www.gusucode.com > rctobsolete 工具箱 matlab源码程序 > rctobsolete/mutools/commands/sdhfsyn.m
%function [k,gfin]=
% sdhfsyn(sdsys,nmeas,ncon,gmin,gmax,tol,h,delay,ricmethd,epr,epp,quiet)
%
% This function computes the H-infinity (sub) optimal n-state
% discrete-time controller for a sampled-data system. Using
% results from Bamieh and Pearson '92, the initial problem is
% converted isomorphically to discrete-time. The discrete-time
% problem is bilinearly mapped to continuous-time where Glover's
% and Doyle's 1988 result is used.
%
% The continuous-time plant SDSYS is partitioned:
% | a b1 b2 |
% sdsys = | c1 0 0 |
% | c2 0 0 |
% where b2 has column size of the number of control inputs (NCON)
% and c2 has row size of the number of measurements (NMEAS) being
% provided to the controller. Note that d must be zero.
%
% Inputs:
% SDSYS - interconnection matrix for control design
% (continuous time)
% NMEAS - # controller inputs (np2)
% NCON - # controller outputs (nm2)
% GMIN - lower bound on gamma (MUST BE GREATER THAN 0)
% GMAX - upper bound on gamma
% TOL - relative difference between final gamma values
% H - sampling period of the controller to be designed
% DELAY - a non-negative integer giving the number of
% computational delays of the controller (default is 0)
% RICMETHD - Riccati solution via
% 1 - eigenvalue reduction (balance)
% -1 - eigenvalue reduction (no balancing)
% 2 - real schur decomposition (balance,default)
% -2 - real schur decomposition (no balancing)
% EPR - measure of when real(eig) of Hamiltonian is zero
% (default EPR = 1e-10)
% EPP - positive definite determination of xinf solution
% (default EPP = 1e-6)
% QUIET - print out information on sampled-data H-infinity iteration
% 0 - do not print results
% 1 - print results to command window (default)
%
%
% Outputs:
% K - H-infinity controller (discrete time)
% GFIN - final gamma value used in control design
%
% _________
% | |
% <-------| sdsys |<--------
% | |
% /--------|_________|<-----\
% | __ |
% | |d | |
% | __ |e | ___ __ |
% |_|S |_|l |__| K |__|H |___|
% |__| |a | |___| |__|
% |y |
% |__|
%
% See also: DHFNORM, DHFSYN, DTRSP, H2SYN, H2NORM, HINFFI, HINFNORM,
% RIC_EIG, RIC_SCHR, SDTRSP and SDHFNORM
% Copyright 1991-2004 MUSYN Inc. and The MathWorks, Inc.
function [k,gfin]= ...
sdhfsyn(sdsys,nmeas,ncon,gmin,gmax,tol,h,delay,ricmethd,epr,epp,quiet);
% Initialize return values
k = []; gfin = [];
% perform type checking
if nargin == 0
disp('usage: [k,gfin] = sdhfsyn(sdsys,nmeas,ncon,gmin,gmax,tol,h,delay,ricmethd,epr,epp) ')
return
end
if nargin <= 7,
disp('usage: [k,gfin] = sdhfsyn(sdsys,nmeas,ncon,gmin,gmax,tol,h,delay,ricmethd,epr,epp) ')
error('incorrect number of input arguments')
return
end
[typ,p,m,n]=minfo(sdsys);
if typ~='syst',
error(' Plant is not a system')
return
end
if h<= 0,
error(' Sampling period H is nonpositive')
return
end
if delay < 0,
error(' DELAY must be a non-negative integer');
return
end
if delay~=floor(delay),
error(' DELAY must be a non-negative integer');
return
end
if gmin > gmax,
error(' GAMMA MIN is greater than GAMMA MAX')
return
end
if tol<=0,
error(' TOL must be positive')
return
end
if gmin <= 0
error(' GMIN must be greater than 0')
return
end
% setup default cases
if nargin == 7
delay=0;
ricmethd = 2;
epr = 1e-10;
epp = 1e-6;
quiet = 1;
elseif nargin == 8
ricmethd = 2;
epr = 1e-10;
epp = 1e-6;
quiet = 1;
elseif nargin == 9
epr = 1e-10;
epp = 1e-6;
quiet = 1;
elseif nargin == 10
epp = 1e-6;
quiet = 1;
elseif nargin == 11
quiet = 1;
end
% check data
[a,b,c,d]=unpck(sdsys);
if rank( diag( exp(eig(a)*h) + ones(n,1) ) ) < n
error(' System is pathologically sampled')
return
end
if max(max(abs(d)))~=0,
error(' D matrix non-zero')
return
end
% 7 nov 95
%
% The problem has more measurements than states with zero observation noise.
% Now in continuous time we would insist on full row rank D21 but
% in sampled-data we insist on D21=0. Hence in the sampled-data case
% if we have nmeas>xd there are redundant measurements and even after we
% have done all the SDEQUIV and converted to c-t via BILINZ2S we
% still essentially have redundant states. The failure is in fact
% in HINFSYNE with the [a b1; c2 d21] being rank deficient.
%
% There are two alternatives,
% - one is to say that nmeas<=xd is required.
% - the other is to detect this situation and then for example
% change c2 to be I and at the end post-multiply the controller
% by a left inverse of c2. The same problem will occur
% if we have ncont>xd and the solution would be then to
% replace b2 by I and then pre-multiply the
% resulting controller by a right inverse of b2.
%
b1 = b(1:n,1:m-ncon)/sqrt(gmin);
b2 = b(1:n,m-ncon+1:m);
c1 = c(1:p-nmeas,1:n)/sqrt(gmin);
c2 = c(p-nmeas+1:p,1:n);
realnmeas = nmeas; % MOVED for matlab v5
if nmeas>n,
realc2 = c2;
c2 = eye(n);
nmeas = n;
end
realncont = ncon; % MOVED for matlab V5
if ncon>n,
realb2 = b2;
b2 = eye(n);
ncon = n;
end
[T,invT,S,s]=ham2schr(a,b1,c1,0.02/h);
sys1eye=pck(a,[b1 b2],[c1;c2]);
compnormltgmin=compnorm(T,invT,S,s,h);
% gamma iteration
if quiet == 1
fprintf('Test bounds: %10.4f < gamma <= %10.4f\n\n',gmin,gmax)
fprintf(' gamma hamx_eig xinf_eig hamy_eig yinf_eig nrho_xy p/f\n')
end
%initialize loop control variables
gtmp=gmax;
gold=gmax-2*tol;
itn=0; %flags the first iteration
if quiet == 1
dquiet = 0;
else
dquiet = 1;
end
%main driving loop
while abs(gold-gtmp)>tol/2,
b1=b(1:n,1:m-ncon)/sqrt(gtmp);
c1=c(1:p-nmeas,1:n)/sqrt(gtmp);
[T,invT,S,s]=ham2schr(a,b1,c1,0.02/h);
if compnormltgmin==0,
hcompnorm=compnorm(T,invT,S,s,h);
else
hcompnorm=1;
end
if hcompnorm==1,
dsdsys=sdequiv(a,b1,b2,c1,c2,T,invT,S,s,h,delay);
[dsdsystype,dsdsysp,dsdsysm,dsdsysn]=minfo(dsdsys);
% rescale gamma back from one to gtmp
if strcmp(dsdsystype,'syst'),
dsdsys(dsdsysn+1:dsdsysn+dsdsysp-nmeas,:) = ...
dsdsys(dsdsysn+1:dsdsysn+dsdsysp-nmeas,:)*sqrt(gtmp);
dsdsys(:,dsdsysn+1:dsdsysn+dsdsysm-ncon) = ...
dsdsys(:,dsdsysn+1:dsdsysn+dsdsysm-ncon)*sqrt(gtmp);
[ktmp]= ...
dhfsyn(dsdsys,nmeas,ncon,gtmp,gtmp,tol,h,inf,...
dquiet,ricmethd,epr,epp);
end %if if strcmp(dsdsystype,'syst')
if ~strcmp(dsdsystype,'syst') | isempty(ktmp),
soln=0;
else
soln=1;
end; %if isempty(ktmp)
else
soln=0;
end
if soln==0,
if itn==0,
fprintf('Gamma max, %10.4f, is too small !!\n',gmax);
return;
else
gmin=gtmp;
gold=gtmp;
gtmp=(gmax+gmin)/2;
itn=1;
if hcompnorm==1 & isempty(ktmp),
compnormltgmin=1;
end
end
else
if soln==1,
gmax=gtmp;
gold=gtmp;
gfin=gtmp;
gtmp=(gmax+gmin)/2;
k=(ktmp);
if realnmeas>n,
k=mmult(k,pinv(realc2));
end
if realncont>n,
k=mmult(pinv(realb2),k);
end
itn=1;
end
end
end % end of gamma iteration
if quiet == 1
fprintf('\n Gamma value achieved: %10.4f\n',gfin)
end
%end of function
%
%