, gka, gnu)) + Xkn(1, gka, gnu) * cos(Xkn(4, gka, gnu)));
|
|---|
| 407 | tPkn = mA * (Pkn(:, :, gka, gnu) - Pkn(:, :, gka, gnu) * mC' * inv(mRy) * mC * Pkn(:, :, gka, gnu)) * mA' + mQ;
|
|---|
| 408 | tf = zeros(6,1);
|
|---|
| 409 | tf(1:4) = tXkn;
|
|---|
| 410 | tfpdiag = diag(tPkn);
|
|---|
| 411 | tf(5:6) = tfpdiag(3:4);
|
|---|
| 412 |
|
|---|
| 413 | % loss = (tXkn(3) - omega_t_stripe)^2;
|
|---|
| 414 | % 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;
|
|---|
| 415 | % if(gka == 1)
|
|---|
| 416 | % loss = (tXkn(3) - omega_t_stripe)^2;
|
|---|
| 417 | % else
|
|---|
| 418 | % 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;
|
|---|
| 419 | % end
|
|---|
| 420 | % 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;
|
|---|
| 421 |
|
|---|
| 422 |
|
|---|
| 423 | % loss = loss + cPenPsi*(u_ham(1)^2 + u_ham(2)^2);
|
|---|
| 424 | loss = ( Cd*(Cd*Xkn(3, gka, gnu)...
|
|---|
| 425 | + Ce*Xkn(2, gka, gnu)*cos(Xkn(4, gka, gnu))...
|
|---|
| 426 | - Ce*Xkn(1, gka, gnu)*sin(Xkn(4, gka, gnu)))...
|
|---|
| 427 | + 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))...
|
|---|
| 428 | -(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)))...
|
|---|
| 429 | + Ce*Cc*u_ham(2)*cos(Xkn(4, gka, gnu)+DELTAt*Xkn(3, gka, gnu))...
|
|---|
| 430 | - Ce*Cc*u_ham(1)*sin(Xkn(4, gka, gnu)+DELTAt*Xkn(3, gka, gnu))...
|
|---|
| 431 | - omega_t_stripe )^2;
|
|---|
| 432 |
|
|---|
| 433 | val_ham = mag*(loss + tf' * Vtilde_dx(gka+1, Xkn(:, gka, gnu), Pkn(:, :, gka, gnu)) + 1/2 * trace(mQ * Vtilde_dx_dx(gka+1)));
|
|---|
| 434 |
|
|---|
| 435 | end
|
|---|
| 436 |
|
|---|
| 437 | function [val_Vt] = Vtilde(k_Vt, x_Vt, p_Vt)
|
|---|
| 438 | if(k_Vt == K)
|
|---|
| 439 | val_Vt = h_bel;
|
|---|
| 440 | else
|
|---|
| 441 | Epsl = zeros(6, 1);
|
|---|
| 442 | Epsl(1:4) = x_Vt(1:4) - Xstripe(1:4, k_Vt);
|
|---|
| 443 | tpdiag = diag(p_Vt ./ Pstripe(:, :, k));
|
|---|
| 444 | Epsl(5:6) = tpdiag(3:4);
|
|---|
| 445 |
|
|---|
| 446 | val_Vt = vectFi(Epsl)' * Wv(:,k_Vt);
|
|---|
| 447 | end
|
|---|
| 448 | end
|
|---|
| 449 |
|
|---|
| 450 | function [val_Vt] = Vtilde_dx(k_Vt, x_Vt, p_Vt)
|
|---|
| 451 | if(k_Vt == K)
|
|---|
| 452 | val_Vt = h_beldx;
|
|---|
| 453 | else
|
|---|
| 454 | Epsl = zeros(6, 1);
|
|---|
| 455 | Epsl(1:4) = x_Vt(1:4) - Xstripe(1:4, k_Vt);
|
|---|
| 456 | tpdiag = diag(p_Vt ./ Pstripe(:, :, k));
|
|---|
| 457 | Epsl(5:6) = tpdiag(3:4);
|
|---|
| 458 |
|
|---|
| 459 | val_Vt = difFi(Epsl)' * Wv(:,k_Vt);
|
|---|
| 460 | end
|
|---|
| 461 | end
|
|---|
| 462 |
|
|---|
| 463 | function [val_Fi] = vectFi(x_Fi)
|
|---|
| 464 | val_Fi = [ ...
|
|---|
| 465 | 1; ... %1
|
|---|
| 466 | x_Fi(1); ... %Xi pro 1-4
|
|---|
| 467 | x_Fi(2); ...
|
|---|
| 468 | x_Fi(3); ...
|
|---|
| 469 | x_Fi(4); ...
|
|---|
| 470 | log(x_Fi(5)); ... %ln Xi pro 5-8 tj diagonala matice Pt 4x4
|
|---|
| 471 | log(x_Fi(6)); ...
|
|---|
| 472 | x_Fi(1)^2; ... %kvadraticke cleny jen v Xi 1-4 a kombinovane
|
|---|
| 473 | x_Fi(1)*x_Fi(2); ...
|
|---|
| 474 | x_Fi(1)*x_Fi(3); ...
|
|---|
| 475 | x_Fi(1)*x_Fi(4); ...
|
|---|
| 476 | x_Fi(1)*log(x_Fi(5)); ...
|
|---|
| 477 | x_Fi(1)*log(x_Fi(6)); ...
|
|---|
| 478 | x_Fi(2)^2; ...
|
|---|
| 479 | x_Fi(2)*x_Fi(3); ...
|
|---|
| 480 | x_Fi(2)*x_Fi(4); ...
|
|---|
| 481 | x_Fi(2)*log(x_Fi(5)); ...
|
|---|
| 482 | x_Fi(2)*log(x_Fi(6)); ...
|
|---|
| 483 | x_Fi(3)^2; ...
|
|---|
| 484 | x_Fi(3)*x_Fi(4); ...
|
|---|
| 485 | x_Fi(3)*log(x_Fi(5)); ...
|
|---|
| 486 | x_Fi(3)*log(x_Fi(6)); ...
|
|---|
| 487 | x_Fi(4)^2; ...
|
|---|
| 488 | x_Fi(4)*log(x_Fi(5)); ...
|
|---|
| 489 | x_Fi(4)*log(x_Fi(6)); ...
|
|---|
| 490 | ];
|
|---|
| 491 | end
|
|---|
| 492 |
|
|---|
| 493 | function [val_Fi] = matrixFi(x_Fi)
|
|---|
| 494 | val_Fi = [ ...
|
|---|
| 495 | ones(1, N); ... %1
|
|---|
| 496 | x_Fi(1, :); ... %Xi pro 1-4
|
|---|
| 497 | x_Fi(2, :); ...
|
|---|
| 498 | x_Fi(3, :); ...
|
|---|
| 499 | x_Fi(4, :); ...
|
|---|
| 500 | log(x_Fi(5, :)); ... %ln Xi pro 5-8 tj diagonala matice Pt 4x4
|
|---|
| 501 | log(x_Fi(6, :)); ...
|
|---|
| 502 | x_Fi(1, :).^2; ... %kvadraticke cleny jen v Xi 1-4 a kombinovane
|
|---|
| 503 | x_Fi(1, :).*x_Fi(2, :); ...
|
|---|
| 504 | x_Fi(1, :).*x_Fi(3, :); ...
|
|---|
| 505 | x_Fi(1, :).*x_Fi(4, :); ...
|
|---|
| 506 | x_Fi(1, :).*log(x_Fi(5, :)); ...
|
|---|
| 507 | x_Fi(1, :).*log(x_Fi(6, :)); ...
|
|---|
| 508 | x_Fi(2, :).^2; ...
|
|---|
| 509 | x_Fi(2, :).*x_Fi(3, :); ...
|
|---|
| 510 | x_Fi(2, :).*x_Fi(4, :); ...
|
|---|
| 511 | x_Fi(2, :).*log(x_Fi(5, :)); ...
|
|---|
| 512 | x_Fi(2, :).*log(x_Fi(6, :)); ...
|
|---|
| 513 | x_Fi(3, :).^2; ...
|
|---|
| 514 | x_Fi(3, :).*x_Fi(4, :); ...
|
|---|
| 515 | x_Fi(3, :).*log(x_Fi(5, :)); ...
|
|---|
| 516 | x_Fi(3, :).*log(x_Fi(6, :)); ...
|
|---|
| 517 | x_Fi(4, :).^2; ...
|
|---|
| 518 | x_Fi(4, :).*log(x_Fi(5, :)); ...
|
|---|
| 519 | x_Fi(4, :).*log(x_Fi(6, :)); ...
|
|---|
| 520 | ];
|
|---|
| 521 |
|
|---|
| 522 | end
|
|---|
| 523 |
|
|---|
| 524 | function [val_Fi] = difFi(x_Fi)
|
|---|
| 525 | val_Fi = [ ...
|
|---|
| 526 | 0 0 0 0 0 0; ...1
|
|---|
| 527 | 1 0 0 0 0 0; ...2
|
|---|
| 528 | 0 1 0 0 0 0; ...3
|
|---|
| 529 | 0 0 1 0 0 0; ...4
|
|---|
| 530 | 0 0 0 1 0 0; ...5
|
|---|
| 531 | 0 0 0 0 1/x_Fi(5) 0; ...6
|
|---|
| 532 | 0 0 0 0 0 1/x_Fi(6); ...7
|
|---|
| 533 | 2*x_Fi(1) 0 0 0 0 0; ...8
|
|---|
| 534 | x_Fi(2) x_Fi(1) 0 0 0 0; ...9
|
|---|
| 535 | x_Fi(3) 0 x_Fi(1) 0 0 0; ...10
|
|---|
| 536 | x_Fi(4) 0 0 x_Fi(1) 0 0; ...11
|
|---|
| 537 | log(x_Fi(5)) 0 0 0 x_Fi(1)/x_Fi(5) 0; ...12
|
|---|
| 538 | log(x_Fi(6)) 0 0 0 0 x_Fi(1)/x_Fi(6); ...13
|
|---|
| 539 | 0 2*x_Fi(2) 0 0 0 0; ...14
|
|---|
| 540 | 0 x_Fi(3) x_Fi(2) 0 0 0; ...15
|
|---|
| 541 | 0 x_Fi(4) 0 x_Fi(2) 0 0; ...16
|
|---|
| 542 | 0 log(x_Fi(5)) 0 0 x_Fi(2)/x_Fi(5) 0; ...17
|
|---|
| 543 | 0 log(x_Fi(6)) 0 0 0 x_Fi(2)/x_Fi(6); ...18
|
|---|
| 544 | 0 0 2*x_Fi(3) 0 0 0; ...19
|
|---|
| 545 | 0 0 x_Fi(4) x_Fi(3) 0 0; ...20
|
|---|
| 546 | 0 0 log(x_Fi(5)) 0 x_Fi(3)/x_Fi(5) 0; ...21
|
|---|
| 547 | 0 0 log(x_Fi(6)) 0 0 x_Fi(3)/x_Fi(6); ...22
|
|---|
| 548 | 0 0 0 2*x_Fi(4) 0 0; ...23
|
|---|
| 549 | 0 0 0 log(x_Fi(5)) x_Fi(4)/x_Fi(5) 0; ...24
|
|---|
| 550 | 0 0 0 log(x_Fi(6)) 0 x_Fi(4)/x_Fi(6); ...25
|
|---|
| 551 | ];
|
|---|
| 552 | end
|
|---|
| 553 |
|
|---|
| 554 | function [valvt] = Vtilde_dx_dx(kin)
|
|---|
| 555 | if(kin == K)
|
|---|
| 556 | valvt = h_beldxdx;
|
|---|
| 557 | else
|
|---|
| 558 | valvt = Wv(8, kin)*diag([2 0 0 0]) +...
|
|---|
| 559 | Wv(9, kin)*[0 1 0 0; 1 0 0 0; 0 0 0 0; 0 0 0 0] +...
|
|---|
| 560 | Wv(10, kin)*[0 0 1 0; 0 0 0 0; 1 0 0 0; 0 0 0 0] +...
|
|---|
| 561 | Wv(11, kin)*[0 0 0 1; 0 0 0 0; 0 0 0 0; 1 0 0 0] +...
|
|---|
| 562 | Wv(14, kin)*diag([0 2 0 0]) +...
|
|---|
| 563 | Wv(15, kin)*[0 0 0 0; 0 0 1 0; 0 1 0 0; 0 0 0 0] +...
|
|---|
| 564 | Wv(16, kin)*[0 0 0 0; 0 0 0 1; 0 0 0 0; 0 1 0 0] +...
|
|---|
| 565 | Wv(19, kin)*diag([0 2 0 0]) +...
|
|---|
| 566 | Wv(20, kin)*[0 0 0 0; 0 0 0 0; 0 0 0 1; 0 0 1 0] +...
|
|---|
| 567 | Wv(23, kin)*diag([0 2 0 0]);
|
|---|
| 568 | end
|
|---|
| 569 | end
|
|---|
| 570 |
|
|---|
| 571 | function [c, ceq, GC, GCeq] = Cond2(x)
|
|---|
| 572 | c = x(1)*x(1) + x(2)*x(2) - cC1^2;
|
|---|
| 573 | ceq = [];
|
|---|
| 574 | GC = [2*x(1); 2*x(2)];
|
|---|
| 575 | GCeq = [];
|
|---|
| 576 | end
|
|---|
| 577 |
|
|---|
| 578 | function [x_ret] = fceG(x_in, u_in)
|
|---|
| 579 | x_ret = zeros(4, 1);
|
|---|
| 580 | x_ret(1) = Ca * x_in(1) + Cb * x_in(3) * sin(x_in(4)) + Cc * u_in(1);
|
|---|
| 581 | x_ret(2) = Ca * x_in(2) - Cb * x_in(3) * cos(x_in(4)) + Cc * u_in(2);
|
|---|
| 582 | x_ret(3) = Cd * x_in(3) + Ce * (x_in(2) * cos(x_in(4)) - x_in(1) * sin(x_in(4)));
|
|---|
| 583 | x_ret(4) = x_in(4) + x_in(3) * DELTAt;
|
|---|
| 584 | end
|
|---|
| 585 |
|
|---|
| 586 | function [y_ret] = fceH(x_in)
|
|---|
| 587 | y_ret = zeros(2, 1);
|
|---|
| 588 | y_ret(1) = x_in(1);
|
|---|
| 589 | y_ret(2) = x_in(2);
|
|---|
| 590 | end
|
|---|
| 591 |
|
|---|
| 592 | end
|
|---|
