acker.m

数字通信第四版原书的例程

function k = acker(a,b,p)
%ACKER	Pole placement gain selection using Ackermann's formula.
%	K = ACKER(A,B,P)  calculates the feedback gain matrix K such that
%	the single input system
%	        .
%	        x = Ax + Bu 
%
%	with a feedback law of  u = -Kx  has closed loop poles at the 
%	values specified in vector P, i.e.,  P = eig(A-B*K).
%
%	See also PLACE.
%
%	Note: This algorithm uses Ackermann's formula.  This method
%	is NOT numerically reliable and starts to break down rapidly
%	for problems of order greater than 10, or for weakly controllable
%	systems.  A warning message is printed if the nonzero closed loop
%	poles are greater than 10% from the desired locations specified 
%	in P.

%	Algorithm is from page 201 of:
%	Kailath, T.  "Linear Systems", Prentice-Hall, 1980.

%	Copyright (c) 1986-93 by the MathWorks, Inc.

error(nargchk(3,3,nargin));
error(abcdchk(a,b));

[m,n] = size(b);
if n ~= 1
	error('System must be single input');
end
p = p(:);		% Make sure roots are in a column vector
[mp,np] = size(p);
[m,n] = size(a);
if (m ~= mp)
	error('Vector P must have SIZE(A) elements');
end

% Form gains using Ackerman's formula
k = ctrb(a,b)\polyvalm(real(poly(p)),a);
k = k(n,:);

% Check results. Start by removing 0.0 pole locations
p = sort(p);
i = find(p ~= 0);
p = p(i);
pc = sort(eig(a-b*k));
pc = pc(i);
if max(abs(p-pc)./abs(p)) > .1
	disp('Warning: Pole locations are more than 10% in error.')
end