Demonstrate eigenvector assignment using an STOVL Model for transition.
The example is taken from:
Lee, H. P., Jr., Yousseff, H.M. and R.P. Habek, "Application of Eigenstructure Assignment to the Design of STOVL Flight Control Systems," AIAA 88-4140-CP.
------------------------------------------------------------------------ See also CCVSobel, ESAssign ------------------------------------------------------------------------
Contents
%-------------------------------------------------------------------------- % Copyright (c) 2003 Princeton Satellite Systems, Inc. % All rights reserved. %--------------------------------------------------------------------------
System
%------- g = CCVSobel( 'pitch pointing' ); disp(' ') disp('---------------------') disp('Open loop eigenvalues') disp('---------------------') eig(g)
---------------------
Open loop eigenvalues
---------------------
ans =
0
5.4515
-7.6618
-20
-20
Desired eigenvalues
%-------------------- j = sqrt(-1); lambda = [ -5.6 + j*4.2;... -5.6 - j*4.2;... -1.0;... -19;... -19.5]; vD = [0 0 1 nan nan;... 1 nan 0 nan nan;... nan 1 nan nan nan;... nan nan nan 1 nan;... nan nan nan nan 1];
Compute the gain and the achieved eigenvectors
%----------------------------------------------- f = ESAssign( g, lambda, vD ); [a, b, c] = getabcd( g ); gCL = g; aCL = a - b*f*c; gainMatrix = f; closedLoopEigenvalues = eig(aCL); disp(gainMatrix); disp(closedLoopEigenvalues); gCL = set( gCL, aCL, 'a' ); %--------------------------------------
-0.93092 -0.14892 -3.2504 -0.15296 0.74705
0.95418 0.20978 6.1006 0.53685 -1.0352
-1 + 0i
-5.6 + 4.2i
-5.6 - 4.2i
-19 + 0i
-19.5 + 0i