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Comment:Revised to work with LQ on alnalogue circuit example with integration
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SHA3-256: b4a88aed89c459b852ea2f693bb060f52c73abc67c3cafa1d6ce410b6f5fe0db
User & Date: gawthrop@users.sourceforge.net on 2003-10-21 09:30:24
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Context
2003-10-21
09:55:02
Make time horizon tau part of p_c struct check-in: fa74b12eb3 user: gawthrop@users.sourceforge.net tags: origin/master, trunk
09:30:24
Revised to work with LQ on alnalogue circuit example with integration check-in: b4a88aed89 user: gawthrop@users.sourceforge.net tags: origin/master, trunk
2003-10-20
17:10:31
Link ancestry of version-0-1 to it's source branch check-in: 538bbd8286 user: gawthrop@users.sourceforge.net tags: origin/master, trunk
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Modified mttroot/mtt/lib/control/PPP/ppp_lin_quad.m from [2ba9cc3698] to [b791777adb]. 

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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


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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);


endfunction

Modified mttroot/mtt/lib/control/PPP/ppp_lin_run.m from [96369350d9] to [fdb48937ab].

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  endif

  if !struct_contains(p_c,"delta_ol")
    p_c.delta_ol = 0.5;	# OL sample interval
  endif
  
  if !struct_contains(p_c,"T")
    p_c.T = 2.5;			# 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 = "original";
  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;








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  endif

  if !struct_contains(p_c,"delta_ol")
    p_c.delta_ol = 0.5;	# OL sample interval
  endif
  
  if !struct_contains(p_c,"T")
    p_c.T = 10;			# Last time point.
  endif

  if !struct_contains(p_c,"augment")
    p_c.augment = 0;		# Augment basis funs with constant
  endif
  
  if !struct_contains(p_c,"integrate")
    p_c.integrate = 0;		# Augment basis funs with constant
  endif
  
  if !struct_contains(p_c,"Tau_u")
    p_c.Tau_u = [];
    p_c.Min_u = [];
    p_c.Max_u = [];
  endif

  if !struct_contains(p_c,"Tau_y")
    p_c.Tau_y = [];
    p_c.Min_y = [];
    p_c.Max_y = [];
  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 = (0.1^2)*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;
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  if ControlType==0		# Step input
    I = 1;			# 1 large sample
    p_c.delta_ol = p_c.T	# I
    K_w = zeros(p_c.n_U,n_y);
    K_w(1,1) = 1;
    K_w(2,1) = -1;
    K_x = zeros(p_c.n_U,n_x);
    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
  dt = p_c.delta_ol/p_c.N;

  ## Observer design
  G = eye(n_x);		# State noise gain 
  sigma_x = eye(n_x);		# State noise variance








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  if ControlType==0		# Step input
    I = 1;			# 1 large sample
    p_c.delta_ol = p_c.T	# I
    K_w = zeros(p_c.n_U,n_y);
    K_w(1,1) = 1;
    K_w(2,1) = -1;
    K_x = zeros(p_c.n_U,n_x);

  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,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww] =\
	  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]; # 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


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

  ## Initial control U
  U = zeros(p_c.n_U,1);	


  ## Short sample interval
  dt = p_c.delta_ol/p_c.N;

  ## Observer design
  G = eye(n_x);		# State noise gain 
  sigma_x = eye(n_x);		# State noise variance
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  endif
  
  ## Display the poles
  obs_poles

  ## Write the include file for the real-time function
  ## Use double length to allow for overuns
  disp("Writing Ustar.h");
  overrun = 2;
  ppp_ustar2h(ppp_ustar (p_c.A_u, n_u, [0:dt:overrun*p_c.delta_ol], 0,0)); 









  ## Control loop
  y = [];
  u = [];
  t = [];
  y_e = [];
  t_e = [];
  e_e = [];
  tick = time;
  i=0;
  for j=1:10
    for k=1:I
      tim=time;			# Timing
      i++
      if Simulate		# Exact simulation 
	t_sim = [1:p_c.N]*dt;	# Simulation time points
	[yi,ui,xsi] = ppp_ystar(A,B,C,D,x,p_c.A_u,U,t_sim); # Simulate
	x = xsi(:,p_c.N);	# Current state (for next time)
	ti  = [(i-1)*p_c.N:i*p_c.N-1]*dt; 
	y_i = yi(1);	# Current output
	t_i = ti(1);








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  endif
  
  ## Display the poles
  obs_poles

  ## Write the include file for the real-time function
  ## Use double length to allow for overuns

  overrun = 2;
  Ustar = ppp_ustar (p_c.A_u, n_u, [0:dt:overrun*p_c.delta_ol], 0,0);
  if p_c.integrate		# Integrate Ustar
    disp("Integrating Ustar");
    Ustar = cumsum(Ustar)*dt;
  endif
  
  disp("Writing Ustar.h");
  ppp_ustar2h(Ustar); 


  ## Control loop
  y = [];
  u = [];
  t = [];
  y_e = [];
  t_e = [];
  e_e = [];
  tick = time;
  i=0;
  for j=1:4
    for k=1:I
      tim=time;			# Timing
      i++;
      if Simulate		# Exact simulation 
	t_sim = [1:p_c.N]*dt;	# Simulation time points
	[yi,ui,xsi] = ppp_ystar(A,B,C,D,x,p_c.A_u,U,t_sim); # Simulate
	x = xsi(:,p_c.N);	# Current state (for next time)
	ti  = [(i-1)*p_c.N:i*p_c.N-1]*dt; 
	y_i = yi(1);	# Current output
	t_i = ti(1);
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	  Ui = A_ud'*Ui;
	  y_e = [y_e; y_new'];
	  e_e = [e_e; e_est'];
	endfor
      endif
      
      ##Control

      U = K_w*w - K_x*x_est;


















      ## Save data
      if Simulate
	t = [t;ti'];
	y = [y;yi'];
	u = [u;ui'];
      else
	t = [t;t_i];
	y = [y;y_i'];
	u = [u;u_i'];
      endif
      

      if strcmp(p_o.method, "intermittent")
	y_e = [y_e; y_new'];
	e_e = [e_e; e_est'];
	t_e = [t_e; t_i];
      endif

      delta_comp = time-tim;
      usleep(floor(1e6*(p_c.delta_ol-delta_comp-0.01)));


    endfor			# Main loop
    w = -w;
  endfor 			# Outer loop

  if !Simulate
    ppp_put_get(0*U); 		# Reset to zero
  endif

  
  if strcmp(p_o.method, "continuous")
    t_e = t;








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	  Ui = A_ud'*Ui;
	  y_e = [y_e; y_new'];
	  e_e = [e_e; e_est'];
	endfor
      endif
      
      ##Control
      if ( (p_c.Tau_u==[])&&(p_c.Tau_y==[]) )
	U = K_w*w - K_x*x_est;
      else
	## Input constraints 
	[Gamma_u, gamma_u] = \
	    ppp_input_constraints(p_c.A_u,p_c.Tau_u,p_c.Min_u,p_c.Max_u);
	
	## Output constraints
	[Gamma_y,gamma_y] = \
	    ppp_output_constraints(A,B,C,D,x_est,p_c.A_u,\
				   p_c.Tau_y,p_c.Min_y,p_c.Max_y);
	
	## Composite constraints - t=0
	Gamma = [Gamma_u; Gamma_y];
	gamma = [gamma_u; gamma_y];
	
	[u_qp,U] = ppp_qp (x_est,w,J_uu,J_ux,J_uw,Us0,Gamma,gamma,1e-6,1);
      endif
      

      ## Save data
      if Simulate
	t = [t;ti'];
	y = [y;yi'];
	u = [u;ui'];
      else
	t = [t;t_i];
	y = [y;y_i'];
	u = [u;u_i'];
      endif
      

      if strcmp(p_o.method, "intermittent")
	y_e = [y_e; y_new'];
	e_e = [e_e; e_est'];
	t_e = [t_e; t_i];
      endif
      if !Simulate
	delta_comp = time-tim;
	usleep(floor(1e6*(p_c.delta_ol-delta_comp-0.01)));
      endif
      
    endfor			# Main loop
    w = -w;
  endfor 			# Outer loop

  if !Simulate
    ppp_put_get(0*U); 		# Reset to zero
  endif

  
  if strcmp(p_o.method, "continuous")
    t_e = t;
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