Discrit time simulation for a LQR control doesn’t follow reference
Hi!
I’m trying to make a simulation for a discret time LQR control, the model is an inverted pendulum. The simulation doesn’t follow the referecenses. What to do?
Simulink model:
"Sistem discret" subsystem:
"Controller DtT1" subsystem:
Scope:
Matlab code:
clc
clear all
close all
%% parametrii modelelului 2
Mp = 0.272;
dM = 0.071;
g = 9.81;
J = 0.002;
Jw = 3.941*10^-5;
b_theta = 0.82*10^-3;
b_altha_kmke_Ra = 1.202*10^-4;
km_Ra = 1.837*10^-4;
%% matricea modelului spatial
A = [0 1 0 0;
(Mp*dM*g)/J -(b_theta)/J 0 1/J*b_altha_kmke_Ra;
0 0 0 1;
-(Mp*g*dM)/J b_theta/J 0 -(J+Jw)/(J*Jw)*b_altha_kmke_Ra];
B = [0 0;
-1/J*km_Ra 1/J;
0 0;
(J+Jw)/(J*Jw)*km_Ra -1/J];
C = [1 0 0 0;
0 1 0 0;
0 0 1 0;
0 0 0 1];
D = [0 0; 0 0;0 0;0 0];
%% construirea sistemului
sys = ss(A,B,C,0);
xd = [50;0;200;0]; %desired conditions
x0 = 1*randn(4,1); %initial conditions
%% Discretizare
Ts = 0.1;
sys_d = c2d(sys,Ts);
Ad = sys_d.a;
Bd = sys_d.b;
Cd = sys_d.c;
Dd = sys_d.d;
Q = [100 0 0 0;
0 100 0 0;
0 0 10 0;
0 0 0 1];
Rd = eye(size(B, 2));
K_d = dlqr(Ad,Bd,Q,Rd,N);Hi!
I’m trying to make a simulation for a discret time LQR control, the model is an inverted pendulum. The simulation doesn’t follow the referecenses. What to do?
Simulink model:
"Sistem discret" subsystem:
"Controller DtT1" subsystem:
Scope:
Matlab code:
clc
clear all
close all
%% parametrii modelelului 2
Mp = 0.272;
dM = 0.071;
g = 9.81;
J = 0.002;
Jw = 3.941*10^-5;
b_theta = 0.82*10^-3;
b_altha_kmke_Ra = 1.202*10^-4;
km_Ra = 1.837*10^-4;
%% matricea modelului spatial
A = [0 1 0 0;
(Mp*dM*g)/J -(b_theta)/J 0 1/J*b_altha_kmke_Ra;
0 0 0 1;
-(Mp*g*dM)/J b_theta/J 0 -(J+Jw)/(J*Jw)*b_altha_kmke_Ra];
B = [0 0;
-1/J*km_Ra 1/J;
0 0;
(J+Jw)/(J*Jw)*km_Ra -1/J];
C = [1 0 0 0;
0 1 0 0;
0 0 1 0;
0 0 0 1];
D = [0 0; 0 0;0 0;0 0];
%% construirea sistemului
sys = ss(A,B,C,0);
xd = [50;0;200;0]; %desired conditions
x0 = 1*randn(4,1); %initial conditions
%% Discretizare
Ts = 0.1;
sys_d = c2d(sys,Ts);
Ad = sys_d.a;
Bd = sys_d.b;
Cd = sys_d.c;
Dd = sys_d.d;
Q = [100 0 0 0;
0 100 0 0;
0 0 10 0;
0 0 0 1];
Rd = eye(size(B, 2));
K_d = dlqr(Ad,Bd,Q,Rd,N); Hi!
I’m trying to make a simulation for a discret time LQR control, the model is an inverted pendulum. The simulation doesn’t follow the referecenses. What to do?
Simulink model:
"Sistem discret" subsystem:
"Controller DtT1" subsystem:
Scope:
Matlab code:
clc
clear all
close all
%% parametrii modelelului 2
Mp = 0.272;
dM = 0.071;
g = 9.81;
J = 0.002;
Jw = 3.941*10^-5;
b_theta = 0.82*10^-3;
b_altha_kmke_Ra = 1.202*10^-4;
km_Ra = 1.837*10^-4;
%% matricea modelului spatial
A = [0 1 0 0;
(Mp*dM*g)/J -(b_theta)/J 0 1/J*b_altha_kmke_Ra;
0 0 0 1;
-(Mp*g*dM)/J b_theta/J 0 -(J+Jw)/(J*Jw)*b_altha_kmke_Ra];
B = [0 0;
-1/J*km_Ra 1/J;
0 0;
(J+Jw)/(J*Jw)*km_Ra -1/J];
C = [1 0 0 0;
0 1 0 0;
0 0 1 0;
0 0 0 1];
D = [0 0; 0 0;0 0;0 0];
%% construirea sistemului
sys = ss(A,B,C,0);
xd = [50;0;200;0]; %desired conditions
x0 = 1*randn(4,1); %initial conditions
%% Discretizare
Ts = 0.1;
sys_d = c2d(sys,Ts);
Ad = sys_d.a;
Bd = sys_d.b;
Cd = sys_d.c;
Dd = sys_d.d;
Q = [100 0 0 0;
0 100 0 0;
0 0 10 0;
0 0 0 1];
Rd = eye(size(B, 2));
K_d = dlqr(Ad,Bd,Q,Rd,N); matlab, simulink, equation, control, lqr, state-space, discret time MATLAB Answers — New Questions
