tina
Hallo Johan,
for k = 1:N
objective = objective + ((c_p1*z{k} + c_p2 + c_n1*(u{k}(1)-z{k})*0.3108 - u{k}(2)*vp_inv{k})*d1 + d0{k})^2 + beta*(c_p1*z{k} + c_p2 + c_n1*(u{k}(1)-z{k})*0.3108)^2 + rho*(u{k}(1)-U_L{k})^2;
constraints = [constraints, x{k+1}(1) == a*x{k}(1) + b_T*u{k}(1) + disturbance{k}];
constraints = [constraints, x{k+1}(2) == x{k}(2) - c{k}*u{k}(2)];
constraints = [constraints, U1_min{k} <= u{k}(1) <= U1_max{k}];
constraints = [constraints, X1_min{k} <= x{k}(1) <= X1_max{k}];
constraints = [constraints, U2_min <= u{k}(2) <= U2_max];
constraints = [constraints, X2_min <= x{k}(2) <= X2_max];
constraints = [constraints, z{k} >= max(u{k}(1),0)];
constraints = [constraints, c_p1*z{k} + c_p2 + c_n1*(u{k}(1)-z{k})*0.3108 - u{k}(2)*vp_inv{k}>= 0];
end
X = [x{:}];
constraints = [constraints, sum(X(1,:)) >= v2sum];As above the codes are the cost function and
constraints.
Enclosed you can find the two optimal trajectories under two situations. As
respect to them I have two questions.
1 For the first optimal trajectory there is a protruding and then the value of
the trajectory falls back, which locates when the lower constraints of x2
is reached. Is it because of the shape of the parabola of the cost function? But why does the trajectory
fall down back?
2 This trajectory has oscillation. But when the value of the trajectory is
higher (giving larger value for v2sum in the last constraint), the oscillation
will disappear. Is it something to do with the system dynamics and the big
sampling time making the error, which in the near of the bottom of the parabola
makes the optimal solution with oscillation? But when I largely change the
sampling time there is still oscillation.
I'm sorry that I can't give the eproducible code.
Thank you very much!
Liting
