Математическая модель в пространстве состояний линейного стационарного объекта управления

% Приведение системы

b0 = b_0/a_5;

b1 = b_1/a_5;

a5 = a_5/a_5;

a4 = a_4/a_5;

a3 = a_3/a_5;

a2 = a_2/a_5;

a1 = a_1/a_5;

a0 = a_0/a_5;

% ------------------------------------------------------------------------%

% ------------------------------------------------------------------------%

% Представление системы в пространстве состояний

A = [0 1 0 0 0;

0 0 1 0 0;

0 0 0 1 0

0 0 0 0 1;

-a0 -a1 -a2 -a3 -a4];

B = [0; 0; 0; 0; 1];

C = [b0 b1 0 0 0];

% Начальные условия

X_0 = [10; 0; 6; 4; 8];

Time = 45;

Kolvo_intervalov = 3;

h = 0.01;

H = 0.8;

% ------------------------------------------------------------------------%

% ------------------------------------------------------------------------%

% Получение max значений из файла

load Sostoyaniya X_max U_max

% ------------------------------------------------------------------------%

% Нахождение элементов матриц Q и R

r(1) = 100;

q(1) = 1/poryadok * r(1) * (U_max)^2 / (X_max(1))^2;

for i = 2 : poryadok

q(i) = q(1) * (X_max(1))^2 / (X_max(i))^2;

end

Q = diag(q);

R = diag(r);

% Для изменения коэффициентов

% Q(1,1) = Q(1,1)*1e+13;

% Q(2,2) = Q(2,2)*1e+10;

% Q(3,3) = Q(3,3)*1e+8;

% Q(4,4) = Q(4,4)*1e+5;

% Q(5,5) = Q(5,5)*1e+2;

R(1,1) = R(1,1);

% ------------------------------------------------------------------------%

% ------------------Скользящие интервалы----------------------------------%

shag = Time/Kolvo_intervalov;

Time1 = shag

Time2 = 2*shag

Time3 = Time

% ------------------------------------------------------------------------%

P_nach = zeros(poryadok, poryadok);%+ones(poryadok, poryadok);

% ------------------------------------------------------------------------%

% Решение уравнения Риккати методом обратного интегрирования

P = Solve_Riccati_Method_Revers_Integr(A,B,Q,R,Time1,poryadok, P_nach);

load Solve_Riccati_Method_Revers_Integr_for_slegenie Time_R P N_str

PP = P;

for k = 1 : N_str

P1 = reshape(PP(k, :), poryadok, poryadok);

for i = 1 : poryadok

for j = 1 : poryadok

P2(i,j,k) = P1(i,j);

end

end

end

size_P = size(P2)

% ------------------------------------------------------------------------%

% Нахождение переменных коэффициентов регулятора

for k = 1 : N_str

K_o(k, :) = -inv(R) * B' * P2(:,:,k);

K_pr(k, :) = -inv(R) * B';

end

% ------------------------------------------------------------------------%

tic

% 1 интервал

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Solve_Interval(P_nach, N_str, h, P2, A,B,Q,R, 0, Time1, X_0, poryadok, K_o, K_pr);

load Solve_Interval time_X X u X_o_discrete

time_X1 = time_X;

X1 = X;

u1 = u;

X_o_discrete1 = X_o_discrete;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% 2 интервал

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Solve_Interval(P_nach, N_str, h, P2, A,B,Q,R, Time1, Time2, X1(:,N_str), poryadok, K_o, K_pr);

load Solve_Interval time_X X u X_o_discrete

time_X2 = time_X;

X2 = X;

u2 = u;

X_o_discrete2 = X_o_discrete;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% 3 интервал

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Solve_Interval(P_nach, N_str, h, P2, A,B,Q,R, Time2, Time3, X2(:,N_str), poryadok, K_o, K_pr);

load Solve_Interval time_X X u X_o_discrete

time_X3 = time_X;

X3 = X;

u3 = u;

X_o_discrete3 = X_o_discrete;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

toc

% ------------------------------------------------------------------------%

% Объединение интервалов

time_X = [time_X1 time_X2 time_X3];

u = [u1 u2 u3];

X = [X1 X2 X3];

X_o_discrete = [X_o_discrete1 X_o_discrete2 X_o_discrete3];

% ------------------------------------------------------------------------%

% ------------------------------------------------------------------------%

% Построение u(t) и X(t)

figure(3);

plot(time_X, u, 'r-','LineWidth', 2);

title ('u(t)');

xlabel('t')

hl=legend('u(t) - управление',0);

set(hl,'FontName','Courier');

grid on

figure(4);

plot(time_X, X(1,:),'r-', time_X, X_o_discrete(1,:), time_X, X_o_discrete(1,:)-0.8,'LineWidth', 2)

hold on

title ('x_1(t)');

xlabel('t');

hl=legend('X(t) - слежение','X_o(t) - эталон', 'уровень',0);

set(hl,'FontName','Courier');

grid on

figure(5);

plot(time_X, X(2,:),'r-', time_X, X_o_discrete(2,:), 'LineWidth', 2)

title ('x_2(t)');

xlabel('t');

hl=legend('X(t) - слежение','X_o(t) - эталон',0);

set(hl,'FontName','Courier');

grid on

figure(6);

plot(time_X, X(3,:),'r-', time_X, X_o_discrete(3,:), 'LineWidth', 2)

title ('x_3(t)');

xlabel('t');

hl=legend('X(t) - слежение','X_o(t) - эталон',0);

set(hl,'FontName','Courier');

grid on

figure(7);

plot(time_X, X(4,:),'r-', time_X, X_o_discrete(4,:), 'LineWidth', 2)

title ('x_4(t)');

xlabel('t');

hl=legend('X(t) - слежение','X_o(t) - эталон',0);

set(hl,'FontName','Courier');

grid on

figure(8);

plot(time_X, X(5,:),'r-', time_X, X_o_discrete(5,:), 'LineWidth', 2)

title ('x_5(t)');

xlabel('t');

hl=legend('X(t) - слежение','X_o(t) - эталон',0);

set(hl,'FontName','Courier');

grid on

function Solve_Interval(P_nach, N_str, h, P2, A,B,Q,R, T_nach, T_konech, X_0, poryadok, K_o, K_pr)

Zadayushee_Vozdeistvie_Discrete_Revers_Modern(h, T_nach, T_konech);

load Zadayushee_Vozdeistvie_Discrete_Revers X_o_discrete_rev

% ------------------------------------------------------------------------%

% Нахождение q(t)

for i = 1 : poryadok

qq = -P_nach(:,:,1) * X_o_discrete_rev(i,1);

q(i,1) = qq(i,1);

end

% Интегрирование q(t) в обратном времени

for k = 1 : N_str

q(:, k+1) = q(:, k) - h * ((P2(:,:,k)*B*inv(R)*B'-A') * q(:, k) + Q*X_o_discrete_rev(:,k));

end

q(:, k+1) = [];

size_q = size(q)

% ------------------------------------------------------------------------%

% Формирование вектора коэффициентов регулятора, значений задающего

% воздействия, значений вспомогательной функции в прямом порядке

K_pr_p = K_pr;

i = 1;

for j = N_str : -1 : 1

K_o_p(i,:) = K_o(j,:);

X_o_discrete(:,i) = X_o_discrete_rev(:,j);

q_pr(:, i) = q(:, j);

i = i + 1;

end

% ------------------------------------------------------------------------%

% ------------------------------------------------------------------------%

for k = 1 : N_str

A_(:,:,k) = A + B * K_o_p(k,:);

end

size_A_ = size(A_)

% ------------------------------------------------------------------------%

% ------------------------------------------------------------------------%

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