function [name,T,y,u,ys,us,J] = ppp_ex11 (ReturnName) ## usage: [name,T,y,u,ys,us,T1,du,dus] = ppp_ex11 (ReturnName) ## ## PPP example ## $Id$ ## Example name name = "Input constraints +-1.5 on u* at tau=0,0.5,1,1.5,2"; if nargin>0 return 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 = [6:0.02:7]; # 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 Gamma = []; gamma = []; ## Constraints - u Tau_u = [0:0.5:2]; one = ones(size(Tau_u)); limit = 1.5; Min_u = -limit*one; Max_u = limit*one; Order_u = 0*one; ## Constraints - y Tau_y = []; # No output constraints one = ones(size(Tau_y)); limit = 1.5; Min_y = -limit*one; Max_y = limit*one; Order_y = 0*one; ## Simulation W=1; x_0 = zeros(3,1); ## Constrained - open-loop disp("Designing controller"); [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 = Gamma_u; gamma = gamma_u; ## Constrained OL simulation disp("Computing constrained ol response"); [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 disp("Computing unconstrained ol response"); [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("Constrained and unconstrained y*"); xlabel("t"); grid; figure(1); plot(T,ys,"-;y*: constrained;", T,ysu, "--;y*: unconstrained;") ## Non-linear - closed-loop disp("Computing constrained closed-loop response"); [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); title("Constrained closed-loop response"); xlabel("t"); grid; figure(2); plot(T,y,"-;y;", T,u,"--;u;"); # ## 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