Description of qp_sim

qp_sim

PURPOSE

QP_SIM - QP control allocation simulation.

SYNOPSIS

function [u,W,time,iter] = qp_sim(B,v,plim,varargin)

DESCRIPTION

 QP_SIM - QP control allocation simulation. 

  [u,W,time,iter] = qp_sim(B,v,plim,[rlim,T,Wv,Wu,ud],options)

 Performs l2-optimal control allocation for a sequence of virtual
 control commands stored in v. For each value of v, the control
 signal u is determined by solving the quadratic program
  
   min ||Wu(u-ud)||   subj. to   u in M

 where M is the set of control signals solving

   min ||Wv(Bu-v)||   subj. to   u in U

 where U is the set of feasible control signals with respect to
 position limits and, optionally, rate limits.

  Inputs:
  -------
 B     control effectiveness matrix (k x m)
 v     commanded virtual control trajectory (k x N)
 plim  position limits [min max] (m x 2)
 rlim  rate limits [min max] (m x 2) ([] --> no rate limits)
 T     sampling time [1]
 Wv    virtual control weighting matrix (k x k) [I]
 Wu    control weighting matrix (m x m) [I]
 ud    desired control (m x 1) [0]

  Options: options = option_1,value_1,option_2,value_2,...
  --------
 'alg'    numerical algorithm: 'sls'    SLS_ALLOC
                               'wls'    WLS_ALLOC (default)
                               'wlsc'   WLSC_ALLOC
                               'mls'    MLS_ALLOC
                               'ip'     IP_ALLOC
                               'cgi'    CGI_ALLOC
                               'fxp'    FXP_ALLOC
 'imax'   max no. of iterations [100]
 'gam'    weight used in algorithms based on weighted LS [1e6]
 'tol'    tolerance used in IP_ALLOC stopping criterion [1e-6]
 'hot'    hotstart solver (not ip/cgi) with previous solution (0/[1])
 'ui'     initial control signal
 'Wi'     initial active constraints
 'rep'    no. of repetitions [1]

  Outputs:
  -------
 u     optimal control
 W     active constraints in u (+/- : max/min, 1/2 : position/rate)
 time  average computation time per sample
 iter  no. of iterations

 Flight example:
   load admiredata
   u=qp_sim(B,v,plim,rlim,T);
   figure(1),plot(t,u*180/pi),legend('can','elev (r)','elev (l)','rud')
   figure(2),plot(t,B*u,t,v,'k--'),legend('roll','pitch','yaw')

 See also: DIR_SIM, DYN_SIM, and the allocation algorithms above.

CROSS-REFERENCE INFORMATION

This function calls:

• alloc_sim ALLOC_SIM - Control allocation simulation.

This function is called by:

SOURCE CODE

0001 function [u,W,time,iter] = qp_sim(B,v,plim,varargin)
0002 
0003 % QP_SIM - QP control allocation simulation.
0004 %
0005 %  [u,W,time,iter] = qp_sim(B,v,plim,[rlim,T,Wv,Wu,ud],options)
0006 %
0007 % Performs l2-optimal control allocation for a sequence of virtual
0008 % control commands stored in v. For each value of v, the control
0009 % signal u is determined by solving the quadratic program
0010 %
0011 %   min ||Wu(u-ud)||   subj. to   u in M
0012 %
0013 % where M is the set of control signals solving
0014 %
0015 %   min ||Wv(Bu-v)||   subj. to   u in U
0016 %
0017 % where U is the set of feasible control signals with respect to
0018 % position limits and, optionally, rate limits.
0019 %
0020 %  Inputs:
0021 %  -------
0022 % B     control effectiveness matrix (k x m)
0023 % v     commanded virtual control trajectory (k x N)
0024 % plim  position limits [min max] (m x 2)
0025 % rlim  rate limits [min max] (m x 2) ([] --> no rate limits)
0026 % T     sampling time [1]
0027 % Wv    virtual control weighting matrix (k x k) [I]
0028 % Wu    control weighting matrix (m x m) [I]
0029 % ud    desired control (m x 1) [0]
0030 %
0031 %  Options: options = option_1,value_1,option_2,value_2,...
0032 %  --------
0033 % 'alg'    numerical algorithm: 'sls'    SLS_ALLOC
0034 %                               'wls'    WLS_ALLOC (default)
0035 %                               'wlsc'   WLSC_ALLOC
0036 %                               'mls'    MLS_ALLOC
0037 %                               'ip'     IP_ALLOC
0038 %                               'cgi'    CGI_ALLOC
0039 %                               'fxp'    FXP_ALLOC
0040 % 'imax'   max no. of iterations [100]
0041 % 'gam'    weight used in algorithms based on weighted LS [1e6]
0042 % 'tol'    tolerance used in IP_ALLOC stopping criterion [1e-6]
0043 % 'hot'    hotstart solver (not ip/cgi) with previous solution (0/[1])
0044 % 'ui'     initial control signal
0045 % 'Wi'     initial active constraints
0046 % 'rep'    no. of repetitions [1]
0047 %
0048 %  Outputs:
0049 %  -------
0050 % u     optimal control
0051 % W     active constraints in u (+/- : max/min, 1/2 : position/rate)
0052 % time  average computation time per sample
0053 % iter  no. of iterations
0054 %
0055 % Flight example:
0056 %   load admiredata
0057 %   u=qp_sim(B,v,plim,rlim,T);
0058 %   figure(1),plot(t,u*180/pi),legend('can','elev (r)','elev (l)','rud')
0059 %   figure(2),plot(t,B*u,t,v,'k--'),legend('roll','pitch','yaw')
0060 %
0061 % See also: DIR_SIM, DYN_SIM, and the allocation algorithms above.
0062 
0063 % F18 example
0064 %   load f18data
0065 %   u=qp_sim(B,v,plim,rlim,T1);
0066 %   plot(tn,u)
0067 %   plot(tn,v,'k',tn,B*u)
0068   
0069 % Number of variables
0070   [k,m] = size(B);
0071 
0072   % Find no. of optional arguments (excluding options)
0073   iopt = length(varargin)+1;
0074   for i = 1:length(varargin)
0075     if ischar(varargin{i})
0076       iopt = i; % index of first option string
0077       break;
0078     end
0079   end
0080   narg = iopt-1;
0081   
0082   % Set default values of optional arguments
0083   rlim = [];
0084   T    = 1;
0085   Wv   = eye(k);
0086   Wu   = eye(m);
0087   ud   = zeros(m,1);
0088 
0089   % Set values of submitted optional arguments
0090   for i=1:narg
0091     switch i
0092      case 1, rlim = varargin{i};
0093      case 2, T      = varargin{i};
0094      case 3, Wv      = varargin{i};
0095      case 4, Wu      = varargin{i};
0096      case 5, ud      = varargin{i};
0097     end
0098   end
0099 
0100   % Call generic control allocation simulation subroutine.
0101   [u,W,time,iter] = alloc_sim('qp',B,v,plim,rlim,T,'Wv',Wv,...
0102                   'Wu',Wu,'ud',ud,varargin{iopt:end});
0103

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