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Comment:Updated for liuping's qp_hild.m
Used on IP experiment
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SHA3-256: f0bc59b1f11aefdce7c1595bbe0f27638cf68c49f032717d2691aa38ee597c8d
User & Date: gawthrop@users.sourceforge.net on 2004-10-20 21:58:12
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Context
2005-01-06
12:28:36
Minor typos. check-in: e11dbdc5f8 user: geraint@users.sourceforge.net tags: origin/master, trunk
2004-10-20
21:58:12
Updated for liuping's qp_hild.m
Used on IP experiment check-in: f0bc59b1f1 user: gawthrop@users.sourceforge.net tags: origin/master, trunk
2004-10-14
21:42:44
Changed timing - now works with inverted pendulum. check-in: c3fad309c5 user: gawthrop@users.sourceforge.net tags: origin/master, trunk
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Modified mttroot/mtt/lib/control/PPP/ppp_are.m from [374eed77eb] to [36a7ac48d8]. 

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function [P,A_u,A_w,k] = ppp_are (A,B,C,D,Q,R)

  ## usage:  [P,A_u,A_w] = ppp_are (A,B,C,D,Q,R)
  ##
  ## 











  ## Steady-state Linear Quadratic solution
  ## using Algebraic Riccati equation (ARE)
  Q_x =  C'*Q*C;			# Weighting on x
  [k, P, poles] = lqr (A, B, Q_x, R); # Algebraic Riccati solution

  ## Basis functions

  A_u = compan(poly(poles));






  ## Avoid spurious imag parts due to rounding
  A_u = real(A_u);		

  ## Setpoint basis functions
  A_w = 0;

endfunction

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function [P,A_u,A_w,k] = ppp_are (A,B,C,D,Q,R,A_type)

  ## usage:  [P,A_u,A_w] = ppp_are (A,B,C,D,Q,R,A_type)
  ##
  ## 

  if nargin<1
    disp("usage:  [P,A_u,A_w] = ppp_are (A,B,C,D,Q,R,A_type)");
    return
  endif
  
  if nargin<7
    A_type = "feedback";
  endif
  

  ## Steady-state Linear Quadratic solution
  ## using Algebraic Riccati equation (ARE)
  Q_x =  C'*Q*C;			# Weighting on x
  [k, P, poles] = lqr (A, B, Q_x, R); # Algebraic Riccati solution

  ## Basis functions
  if strcmp(A_type,"companion")
    A_u = compan(poly(poles));
  elseif strcmp(A_type,"feedback")
    A_u = A-B*k;
  else
    error(sprintf("A_type must be %s, not %s", "companion or feedback", A_type));
  endif
  
    ## Avoid spurious imag parts due to rounding
    A_u = real(A_u);		

  ## Setpoint basis functions
  A_w = 0;

endfunction

Modified mttroot/mtt/lib/control/PPP/ppp_lin_run.m from [2ee57392e6] to [10c572cbb5].

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  ## Control = 0:  step test
  ## Control = 1:  PPP open-loop
  ## Control = 2:  PPP closed-loop
  ## w is the (constant) setpoint
  ## par_control and par_observer are structures containing parameters
  ## for the observer and controller

  disp("Special version");

  ##Defaults
  if nargin<1			# Default name to dir name
    names = split(pwd,"/");
    [n_name,m_name] = size(names);
    Name = deblank(names(n_name,:));
  endif









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  ## Control = 0:  step test
  ## Control = 1:  PPP open-loop
  ## Control = 2:  PPP closed-loop
  ## w is the (constant) setpoint
  ## par_control and par_observer are structures containing parameters
  ## for the observer and controller



  ##Defaults
  if nargin<1			# Default name to dir name
    names = split(pwd,"/");
    [n_name,m_name] = size(names);
    Name = deblank(names(n_name,:));
  endif
︙︙

Modified mttroot/mtt/lib/control/PPP/ppp_qp.m from [fa82338072] to [78c9145b4b]. 

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function [u,U,iterations] = ppp_qp (x,W,J_uu,J_ux,J_uw,Us0,Gamma,gamma,mu,test)

  ## usage:  [u,U] = ppp_qp (x,W,J_uu,J_ux,J_uw,Gamma,gamma)
  ## INPUTS:
  ##      x: system state    
  ##      W: Setpoint vector
  ##      J_uu,J_ux,J_uw: Cost derivatives (see ppp_lin)
  ##      Us0: value of U* at tau=0 (see ppp_lin)

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function [u,U,n_active] = ppp_qp (x,W,J_uu,J_ux,J_uw,Us0,Gamma,gamma,mu,test)

  ## usage:  [u,U] = ppp_qp (x,W,J_uu,J_ux,J_uw,Gamma,gamma)
  ## INPUTS:
  ##      x: system state    
  ##      W: Setpoint vector
  ##      J_uu,J_ux,J_uw: Cost derivatives (see ppp_lin)
  ##      Us0: value of U* at tau=0 (see ppp_lin)
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  if (n != n_U)||(m != n_x)
    error("J_ux should be %ix%i not %ix%i",n_U,n_x,n,m);
  endif


  if length(gamma)>0		# Constraints exist: do the QP algorithm
    ## QP solution for weights U	

    [U,iterations] = qp_mu(J_uu,(J_ux*x - J_uw*W),Gamma,gamma,mu,[],[],0,test);


    ##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








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  if (n != n_U)||(m != n_x)
    error("J_ux should be %ix%i not %ix%i",n_U,n_x,n,m);
  endif


  if length(gamma)>0		# Constraints exist: do the QP algorithm
    ## QP solution for weights U	
##    [U,iterations] = qp_mu(J_uu,(J_ux*x-J_uw*W),Gamma,gamma,mu,[],[],0,test);
    [U,n_active] = qp_hild(J_uu,(J_ux*x - J_uw*W),Gamma,gamma);	# 
##    iterations = 0;

    ##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
    n_active = 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

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