183742 (Математическая модель в пространстве состояний линейного стационарного объекта управления), страница 9
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Документ из архива "Математическая модель в пространстве состояний линейного стационарного объекта управления", который расположен в категории "". Всё это находится в предмете "экономико-математическое моделирование" из , которые можно найти в файловом архиве . Не смотря на прямую связь этого архива с , его также можно найти и в других разделах. Архив можно найти в разделе "курсовые/домашние работы", в предмете "экономико-математическое моделирование" в общих файлах.
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end
size_u = size(u)
% ------------------------------------------------------------------------%
toc
% Построение u(t) и X(t)
figure(5);
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(6);
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(7);
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(8);
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(9);
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(10);
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
AKOR_slegenie_so_skolz_intervalami_Modern.m
function AKOR_slegenie_so_skolz_intervalami_Modern
clc
clear all
close all
poryadok = 5;
% ------------------------------------------------------------------------%
b_0 = 5;
b_1 = 9;
% Укороченная система данного объекта
a_5 = 0.1153;
a_4 = 1.78;
a_3 = 3.92;
a_2 = 14.42;
a_1 = 8.583;
a_0 = 0;
% ------------------------------------------------------------------------%
% 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_)
% ------------------------------------------------------------------------%
% ------------------------------------------------------------------------%
% Нахождение фазовых координат
X(:,1) = X_0;
time_X(1) = T_nach;
for k = 1 : N_str
X(:, k+1) = X(:, k) + h * (A_(:,:,k) * X(:, k) + B * K_pr_p(k,:) * q_pr(:,k));
time_X(k+1) = time_X(k) + h;
end
X(:, k+1) = [];
time_X(k+1) = [];
size_X = size(X)
% ------------------------------------------------------------------------%
% ------------------------------------------------------------------------%
% Нахождение управления
for k = 1 : N_str
u(k) = K_o_p(k,:) * X(:,k) + K_pr_p(k,:) * q_pr(:,k);
end
size_u = size(u)
save Solve_Interval time_X X u X_o_discrete
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Sintez_nablyud_polnogo_poryadka.m
clc
clear all
close all
poryadok = 5;
% ------------------------------------------------------------------------%
b_0 = 5;
b_1 = 9;
% Укороченная система данного объекта
a_5 = 0.1153;
a_4 = 1.78;
a_3 = 3.92;
a_2 = 14.42;
a_1 = 8.583;
a_0 = 0;
% ------------------------------------------------------------------------%
% 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 = 10;
% ------------------------------------------------------------------------%
% ------------------------------------------------------------------------%
% 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);
Q(2,2) = Q(2,2);
Q(3,3) = Q(3,3);
Q(4,4) = Q(4,4);
Q(5,5) = Q(5,5);
% Q(1,1) = Q(1,1)*1e+12;
% Q(2,2) = Q(2,2)*1e+8;
% Q(3,3) = Q(3,3)*1e+7;
% Q(4,4) = Q(4,4)*1e+0;
% Q(5,5) = Q(5,5)*1e+2;
R(1,1) = R(1,1);
% ------------------------------------------------------------------------%
P_nach = zeros(poryadok, poryadok);%+ones(poryadok, poryadok);
% ------------------------------------------------------------------------%
% Решение уравнения Риккати методом обратного интегрирования
P1 = Solve_Riccati_Method_Revers_Integr(A,B,Q,R,Time,poryadok, P_nach)
% ------------------------------------------------------------------------%
% Построение графика коэффициентов регулятора
load Solve_Riccati_Method_Revers_Integr Time_R P N_str
PP = P;
for i = 1 : N_str
P = reshape(PP(i, :), poryadok, poryadok);
K(i, :) = -inv(R)*B'*P;
end
figure(2)
plot(Time_R,K(:,1),'-',Time_R,K(:,2),'-',Time_R,K(:,3),'-',Time_R,K(:,4),'-',Time_R,K(:,5),'-', 'LineWidth', 2);
xlabel('t')
