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function [T,y,u,Iterations] = ppp_qp_sim (A,B,C,D,A_u,A_w,t,Q, Tau_u,Min_u,Max_u,Order_u, Tau_y,Min_y,Max_y,Order_y, W,x_0,Delta_ol,mu,movie)
function [T,y,u,X,Iterations] = ppp_qp_sim (A,B,C,D,A_u,A_w,t,Q, Tau_u,Min_u,Max_u,Order_u, Tau_y,Min_y,Max_y,Order_y, W,x_0,Delta_ol,mu,movie)
## usage: [T,y,u,J] = ppp_qp_sim (A,B,C,D,A_u,A_w,t,Q, Tau_u,Min_u,Max_u,Order_u, Tau_y,Min_y,Max_y,Order_y, W,x_0,movie)
## Needs documentation - see ppp_ex11 for example of use.
## OUTPUTS
## T: Time vector
## y,u,J output, input and cost
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## Set up various time vectors
dt = t(2)-t(1); # Time increment
## Make sure Delta_ol is multiple of dt
Delta_ol = floor(Delta_ol/dt)*dt;
if Delta_ol>0 # Intermittent control
T_ol = 0:dt:Delta_ol-dt; # Create the open-loop time vector
T_ol = 0:dt:Delta_ol; # Create the open-loop time vector
else
T_ol = 0;
T_ol = [0,dt];
Delta_ol = dt;
endif
## Discrete-time system
csys = ss2sys(A,B,C,D);
dsys = c2d(csys,dt);
[Ad, Bd] = sys2ss(dsys);
# ## Discrete-time system
# csys = ss2sys(A,B,C,D);
# dsys = c2d(csys,dt);
# [Ad, Bd] = sys2ss(dsys)
x = x_0; # Initialise state
## Initialise the saved variable arrays
X = [];
u = [];
Iterations = [];
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## Output constraints
[Gamma_y,gamma_y] = ppp_output_constraint (A,B,C,D,x,A_u,Tau_y,Min_y,Max_y,Order_y);
## Composite constraints
Gamma = [Gamma_u; Gamma_y];
gamma = [gamma_u; gamma_y];
## Compute U(t)
## Compute U(t) via QP optimisation
[uu, U, iterations] = ppp_qp (x,W,J_uu,J_ux,J_uw,Us0,Gamma,gamma,mu); # Compute U
## Simulation loop
## OL Simulation (exact)
i_ol = 0;
for t_ol=T_ol # Inner loop at dt
## Compute ol control
i_ol = i_ol+1;
range = (i_ol-1)*n_U + 1:i_ol*n_U; # Extract current U*
ut = Ustar_ol(:,range)*U; # Compute OL control (U* U)
## Simulate the system
i = i+1;
X = [X x]; # Save state
u = [u ut]; # Save input
Iterations = [Iterations iterations]; # Save iteration count
x = Ad*x + Bd*ut; # System
# if movie # Plot the moving horizon
# tau = T(1:n_T-i); # Tau with moving horizon
# tauT = T(i+1:n_T); # Tau with moving horizon + real time
# [ys,us,xs,xu,AA] = ppp_ystar (A,B,C,D,x,A_u,U,tau); # OL response
# plot(tauT,ys, tauT(1), ys(1), "*")
# endif
endfor
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