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annotate m-toolbox/classes/+utils/@math/pf2ss.m @ 21:8be9deffe989 database-connection-manager

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Update ltpda_uo.update
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
parents f0afece42f48
children
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 % PF2SS Convert partial fraction models to state space matrices
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Daniele Nicolodi <nicolodi@science.unitn.it>
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2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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3 % DESCRIPTION:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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4 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 % Convert partial fraction models to state space matrices. This method
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 % works only for poles of multiplicity one. In case of multiple parfrac
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 % models they must have the same set of poles.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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10 % CALL:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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11 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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12 % [A,B,C,D] = pf2ss(pf)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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13 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 % INPUTS:
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15 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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16 % Assuming to have M pf models with N poles (common to every model)
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17 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 % - res, vector of matrix of residuals NxM, M is the number of pf
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Daniele Nicolodi <nicolodi@science.unitn.it>
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19 % models
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Daniele Nicolodi <nicolodi@science.unitn.it>
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20 % - poles, vector of poles Nx1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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21 % - dterm, vector of direct terms, Mx1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 % OUTPUT:
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24 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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25 % - A matrix
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 % - B matrix
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27 % - C matrix
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28 % - D matrix
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Daniele Nicolodi <nicolodi@science.unitn.it>
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29 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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31 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 % NOTE:
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33 %
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34 % This method works only for poles of multiplicity one.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 % In case of multiple parfrac models they must have the same set of poles
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 % HISTORY: 29-01-2010 L Ferraioli
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38 % Creation
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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40 % VERSION: '$Id: vcfit.m,v 1.10 2009/04/21 10:15:35 luigi Exp $';
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41 %
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42 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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43 function [A,B,C,D] = pf2ss(res,poles,dterm)
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44
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Daniele Nicolodi <nicolodi@science.unitn.it>
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45 [N,M]=size(res);
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46
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Daniele Nicolodi <nicolodi@science.unitn.it>
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47 % pf = varargin{:};
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48 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 % %%% get poles, residues and direct terms
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Daniele Nicolodi <nicolodi@science.unitn.it>
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50 % poles = pf(1).poles; % a common set of poles is assumed
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51 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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52 % N = length(poles);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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53 % M = numel(pf);
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54 %
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55 % res = zeros(N,M); % init residues matrix
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56 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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57 % if size(poles,2)>1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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58 % poles = poles.';
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Daniele Nicolodi <nicolodi@science.unitn.it>
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59 % end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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60 % dterm = zeros(M,1); % init dterm matrix
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61 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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62 % for ii=1:M
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63 % r = pf(ii).res;
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64 % if size(r,2)>1
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65 % r = r.';
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66 % end
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67 % res(:,ii) = r;
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68 % dterm(ii,1) = pf(ii).dir;
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69 % end
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70
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Daniele Nicolodi <nicolodi@science.unitn.it>
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71 %%% Marking complex and real poles
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Daniele Nicolodi <nicolodi@science.unitn.it>
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72 % cindex = 1; pole is complex, next conjugate pole is marked with cindex
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Daniele Nicolodi <nicolodi@science.unitn.it>
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73 % = 2. cindex = 0; pole is real
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Daniele Nicolodi <nicolodi@science.unitn.it>
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74 cindex=zeros(1,N);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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75 for m=1:N
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Daniele Nicolodi <nicolodi@science.unitn.it>
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76 if imag(poles(m))~=0
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Daniele Nicolodi <nicolodi@science.unitn.it>
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77 if m==1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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78 cindex(m)=1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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79 else
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80 if cindex(m-1)==0 || cindex(m-1)==2
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81 cindex(m)=1; cindex(m+1)=2;
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82 else
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83 cindex(m)=2;
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84 end
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85 end
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86 end
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87 end
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88
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89 %%% Build SS matrices
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90 % init matrices
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Daniele Nicolodi <nicolodi@science.unitn.it>
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91 A = diag(poles);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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92 B = ones(N,M);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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93 C = res.';
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Daniele Nicolodi <nicolodi@science.unitn.it>
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94 D = dterm;
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95
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Daniele Nicolodi <nicolodi@science.unitn.it>
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96 for kk = 1:N
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Daniele Nicolodi <nicolodi@science.unitn.it>
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97 if cindex(kk) == 1
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98 A(kk,kk)=real(poles(kk));
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99 A(kk,kk+1)=imag(poles(kk));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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100 A(kk+1,kk)=-1*imag(poles(kk));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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101 A(kk+1,kk+1)=real(poles(kk));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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102 B(kk,:) = 2;
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103 B(kk+1,:) = 0;
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104 C(:,kk+1) = imag(C(:,kk));
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105 C(:,kk) = real(C(:,kk));
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106 end
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107 end
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108
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109 end
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110