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Comment:augment option - constant term in basis
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SHA3-256: f5f8cb8a8104641fb4d88bbcc771593da508c22017f9a9374c2d4ba35e4eaac8
User & Date: gawthrop@users.sourceforge.net on 2003-10-06 08:36:44
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Context
2003-10-06
09:15:32
Revised for RTlab check-in: c43f9e9fc7 user: gawthrop@users.sourceforge.net tags: origin/master, trunk
08:36:44
augment option - constant term in basis check-in: f5f8cb8a81 user: gawthrop@users.sourceforge.net tags: origin/master, trunk
08:22:55
Removed y_u arg from ppp_lin_quad check-in: dd760bdfd4 user: gawthrop@users.sourceforge.net tags: origin/master, trunk
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Modified mttroot/mtt/lib/control/PPP/ppp_lin_quad.m from [c0426fddbf] to [2ba9cc3698]. 

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function [k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww,A_u] = \
      ppp_lin_quad (A,B,C,D,tau,Q,R)

  ## usage:[k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww,A_u] =
  ## ppp_lin_quad (A,B,C,D,tau,Q,R)
  ##
  ## 

  ## Steady-state Linear Quadratic solution
  ## using Algebraic Riccati equation (ARE)
  [P,A_u,A_w] = ppp_are (A,B,C,D,Q,R);






  ## PPP solution
  [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,tau,Q,R,P);

A_u
endfunction


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function [k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww,A_u] = \
      ppp_lin_quad (A,B,C,D,tau,Q,R,augment)

  ## usage:[k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww,A_u] =
  ## ppp_lin_quad (A,B,C,D,tau,Q,R)
  ##
  ## 

  ## Steady-state Linear Quadratic solution
  ## using Algebraic Riccati equation (ARE)
  [P,A_u,A_w] = ppp_are (A,B,C,D,Q,R);

  ## Augment with a constant term
  if augment
    A_u = ppp_aug(0,A_u);
  endif
  
  ## PPP solution
  [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,tau,Q,R,P);


endfunction

Modified mttroot/mtt/lib/control/PPP/ppp_lin_run.m from [b26b35c63c] to [39b3104ab9].

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  if !struct_contains(p_c,"delta_ol")
    p_c.delta_ol = 1.0;	# OL sample interval
  endif
  
  if !struct_contains(p_c,"T")
    p_c.T = 10.0;			# Last time point.
  endif




  
  if !struct_contains(p_c,"Method")
    p_c.Method = "lq";
  endif

  if struct_contains(p_c,"Method")
    if strcmp(p_c.Method,"lq") 
      p_c.Q = eye(n_y);
      p_c.R = (0.25^2)*eye(n_u);
      p_c.n_U = n_x;
    elseif strcmp(p_c.Method,"original");
      if !struct_contains(p_c,"A_w")
	p_c.A_w = 0;
      endif
      if !struct_contains(p_c,"A_u")
	p_c.n_U = n_x;
	a_u = 2.0;
	p_c.A_u = laguerre_matrix(p_c.n_U,a_u)



      endif
    else
      error(sprintf("Method %s not recognised", p_c.Method));
    endif
  endif
  
  if !struct_contains(p_o,"x_0")
    p_o.x_0 = zeros(n_x,1);
  endif
  
  if !struct_contains(p_o,"method")
    p_o.method = "continuous";
    ##    p_o.method = "intermittent";
  endif
  

  ## Check w.
  [n_w,m_w] = size(w);
  if ( (n_w!=n_y) || (m_w!=1) )
    error(sprintf("ppp_lin_run: w must a column vector with %i elements",n_y));








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  if !struct_contains(p_c,"delta_ol")
    p_c.delta_ol = 1.0;	# OL sample interval
  endif
  
  if !struct_contains(p_c,"T")
    p_c.T = 10.0;			# Last time point.
  endif

  if !struct_contains(p_c,"augment")
    p_c.augment = 1;		# Augment basis funs with contand
  endif
  
  if !struct_contains(p_c,"Method")
    p_c.Method = "lq";
  endif

  if struct_contains(p_c,"Method")
    if strcmp(p_c.Method,"lq") 
      p_c.Q = eye(n_y);
      p_c.R = (0.25^2)*eye(n_u);
      p_c.n_U = n_x;
    elseif strcmp(p_c.Method,"original");
      if !struct_contains(p_c,"A_w")
	p_c.A_w = 0;
      endif
      if !struct_contains(p_c,"A_u")
	p_c.n_U = n_x;
	a_u = 2.0;
	p_c.A_u = laguerre_matrix(p_c.n_U,a_u);
	if p_c.augment		# Put in constant term
	  A_u = ppp_aug(0,A_u);
	endif
      endif
    else
      error(sprintf("Method %s not recognised", p_c.Method));
    endif
  endif
  
  if !struct_contains(p_o,"x_0")
    p_o.x_0 = zeros(n_x,1);
  endif
  
  if !struct_contains(p_o,"method")
    ##p_o.method = "continuous";
    p_o.method = "intermittent";
  endif
  

  ## Check w.
  [n_w,m_w] = size(w);
  if ( (n_w!=n_y) || (m_w!=1) )
    error(sprintf("ppp_lin_run: w must a column vector with %i elements",n_y));
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    U = K_w*w;			# Initial control U
  else
    I = ceil(p_c.T/p_c.delta_ol) # Number of large samples
    if strcmp(p_c.Method, "original")
      tau = [10:0.1:11]*(2/a_u);	# Time horizons
      [k_x,k_w,K_x,K_w] = ppp_lin(A,B,C,D,p_c.A_u,p_c.A_w,tau); # Design
    elseif strcmp(p_c.Method, "lq") # LQ design
      tau = [0:0.001:1.0]*5; # Time horizons
      [k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww,A_u] \
	  = ppp_lin_quad (A,B,C,D,tau,p_c.Q,p_c.R);
      p_c.A_u = A_u
    else
      error(sprintf("Control method %s not recognised", p_c.Method));
    endif

    ##Sanity check A_u
    [p_c.n_U,M_u] = size(p_c.A_u);
    if (p_c.n_U!=M_u)
      error("A_u must be square");
    endif
    
    K_w,w
    U = K_w*w			# Initial control U

    ## Checks
    [ol_zeros, ol_poles] = sys2zp(sys)
    cl_poles = eig(A - B*k_x)
  endif

  ## Short sample interval








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    U = K_w*w;			# Initial control U
  else
    I = ceil(p_c.T/p_c.delta_ol) # Number of large samples
    if strcmp(p_c.Method, "original")
      tau = [10:0.1:11]*(2/a_u);	# Time horizons
      [k_x,k_w,K_x,K_w] = ppp_lin(A,B,C,D,p_c.A_u,p_c.A_w,tau); # Design
    elseif strcmp(p_c.Method, "lq") # LQ design
      tau = [0:0.1:2.0]*1; # Time horizons
      [k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww,A_u] \
	  = ppp_lin_quad (A,B,C,D,tau,p_c.Q,p_c.R,p_c.augment);
      p_c.A_u = A_u;
    else
      error(sprintf("Control method %s not recognised", p_c.Method));
    endif

    ##Sanity check A_u
    [p_c.n_U,M_u] = size(p_c.A_u);
    if (p_c.n_U!=M_u)
      error("A_u must be square");
    endif
    

    U = K_w*w;			# Initial control U

    ## Checks
    [ol_zeros, ol_poles] = sys2zp(sys)
    cl_poles = eig(A - B*k_x)
  endif

  ## Short sample interval
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