Hi,
I writing a matlab mfile code to generate an optimal control for my system so that the system state variables will follow a tracking reference r(t)= t^2,
Since this is a linear quadratic tracking problem, I need to use ode45 to generate the control u at each time step with respect to time
This is my main script:
%% System Parameters
%
global a b p q R T ST VT x0 % global all parameters
a = 1; % system A matrix
b = 1; % system B matrix
p = 10; % final time weight value
q = 5; % tracking weight value
R = 2; % control effort
T = 20; % final time (seconds)
x0 = 3; % initial condition x(t0)=3
%
%% System Model and Boundry Conditions
% since the system is scalar, we use scalar functions for table 4.1-1
%
ST = p; % S(T)=p
T = 20; % final time (secs)
tspan = 0:1:T; % define time span
syms t; % define t as a variable
r(t) = t^2; % define tracking function
VT = p*r(T); %V(T) = p*r(T)
sysc = ss(a, b ,0, 0); % generate the system
% plot (r(tspan)) %generate r(t) plot
% hold on
% grid on
%
%% Simulation (backwards in time)
%
[tor yb] = ode45(@q1fcn1,[0 T],[ST, VT]);
This is my ode function script:
function dyb = q1fcn1(tor, yb)
dyb = zeros(2,1);
global a b p q R T ST VT x0 % global all parameters
a = 1; % system A matrix
b = 1; % system B matrix
p = 10; % final time weight value
q = 5; % tracking weight value
R = 2; % control effort
ST = p; % S(T)=p
T = 20; % final time (secs)
tspan = 0:1:T; % define time span
syms t; % define t as a variable
r(t) = t^2; % define tracking function
VT = p*r(T); %V(T) = p*r(T)
S = yb(1);
V = yb(2);
dS = -(2*a*S-((b^2)*(S^2))/R+q);
dV = -(((a-(b^2)*S)/R)*V+q*r(tspan));
dyb(1)=S;
dyb(2)=V;
end
I know something is off, but after some searching online, I still have no idea which part in my ode fuction got wrong.
Thank you very much in advance for any help I get.
