% main - hlavni skript
clear all;
% oznaceni: s ... system
%           k ... kalman (EKF)
%           l ... rizeni (LQR)

% KONSTANTY
T = 40000; %horizont
dt = 0.000125; %casovy krok

% Rs = 0.28;
% Ls = 0.003465;
% psipm = 0.1989;
% B = 0;    
% kp = 1.5;
% pp = 4.0;
% J = 0.04;

% Lq = 1.05*Ls;
% Ld = 0.95*Ls;

a = 0.9898;
b = 0.0072;
c = 0.0361;
d = 1.0;
e = 0.0149;

Ls = 0.003465;
psipm = 0.1989;

% ref_profile = [0, -1, 3, 6, 9, 6, 3, 0, 0, 0, 0, 0, 0,-3, -6, -3];%/9*200;
ref_profile = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];

%kovariance EKF na stavu
% Q_k = diag([0.001, 0.00001]);
% R_k = diag([0.015, 0.015]);
Q_k = diag([0.01, 0.0001]);
R_k = diag([0.15, 0.15]);

%hodnoty sumu v systemu
nQ = diag([0.0013, 0.0013, 5.0e-6, 1.0e-10]);
nR = diag([0.0006, 0.0006]);

iter_l = 10;% pocet iteraci ve vypoctu rizeni

% B_l = zeros(3,2);
% B_l = zeros(2,2);
% B_l(1,1) = c;
% B_l(2,2) = c;

Q_l = diag([1 0 0]);
% % Q_l = diag([0 0 1 0 0]);
r = 0.01;
R_l = diag([r, r]);

% PROMENNE
x_s = zeros(4,T); %stav
y_s = zeros(2,T); %mereni
x_k = zeros(2,T); %odhad stavu
P_k = zeros(2); %kovariance stavu
u_l = zeros(2,T); %rizeni
% S_l = zeros(3); %jadro ztraty
S_l = zeros(2);

% POCATECNI HODNOTY
noise = 1; %prepinac sumu
% noise = 0;

theta0 = 1.5;%1.7; %pocatecni poloha
P0 = eye(2); %odhad pocatecni kovariance stavu (apriorni)
% ST = zeros(3); %koncova ztrata
ST = ones(3);


% INICIALIZACE
x_s(4,1) = theta0;
% x_s(3,1) = 5;
P_k = P0;
S_l = ST;

ref_ome = zeros(1, T);  
    for k = 1:T,
           index = floor(k*dt);
           if(index>0)
               lower = ref_profile(index);
           else
               lower = 0;
           end
           if(index<T*dt)
               upper = ref_profile(index+1);
           else
               upper = 0;
           end
           ref_ome(k) = lower + (upper-lower)*dt*(k-index/dt);
    end
% ref_ome = 0*ones(1, T);

% Derivace pro prvni EKF 
ome = x_k(1,1);
the = x_k(2,1);    
ia = y_s(1,1);
ib = y_s(2,1);
A = [d, -e*(ia*cos(the)+ib*sin(the)); dt, 1.0];
C = [b*sin(the), b*ome*cos(the); -b*cos(the), b*ome*sin(the)];


ri = 0.0001;
ai = (1-a*a)/c/c;
Si = (1 - ai*r + sqrt((ai*r-1)^2+4*r/c/c))/2;
Li = a*c*Si/(c*c*Si+ri);
    
A_l = [d,0,0;dt,1,dt;0,0,1];
% B_l = zeros(2);
% % A_l = [a 0 0 0 0; 0 a 0 0 0; 0 0 d 0 (d-1); 0 0 dt 1 dt; 0 0 0 0 1];
% % B_l = zeros(5,2);
% % B_l(1:2,1:2) = [c 0;0 c];

%PI vektorove
% kon_pi = 3.0;
% kon_ii = 0.00375;
% kon_pu = 20.0;
% kon_iu = 0.05;
% sum_iq = 0;
% sum_ud = 0;
% sum_uq = 0;



% HLAVNI SMYCKA
for t = 1:T-1,
    % EKF      
    Pp = A*P_k*A' + Q_k;
    S = C*Pp*C' + R_k;
    K = Pp*C'/S;
    P_k = Pp - K*C*Pp;    
    
    xp = zeros(2,1);
    xp(1) = d*x_k(1,t) + e*(y_s(2,t)*cos(x_k(2,t)) - y_s(1,t)*sin(x_k(2,t)));
    xp(2) = x_k(2,t) + dt*x_k(1,t);    
    yp = zeros(2,1);
    yp(1) = a*y_s(1,t) + b*x_k(1,t)*sin(x_k(2,t)) + c*u_l(1,t);
    yp(2) = a*y_s(2,t) - b*x_k(1,t)*cos(x_k(2,t)) + c*u_l(2,t);
    
    x_k(:,t+1) = xp + K*(y_s(:,t) - yp);
    
    %!!!
%     tmp = x_k(:,t+1);
%     x_k(:,t+1) = x_s(3:4,t);
    
    % Derivace    
    ome = x_k(1,t+1);
    the = x_k(2,t+1);    
    ia = y_s(1,t);
    ib = y_s(2,t);
    A = [d, -e*(ia*cos(the)+ib*sin(the)); dt, 1.0];
    C = [b*sin(the), b*ome*cos(the); -b*cos(the), b*ome*sin(the)];
    
%     id = ia*cos(the) + ib*sin(the);
%     iq = ib*cos(the) - ia*sin(the);
    
    % LQ
%     phi = zeros(2,1);
%     phi(1) = d*x_k(1,t+1) + e*(y_s(2,t)*cos(x_k(2,t+1)) - y_s(1,t)*sin(x_k(2,t+1)));
%     phi(2) = x_k(2,t+1) + dt*x_k(1,t+1);
%     y = x_k(:,t+1);
%     y(1) = y(1) - ref_ome(t);
%     A_l = zeros(3);
%     A_l(1:2,1:2) = A;
%     A_l = A;
%     A_l(1,2) = 0;
%     A_l(1:2,3) = phi - A*y;
%     A_l(3,3) = 1;
    B_l = [-e*sin(the), e*cos(the); 0, 0; 0,0];
    y = [(ome-ref_ome(t)); the; ref_ome(t)];
% %     y = [ia; ib; (ome-ref_ome(t)); the; ref_ome(t)];    
% %     A_l(1, 3) = b*sin(the);
% %     A_l(2, 3) = -b*cos(the);
% %     A_l(1, 5) = b*sin(the);
% %     A_l(2, 5) = -b*cos(the);
% %     A_l(3, 1) = -e*sin(the);
% %     A_l(3, 2) = e*cos(the);
    for i = 1:iter_l
       S_l = A_l'*(S_l - S_l*B_l/(B_l'*S_l*B_l + R_l)*B_l'*S_l)*A_l + Q_l;
    end
    L = (B_l'*S_l*B_l + R_l)\B_l'*S_l*A_l;    
%     yref = -L*y;%referencni proudy
%     u_l(:,t+1) = b/c*ome*[-sin(the);cos(the)] + yref/c - Li*y_s(:,t);
    
%     sum_iq = sum_iq + ref_ome(t) - ome;
%     ref_iq = kon_pi*(ref_ome(t) - ome) + kon_ii*sum_iq;
%     sum_ud = sum_ud - id;
%     u_d = kon_pu*(-id) + kon_iu*sum_ud;
%     sum_uq = sum_uq + ref_iq - iq;
%     u_q = kon_pu*(ref_iq - iq) + kon_iu*sum_uq;
%     u_d = u_d - Ls*ome*ref_iq;
%     u_q = u_q + psipm*ome;
%        
%     u_l(1, t+1) = u_d*cos(the) - u_q*sin(the);
%     u_l(2, t+1) = u_q*cos(the) + u_d*sin(the);
%     u_l(:,t+1) = b/c*ome*[-sin(the);cos(the)] + yref/c*[sin(the);-cos(the)] - Li*y_s(:,t);

%     u_l(:,t+1) = yref/c - Li*y_s(:,t);
%     u_l(:,t+1) = -L*[y;1];
    u_l(:,t+1) = -L*y + b/c*ome*[-sin(the);cos(the)] - Li*y_s(:,t);
    if u_l(1,t+1) > 100
        u_l(1,t+1) = 100;
    elseif u_l(1,t+1) < -100
        u_l(1,t+1) = -100;
    end
    if u_l(2,t+1) > 100
        u_l(2,t+1) = 100;
    elseif u_l(2,t+1) < -100
        u_l(2,t+1) = -100;
    end
%     u_l(:,t+1) = 0;
    % Vyvoj systemu
    [x_s(:,t+1), y_s(:,t+1)] = evolSys(x_s(:,t), u_l(:,t+1), nQ, nR, noise);
    
    %!!!
%     x_k(:,t+1) = tmp;
end

figure;
subplot(2,1,1);
plot(1:T,x_k(1,:),1:T,x_s(3,:),1:T,ref_ome);
subplot(2,1,2);
plot(1:T,atan2(sin(x_k(2,:)),cos(x_k(2,:))),1:T,atan2(sin(x_s(4,:)),cos(x_s(4,:))));