function [name,T,y,u,ys,us,ysu,usu,J] = ppp_ex17 (ReturnName) ## usage: [name,T,y,u,ys,us,ysu,usu,J] = ppp_ex17 (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 - intermittent control"; 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 = [9:0.02:10]; # Time horizon A_w = 0; # Setpoint A_u = ppp_aug(laguerre_matrix(3,2.0), A_w); # Input functions Q = ones(n_y,1);; ## Constraints - 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))]; ## OL solution [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 delta_ol = 0.1; [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,delta_ol); title("y,y*,u and u*"); xlabel("t"); grid; plot(T,y,T,u,T,ysu,T,usu); endfunction