Description of dyn_sim

dyn_sim

PURPOSE

DYN_SIM - Dynamic control allocation simulation.

SYNOPSIS

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

DESCRIPTION

 DYN_SIM - Dynamic control allocation simulation. 

  [u,W,time,iter] = dyn_sim(B,v,plim,[rlim,T,Wv,W1,W2,S],options)

 Performs dynamic 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
  
   min   ||W1(u(t)-Sv(t))||^2 + ||W2(u(t)-u(t-T))||^2
  u in M

 where M is the set of control signals solving

   min   ||Wv(Bu-v)||
  u in U

 where U is the set of feasible control signals with respect to
 position and, possibly, 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]
 W1    control position weighting matrix (m x m) [I]
 W2    control rate weighting matrix (m x m) [0]
 S     steady state control distribution (m x k) [0]

  Options: See QP_SIM
  --------

  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

  Step response example:

   B = [2 1]; t = 0:.2:10; v = 1*(t>1); plim = [-1 1;-1 1];
   W1 = eye(2); W2 = diag([5 0]); S = pinv(B);
   u = dyn_sim(B,v,plim,[],.2,1,W1,W2,S);
   figure(1),bodemag(dca(B,S,W1,W2,.2))
   figure(2),stairs(t,[u' v']),legend('u_1','u_2','v=2u_1+u_2')

 See also: DCA, QP_SIM, DIR_SIM.

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] = dyn_sim(B,v,plim,varargin)
0002 
0003 % DYN_SIM - Dynamic control allocation simulation.
0004 %
0005 %  [u,W,time,iter] = dyn_sim(B,v,plim,[rlim,T,Wv,W1,W2,S],options)
0006 %
0007 % Performs dynamic 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
0010 %
0011 %   min   ||W1(u(t)-Sv(t))||^2 + ||W2(u(t)-u(t-T))||^2
0012 %  u in M
0013 %
0014 % where M is the set of control signals solving
0015 %
0016 %   min   ||Wv(Bu-v)||
0017 %  u in U
0018 %
0019 % where U is the set of feasible control signals with respect to
0020 % position and, possibly, rate limits.
0021 %
0022 %  Inputs:
0023 %  -------
0024 % B     control effectiveness matrix (k x m)
0025 % v     commanded virtual control trajectory (k x N)
0026 % plim  position limits [min max] (m x 2)
0027 % rlim  rate limits [min max] (m x 2) ([] --> no rate limits)
0028 % T     sampling time [1]
0029 % Wv    virtual control weighting matrix (k x k) [I]
0030 % W1    control position weighting matrix (m x m) [I]
0031 % W2    control rate weighting matrix (m x m) [0]
0032 % S     steady state control distribution (m x k) [0]
0033 %
0034 %  Options: See QP_SIM
0035 %  --------
0036 %
0037 %  Outputs:
0038 %  -------
0039 % u     optimal control
0040 % W     active constraints in u (+/- : max/min, 1/2 : position/rate)
0041 % time  average computation time per sample
0042 % iter  no. of iterations
0043 %
0044 %  Step response example:
0045 %
0046 %   B = [2 1]; t = 0:.2:10; v = 1*(t>1); plim = [-1 1;-1 1];
0047 %   W1 = eye(2); W2 = diag([5 0]); S = pinv(B);
0048 %   u = dyn_sim(B,v,plim,[],.2,1,W1,W2,S);
0049 %   figure(1),bodemag(dca(B,S,W1,W2,.2))
0050 %   figure(2),stairs(t,[u' v']),legend('u_1','u_2','v=2u_1+u_2')
0051 %
0052 % See also: DCA, QP_SIM, DIR_SIM.
0053   
0054 % Number of variables
0055   [k,m] = size(B);
0056 
0057   % Find no. of optional arguments (excluding options)
0058   iopt = length(varargin)+1;
0059   for i = 1:length(varargin)
0060     if ischar(varargin{i})
0061       iopt = i; % index of first option string
0062       break;
0063     end
0064   end
0065   narg = iopt-1;
0066 
0067   % Set default values of optional arguments
0068   rlim = [];
0069   T    = 1;
0070   Wv   = eye(k);
0071   W1   = eye(m);
0072   W2   = zeros(m);
0073   S    = zeros(m,k);
0074 
0075   % Set values of submitted optional arguments
0076   for i=1:narg
0077     switch i
0078      case 1, rlim = varargin{i};
0079      case 2, T      = varargin{i};
0080      case 3, Wv      = varargin{i};
0081      case 4, W1      = varargin{i};
0082      case 5, W2      = varargin{i};
0083      case 6, S      = varargin{i};
0084     end
0085   end
0086   
0087   % Call generic control allocation simulation subroutine.
0088   [u,W,time,iter] = alloc_sim('dyn',B,v,plim,rlim,T,'Wv',Wv,'W1', ...
0089                   W1,'W2',W2,'S',S,varargin{iopt:end});
0090

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