Overview
Comment:Updated for new ppp_qp (using qp_mu from Will Heath/Adrian Wills
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SHA3-256: 41f2ee5ebba2731b7676605ffde3cc1e283aa5b992618de816b1df8fd323340b
User & Date: gawthrop@users.sourceforge.net on 2002-08-27 17:34:36
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Context
2002-08-28
15:48:01
Updated mttrc to make standalone C++ compilation configuration clearer. check-in: c26e5d9934 user: geraint@users.sourceforge.net tags: origin/master, trunk
2002-08-27
17:34:36
Updated for new ppp_qp (using qp_mu from Will Heath/Adrian Wills check-in: 41f2ee5ebb user: gawthrop@users.sourceforge.net tags: origin/master, trunk
16:09:01
Added port_name to error message when multiple bonds are near a port. check-in: dd777940a7 user: geraint@users.sourceforge.net tags: origin/master, trunk
Changes
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Modified mttroot/mtt/lib/control/PPP/ppp_ex11.m from [8afbccc82d] to [b816bab9e6].

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  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);;
  

  ## Constaints
  Gamma = [];
  gamma = [];

  ## Constaints - 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;









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  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;
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  [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("Constained and unconstrained y*");
  xlabel("t");
  grid;

  plot(T,ys,T,ysu)

  ## 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("y,y*,u and u*");
  xlabel("t");
  grid;

  plot(T,y,T,u,T,ys,T,us);

  ## 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












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  [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

Modified mttroot/mtt/lib/control/PPP/ppp_ex12.m from [4b9ce5134a] to [03125b8f94].

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       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);;









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       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);;
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  [T,y,u,J] = ppp_qp_sim (A,B,C,D,A_u,A_w,t,Q, \
			   Tau,Min,Max,Order, \
			   [],[],[],[], W,x_0);

  title("y,y*,u and u*");
  xlabel("t");
  grid;
  plot(T,y,T,u,T,ys,T,us);

  ## 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);








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  [T,y,u,J] = ppp_qp_sim (A,B,C,D,A_u,A_w,t,Q, \
			   Tau,Min,Max,Order, \
			   [],[],[],[], W,x_0);

  title("y,y*,u and u*");
  xlabel("t");
  grid;
  plot(T,y,"1;y;", T,u,"2;u;", T,ys,"3;y*;", T,us,"4;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);
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Modified mttroot/mtt/lib/control/PPP/ppp_ex15.m from [a26d3cfd27] to [d1ae59f7c7].

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  x_0 = zeros(n_x,1);		# Initial state


  ## Closed-loop intermittent solution
  Delta_ol = 0.5		# Intermittent time

  disp("Intermittent control simulation");
  [T,y,u,J] = ppp_qp_sim (A,B,C,D,A_u,A_w,t,Q, \
			  [],[],[],[], \
			  [],[],[],[],W,x_0,Delta_ol);

  ## Exact closed-loop
  disp("Exact closed-loop");
  [k_x,k_w] = ppp_lin (A,B,C,D,A_u,A_w,t,Q);
  [ye,Xe] = ppp_sm2sr(A-B*k_x, B, C, D, T, k_w*W, x_0); # Compute Closed-loop control

  ue = k_w*ones(size(T))*W - k_x*Xe';


  title("y and u, exact and intermittent");
  xlabel("t");
  grid;
  plot(T,y,T,u,T,ye,T,ue);


endfunction








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  x_0 = zeros(n_x,1);		# Initial state


  ## Closed-loop intermittent solution
  Delta_ol = 0.5		# Intermittent time

  disp("Intermittent control simulation");
  [T,y,u] = ppp_qp_sim (A,B,C,D,A_u,A_w,t,Q, \
			  [],[],[],[], \
			  [],[],[],[],W,x_0,Delta_ol);
size(T)
  ## Exact closed-loop
  disp("Exact closed-loop");
  [k_x,k_w] = ppp_lin (A,B,C,D,A_u,A_w,t,Q)
  [ye,Xe] = ppp_sm2sr(A-B*k_x, B, C, D, T, k_w*W, x_0); # Compute Closed-loop control

  ue = k_w*ones(size(T))*W - k_x*Xe;


  title("y and u, exact and intermittent");
  xlabel("t");
  grid;
  plot(T,y,"1;y (intermittent);", T,u,"2;u (intermittent);",\
       T,ye,"3;y (exact);", T,ue,"4;u (exact);");

endfunction

Modified mttroot/mtt/lib/control/PPP/ppp_ex17.m from [0cc0c0d748] to [fd73fba900].

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  ## 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












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  ## 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;
  figure(1);
  plot(T,ys,"-;y* (constrained);", T,ysu,"--;y* (unconstrained);")

  ## Non-linear - closed-loop
  delta_ol = 0.1; mu = 1e-4;
  [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,mu);

  title("y and u");
  xlabel("t");
  grid;
  plot(T,y,"1;y (constrained);", T,u,"2;u (constrained);");

endfunction

Modified mttroot/mtt/lib/control/PPP/ppp_ex19.m from [667d1947d8] to [8863f79b17].

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  ## 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("Constrained and unconstrained y*");
  xlabel("t");
  grid;
  plot(T,ys,T,ysu)

  ## Non-linear - closed-loop
  disp("Closed-loop simulation");
  [T1,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("y,y*,u and u*");
  xlabel("t");
  grid;

  plot(T1,y,T,ys,T1,u,T,us);
endfunction














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  ## 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("Constrained and unconstrained y*");
  xlabel("t");
  grid;
  plot(T,ys,"-;y* (constrained);", T,ysu,"--;y* (unconstrained);");

  ## Non-linear - closed-loop
  disp("Closed-loop simulation");
  [T1,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("y and u");
  xlabel("t");
  grid;
  plot(T,y,"1;y (constrained);", T,u,"2;u (constrained);");

endfunction

Modified mttroot/mtt/lib/control/PPP/ppp_ex6.m from [ba0ffb029f] to [2c0684bb49].

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  i_u = 1;
  
  ## Simulation
  W=1;
  x_0 = 0;

  ## Linear
  [ol_poles,cl_poles,ol_zeros,cl_zeros,k_x,k_w] = ppp_lin_plot (A,B,C,D,A_u,A_w,t);
  
  ## Non-linear
  movie = 0;
  [T,y,u,J] = ppp_qp_sim (A,B,C,D,A_u,A_w,t,Q, Tau,Min,Max,Order, \
	      [],[],[],[], W,x_0);
  title("y,u_1,u_2");
  xlabel("t");
  grid;
  plot(T,y,T,u);

endfunction











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  i_u = 1;
  
  ## Simulation
  W=1;
  x_0 = 0;

  ## Linear
  ppp_lin_plot (A,B,C,D,A_u,A_w,t);
  
  ## Non-linear
  movie = 0;
  [T,y,u,J] = ppp_qp_sim (A,B,C,D,A_u,A_w,t,Q, Tau,Min,Max,Order, \
	      [],[],[],[], W,x_0);
  title("y,u_1,u_2");
  xlabel("t");
  grid;
  plot(T,y,"-;y;", T,u(1,:),"--;u_1;", T,u(2,:),".-;u_2;");

endfunction

Modified mttroot/mtt/lib/control/PPP/ppp_lin_plot.m from [e00d3bd973] to [460292101c]. 

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function [ol_poles,cl_poles,ol_zeros,cl_zeros,k_x,k_w,K_x,K_w,cond_uu] =  ppp_lin_plot (A,B,C,D,A_u,A_w,t,Q,W,x_0)

  ## usage:   [ol_poles,cl_poles,ol_zeros,cl_zeros,k_x,k_w,K_x,K_w] = ppp_lin_plot (A,B,C,D,A_u,A_w,t,Q,W,x_0)
  ##
  ## Linear PPP (Predictive pole-placement) computation with plotting
  ## INPUTS:
  ## A,B,C,D: system matrices
  ## A_u: composite system matrix for U* generation 
  ##      one square matrix (A_ui) row for each system input
  ##      each A_ui generates U*' for ith system input.



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function [ol_poles,cl_poles,ol_zeros,cl_zeros,k_x,k_w,K_x,K_w,cond_uu] =  ppp_lin_plot (A,B,C,D,A_u,A_w,t,Q,W,x_0)

  ## usage:   [ol_poles,cl_poles,ol_zeros,cl_zeros,k_x,k_w,K_x,K_w,cond_uu] = ppp_lin_plot (A,B,C,D,A_u,A_w,t,Q,W,x_0)
  ##
  ## Linear PPP (Predictive pole-placement) computation with plotting
  ## INPUTS:
  ## A,B,C,D: system matrices
  ## A_u: composite system matrix for U* generation 
  ##      one square matrix (A_ui) row for each system input
  ##      each A_ui generates U*' for ith system input.
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  endif
  

  [n_t,m_t] = size(t);

  ## Default Q
  if nargin<8
    Q = ones(n_y,1);
  endif

  ## Default W
  if nargin<9
    W = ones(n_W,1)
  endif









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  endif
  

  [n_t,m_t] = size(t);

  ## Default Q
  if nargin<8
    Q = ones(n_y,1)
  endif

  ## Default W
  if nargin<9
    W = ones(n_W,1)
  endif
︙︙

Modified mttroot/mtt/lib/control/PPP/ppp_qp.m from [519bc8a390] to [3e26f7769e].

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    [U,iterations] = qp_mu(J_uu,(J_ux*x - J_uw*W),Gamma,gamma,mu); # QP solution for weights U	

    ##U = qp(J_uu,(J_ux*x - J_uw*W),Gamma,gamma); # QP solution for weights U
    ##U = pd_lcp04(J_uu,(J_ux*x - J_uw*W),Gamma,gamma); # QP solution for weights U
    u = Us0*U;			# Control signal
  else			# Do the unconstrained solution
    ## Compute the open-loop gains

    K_w = J_uu\J_uw;
    K_x = J_uu\J_ux;

    ## Closed-loop control
    U = K_w*W - K_x*x;		# Basis functions weights - U(t)
    u = Us0*U;			# Control u(t)
  endif

endfunction








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    [U,iterations] = qp_mu(J_uu,(J_ux*x - J_uw*W),Gamma,gamma,mu); # QP solution for weights U	

    ##U = qp(J_uu,(J_ux*x - J_uw*W),Gamma,gamma); # QP solution for weights U
    ##U = pd_lcp04(J_uu,(J_ux*x - J_uw*W),Gamma,gamma); # QP solution for weights U
    u = Us0*U;			# Control signal
  else			# Do the unconstrained solution
    ## Compute the open-loop gains
    iterations = 0;
    K_w = J_uu\J_uw;
    K_x = J_uu\J_ux;

    ## Closed-loop control
    U = K_w*W - K_x*x;		# Basis functions weights - U(t)
    u = Us0*U;			# Control u(t)
  endif

endfunction

Modified mttroot/mtt/lib/control/PPP/ppp_qp_sim.m from [3484a100c1] to [3b08bbc64d].

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  [Gamma_y,gamma_y] = ppp_output_constraint  (A,B,C,D,x_0,A_u,Tau_y,Min_y,Max_y,Order_y);

  ## Composite constraints - t=0
  Gamma = [Gamma_u; Gamma_y];
  gamma = [gamma_u; gamma_y];

  ## Design the controller
  disp("Designing controller");
  [k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww] = ppp_lin (A,B,C,D,A_u,A_w,t,Q);

  ## 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;








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  [Gamma_y,gamma_y] = ppp_output_constraint  (A,B,C,D,x_0,A_u,Tau_y,Min_y,Max_y,Order_y);

  ## Composite constraints - t=0
  Gamma = [Gamma_u; Gamma_y];
  gamma = [gamma_u; gamma_y];

  ## Design the controller
  ## disp("Designing controller");
  [k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww] = ppp_lin (A,B,C,D,A_u,A_w,t,Q);

  ## 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;
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  X = [];
  u = [];
  Iterations = [];
  du = [];
  J = [];
  tick= time;
  i = 0;
  disp("Simulating ...");
  for t=T_cl			# Outer loop at Delta_ol
    ##disp(sprintf("Time %g", t));
    ## 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];








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  X = [];
  u = [];
  Iterations = [];
  du = [];
  J = [];
  tick= time;
  i = 0;
  ## disp("Simulating ...");
  for t=T_cl			# Outer loop at Delta_ol
    ##disp(sprintf("Time %g", t));
    ## 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];
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  ## Save the last values
  X = [X x];		# Save state
  u = [u ut];		# Save input
  Iterations = [Iterations iterations]; # Save iteration count

  tock = time;
  Elapsed_Time = tock-tick
  y = C*X + D*u;		# System output

  T = 0:dt:t+Delta_ol;		# Overall time vector

endfunction











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  ## Save the last values
  X = [X x];		# Save state
  u = [u ut];		# Save input
  Iterations = [Iterations iterations]; # Save iteration count

  tock = time;
  Elapsed_Time = tock-tick;
  y = C*X + D*u;		# System output

  T = 0:dt:t+Delta_ol;		# Overall time vector

endfunction

MTT: Model Transformation Tools
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