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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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1 % PF2SS Convert partial fraction models to state space matrices
2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3 % DESCRIPTION:
4 %
5 % Convert partial fraction models to state space matrices. This method
6 % works only for poles of multiplicity one. In case of multiple parfrac
7 % models they must have the same set of poles.
8 %
9 %
10 % CALL:
11 %
12 % [A,B,C,D] = pf2ss(pf)
13 %
14 % INPUTS:
15 %
16 % Assuming to have M pf models with N poles (common to every model)
17 %
18 % - res, vector of matrix of residuals NxM, M is the number of pf
19 % models
20 % - poles, vector of poles Nx1
21 % - dterm, vector of direct terms, Mx1
22 %
23 % OUTPUT:
24 %
25 % - A matrix
26 % - B matrix
27 % - C matrix
28 % - D matrix
29 %
30 %
31 %
32 % NOTE:
33 %
34 % This method works only for poles of multiplicity one.
35 % In case of multiple parfrac models they must have the same set of poles
36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
37 % HISTORY: 29-01-2010 L Ferraioli
38 % Creation
39 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
40 % VERSION: '$Id: vcfit.m,v 1.10 2009/04/21 10:15:35 luigi Exp $';
41 %
42 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
43 function [A,B,C,D] = pf2ss(res,poles,dterm)
44
45 [N,M]=size(res);
46
47 % pf = varargin{:};
48 %
49 % %%% get poles, residues and direct terms
50 % poles = pf(1).poles; % a common set of poles is assumed
51 %
52 % N = length(poles);
53 % M = numel(pf);
54 %
55 % res = zeros(N,M); % init residues matrix
56 %
57 % if size(poles,2)>1
58 % poles = poles.';
59 % end
60 % dterm = zeros(M,1); % init dterm matrix
61 %
62 % for ii=1:M
63 % r = pf(ii).res;
64 % if size(r,2)>1
65 % r = r.';
66 % end
67 % res(:,ii) = r;
68 % dterm(ii,1) = pf(ii).dir;
69 % end
70
71 %%% Marking complex and real poles
72 % cindex = 1; pole is complex, next conjugate pole is marked with cindex
73 % = 2. cindex = 0; pole is real
74 cindex=zeros(1,N);
75 for m=1:N
76 if imag(poles(m))~=0
77 if m==1
78 cindex(m)=1;
79 else
80 if cindex(m-1)==0 || cindex(m-1)==2
81 cindex(m)=1; cindex(m+1)=2;
82 else
83 cindex(m)=2;
84 end
85 end
86 end
87 end
88
89 %%% Build SS matrices
90 % init matrices
91 A = diag(poles);
92 B = ones(N,M);
93 C = res.';
94 D = dterm;
95
96 for kk = 1:N
97 if cindex(kk) == 1
98 A(kk,kk)=real(poles(kk));
99 A(kk,kk+1)=imag(poles(kk));
100 A(kk+1,kk)=-1*imag(poles(kk));
101 A(kk+1,kk+1)=real(poles(kk));
102 B(kk,:) = 2;
103 B(kk+1,:) = 0;
104 C(:,kk+1) = imag(C(:,kk));
105 C(:,kk) = real(C(:,kk));
106 end
107 end
108
109 end
110