why in graph in my lqr inversely proportional, one graph minus, one graph plus and why there is two graph zero not moving?

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Ivan Dwi Putra 2020-6-19

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/551026-why-in-graph-in-my-lqr-inversely-proportional-one-graph-minus-one-graph-plus-and-why-there-is-two

关闭： MATLAB Answer Bot 2021-8-20

lqrtry2.png

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this is my code

function dx = trainmodelcontrol(t,x)
%Parameter Massa
m1 = 8095; % massa train set 1 dalam kg
m2 = 8500; % massa train set 2 dalam kg
% %Parameter Gaya
% f1 = 205.10^3; % dalam N
% f2 = 302.10^3; % dalam N
c_0_1 = 0.01176;
c_1_1 = 0.00077616;
c_2_1 = 4.48 ;
c_0_2 = 0.01176 ;
c_1_2 = 0.00077616;
c_2_2 = 4.48;
v_0 = 300;
hstar = 120;
a_1   = -1./m1.*(c_1_1 + 2.*c_2_1.*v_0);  
a_2   = -1./m2.*(c_1_2 + 2.*c_2_2.*v_0); 
a_1_head = 1-(a_1.*hstar);
a_2_head = 1-(a_2.*hstar);
b = 1;
p_1 = -1./m1.*(c_0_1 - c_2_1.*(v_0).^2);
p_2 = -1./m2.*(c_0_2 - c_2_2.*(v_0).^2);
x = [x(1);x(2);x(3);x(4)];
A = [0  a_1_head      0        0;
     0     0          0        0;
     0 (a_2_head - 1) 0 a_2_head;
     0      0         0        0
     ];
 
B = [-b.*hstar         0;
      b                0;
      0        -b.*hstar;
     -b                b
     ];
 
% U_t = [f1; f2;];
W = [((a_1 - 1).*v_0) - (p_1.*hstar);
     0;
     ((a_2 - 1).*v_0) - (p_2.*hstar);
     ((a_1 - 1).*v_0) - (p_1.*hstar);
     ];
Q = [990 0 0 0;
     0 490 0 0;
     0 0 990 0;
     0 0 0 590;];
   
R = [550 295;
     295 550;];
   
K = lqr(A,B,Q,R); 
U_t = -(K*x);
 
dx = (A*x) + (B*U_t) + W;
end

and this is the code fr simulation

clear all, close all
tspan = [0:1:100];
x0 = [0; 0; 10; 0];
[t,x] = ode45(@trainmodelcontrol,tspan,x0);
plot(t,x)
legend('x1','x2','x3','x4')
title('Non Linear Model')
xlabel('Waktu(s)')
ylabel('Jarak(m)')
figure(2)
subplot(2,1,1);
hax1 = plot(t,x(:,1),t,x(:,3))
title('Posisi Rangkaian Kereta')
xlabel('Waktu(s)')
ylabel('Jarak(m)')
legend('x_1','x_3')
subplot(2,1,2);
hax2 = plot(t,x(:,2),t,x(:,4))
title('Kecepatan Rangkaian Kereta')
xlabel('Waktu(s)')
ylabel('Kecepatan(m/s)')
legend('x_2','x_4')