function [name,T,y,u,ys,us,ysu,usu,J] = ppp_ex14m (ReturnName)
## usage: [name,T,y,u,ys,us,ysu,usu,J] = ppp_ex14 (ReturnName)
##
## PPP example - shows output constraints on nonlinear system
## $Id$
## Example name
name = "Output constraints -0.1 on y* at tau=0.1,0.5,1,2";
if nargin>0
if ReturnName
return
endif
endif
## System
A = [-3 -3 -1
1 0 0
0 1 0];
B = [1
0
0];
C = [0 -0.5 1];
D = 0;
[n_x,n_u,n_y] = abcddim(A,B,C,D)
## Controller
t = [4:0.02:5]; # Time horizon
A_w = 0; # Setpoint
A_u = ppp_aug(laguerre_matrix(3,2.0), A_w); # Input functions
Q = ones(n_y,1);;
## Constaints - u
Tau_u = [];
one = ones(size(Tau_u));
limit = 3;
Min_u = -limit*one;
Max_u = limit*one;
Order_u = 0*one;
## Constraints - y
Tau_y = [0.1 0.5 1 2]
one = ones(size(Tau_y));
Min_y = -0.01*one; # Min_y(5) = 0.99;
Max_y = 1e5*one; # Max_y(5) = 1.01;
Order_y = 0*one;
## Simulation
W=1;
x_0 = zeros(3,1);
## Constrained - open-loop
[k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw] = ppp_lin (A,B,C,D,A_u,A_w,t,Q); # Unconstrained design
[Gamma_u,gamma_u] = ppp_input_constraint (A_u,Tau_u,Min_u,Max_u);
[Gamma_y,gamma_y] = ppp_output_constraint (A,B,C,D,x_0,A_u,Tau_y,Min_y,Max_y,Order_y);
Gamma = [Gamma_u; Gamma_y];
gamma = [gamma_u; gamma_y];
## Constrained OL simulation
[u,U] = ppp_qp (x_0,W,J_uu,J_ux,J_uw,Us0,Gamma,gamma);
T = [0:t(2)-t(1):t(length(t))];
[ys,us] = ppp_ystar (A,B,C,D,x_0,A_u,U,T);
## Unconstrained OL simulation
[uu,Uu] = ppp_qp (x_0,W,J_uu,J_ux,J_uw,Us0,[],[]);
[ysu,usu] = ppp_ystar (A,B,C,D,x_0,A_u,Uu,T);
title("Constained and unconstrained y*");
xlabel("t");
grid;
plot(T,ys,T,ysu)
## Non-linear - closed-loop
movie = 1;
if movie
hold on;
endif
[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);
hold off;
# title("y,y*,u and u*");
# xlabel("t");
# grid;
# plot(T,y,T,u,T,ysu,T,usu);
## Compute derivatives.
dt = t(2)-t(1);
du = diff(u)/dt;
dus = diff(us)/dt;
T1 = T(1:length(T)-1);
##plot(T1,du,T1,dus);
endfunction