Mercurial > hg > ltpda

annotate m-toolbox/classes/@ssm/steadyState.m @ 30:317b5f447f3e database-connection-manager

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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 % STEADYSTATE returns a possible value for the steady state of an ssm.
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2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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3 %
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4 % DESCRIPTION: STEADYSTATE returns a possible value for the steady state
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5 % of the state space of an ssm with given inputs.
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6 %
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7 % CALL: [pl_out] = steadyState(sys, pl)
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8 %
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9 % INPUTS:
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10 % - sys, an ssm object
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11 %
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12 % OUTPUTS:
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13 % _ pl_out contains 'state', the random state position
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14 %
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15 % <a href="matlab:utils.helper.displayMethodInfo('ssm', 'steadyState')">Parameters Description</a>
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16 %
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17 % VERSION: $Id: steadyState.m,v 1.11 2011/04/08 08:56:23 hewitson Exp $
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18 %
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19 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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20
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21 % TO DO: Check input aos for the timestep, tsdata, and ssm.timestep
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22 % options to be defined (NL case)
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23 % add check if one input mach no ssm input variable
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24 % allow use of other LTPDA functions to generate white noise
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25
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26
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27 function varargout = steadyState(varargin)
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28
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29 %% starting initial checks
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30
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31 % Check if this is a call for parameters
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32 if utils.helper.isinfocall(varargin{:})
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33 varargout{1} = getInfo(varargin{3});
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34 return
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35 end
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36
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37 utils.helper.msg(utils.const.msg.MNAME, ['running ', mfilename]);
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38
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39 % Collect input variable names
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40 in_names = cell(size(varargin));
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41 for ii = 1:nargin,in_names{ii} = inputname(ii);end
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42
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43 % Collect all SSMs and plists
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44 [sys, ssm_invars, rest] = utils.helper.collect_objects(varargin(:), 'ssm', in_names);
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45 [pl, invars2, rest] = utils.helper.collect_objects(rest(:), 'plist');
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46 if ~isempty(rest)
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47 pl = combine(pl, plist(rest{:}));
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48 end
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49 pl = combine(pl, getDefaultPlist());
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50
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51 %% begin function body
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52
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53 if numel(sys)~=1
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54 error('simulate needs exactly one ssm as an input')
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55 end
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56 if ~sys.isnumerical
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57 error(['error because system ',sys.name,' is not numerical']);
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58 end
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59 timestep = sys.timestep;
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60 if timestep==0
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61 error('timestep should not be 0 in steadyState!!')
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62 end
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63 if pl.isparam('noise variable names')
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64 error('The noise option used must be split between "covariance" and "cpsd". "noise variable names" does not exist anymore!')
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65 end
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66 sssizes = sys.sssizes;
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67 %% collecting simulation i/o data
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68
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69 constants_in = find(pl, 'constants');
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70 cov_in = find(pl, 'covariance');
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71 cpsd_in = find(pl, 'CPSD');
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72 noise_in = blkdiag(cov_in, cpsd_in/(timestep*2));
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73 [U1,S1,V1] = svd(noise_in.');
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74 if (sum(S1<0)>0)
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75 error('Covariance matrix is not positive definite')
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76 end
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77 noise_mat = U1*sqrt(S1);
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78
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79 %% modifying system's ordering
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80 if find(pl, 'reorganize')
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81 sys = reorganize(sys, pl, 'set', 'for simulate', 'internal', 'internal');
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82 end
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83
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84 %% getting system's i/o sizes
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85 inputSizes = sys.inputsizes;
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86
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87 Nnoise = inputSizes(2);
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88 Nconstants = inputSizes(3);
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89
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90 if numel(diag(noise_in))~=Nnoise
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91 error(['There are ' num2str(numel(diag(noise_in))) ' input noise variances and ' num2str(Nnoise) ' corresponding inputs indexed.' ])
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92 elseif numel(constants_in)~=Nconstants
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93 error(['There are ' num2str(numel(constants_in)) ' input constants and ' num2str(Nconstants) ' corresponding inputs indexed.' ])
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94 end
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95
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96 A = sys.amats{1,1};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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97 Bnoise = sys.bmats{1,2} * noise_mat;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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98 Bcst = sys.bmats{1,3} * reshape(constants_in, Nconstants, 1);
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99
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100 %% counting powers of 2 to use for initilization
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Daniele Nicolodi <nicolodi@science.unitn.it>
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101 nSteps = 500;
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102 tSteady = find(pl, 'tSteady');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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103 nPow2 = nextpow2(tSteady/(nSteps*timestep));
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104
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105 %% simulation loop
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106 A_pow2=cell(1,nPow2);
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107 G_pow2=cell(1,nPow2);
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108
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109 A_pow2{1} = A;
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110 G_pow2{1} = Bcst;
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111
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112 %% method 1 : iterate equations with growing time-step for a very long time
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113 E_pow2=cell(1,nPow2);
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114 E_pow2{1} = Bnoise;
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115 for i_pow2 = 2:nPow2
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116 G_pow2{i_pow2} = G_pow2{i_pow2-1} + A_pow2{i_pow2-1}*G_pow2{i_pow2-1};
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117 E_pow2{i_pow2} = E_pow2{i_pow2-1} + A_pow2{i_pow2-1}*E_pow2{i_pow2-1};
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118 A_pow2{i_pow2} = A_pow2{i_pow2-1}^2;
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119 end
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120 lastX = zeros(size(A,1),1);
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121 for i_pow2 = fliplr(1:nPow2)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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122 A = A_pow2{i_pow2};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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123 G = G_pow2{i_pow2};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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124 E = E_pow2{i_pow2};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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125 noise_array = randn(size(E,2), nSteps);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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126 for i_steps = 1:nSteps
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127 lastX = A*lastX + G + E*noise_array(:,i_steps) ;
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128 end
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129 end
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130
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131 %% method 2 : compute the limit state-mean and covariance as i_pow2 tends to infinity
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132 % P_pow2=cell(1,nPow2);
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133 % P_pow2{1} = Bnoise*Bnoise.';
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134 % for i_pow2 = 2:nPow2
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135 % G_pow2{i_pow2} = G_pow2{i_pow2-1} + A_pow2{i_pow2-1}*G_pow2{i_pow2-1}; % taking step response to 2 longer time;
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136 % P_pow2{i_pow2} = P_pow2{i_pow2-1} + A_pow2{i_pow2-1}*P_pow2{i_pow2-1}*(A_pow2{i_pow2-1}.');% taking state covariance to 2 longer time;
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137 % A_pow2{i_pow2} = A_pow2{i_pow2-1}^2;
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138 % end
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139 % [U1,S1,V1] = svd(P_pow2{nPow2});
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140 % lastX = U1*sqrt(S1)*randn(size(A,1),1) + G_pow2{nPow2};
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141
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Daniele Nicolodi <nicolodi@science.unitn.it>
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142 %% construct output analysis object
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143 plist_out = plist('state', ssm.blockMatRecut(lastX,sssizes,1) );
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144 varargout = {plist_out};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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145 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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146
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147
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148 %--------------------------------------------------------------------------
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149 % Get Info Object
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150 %--------------------------------------------------------------------------
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151 function ii = getInfo(varargin)
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152
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Daniele Nicolodi <nicolodi@science.unitn.it>
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153 if nargin == 1 && strcmpi(varargin{1}, 'None')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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154 sets = {};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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155 pl = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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156 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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157 sets = {'Default'};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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158 pl = getDefaultPlist;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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159 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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160 % Build info object
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Daniele Nicolodi <nicolodi@science.unitn.it>
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161 ii = minfo(mfilename, 'ssm', 'ltpda', utils.const.categories.op, '$Id: steadyState.m,v 1.11 2011/04/08 08:56:23 hewitson Exp $', sets, pl);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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162 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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163
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Daniele Nicolodi <nicolodi@science.unitn.it>
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164 %--------------------------------------------------------------------------
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Daniele Nicolodi <nicolodi@science.unitn.it>
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165 % Get Default Plist
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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166 %--------------------------------------------------------------------------
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Daniele Nicolodi <nicolodi@science.unitn.it>
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167 function pl = getDefaultPlist()
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Daniele Nicolodi <nicolodi@science.unitn.it>
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168 pl = plist();
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Daniele Nicolodi <nicolodi@science.unitn.it>
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169
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Daniele Nicolodi <nicolodi@science.unitn.it>
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170 p = param({'cpsd variable names', 'A cell-array of strings specifying the desired input variable names.'}, {} );
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Daniele Nicolodi <nicolodi@science.unitn.it>
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171 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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172
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Daniele Nicolodi <nicolodi@science.unitn.it>
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173 p = param({'cpsd', 'The covariance of this noise between input ports for the <i>time-continuous</i> noise model.'}, []);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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174 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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175
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Daniele Nicolodi <nicolodi@science.unitn.it>
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176 p = param({'covariance variable names', 'A cell-array of strings specifying the desired input variable names.'}, {} );
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Daniele Nicolodi <nicolodi@science.unitn.it>
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177 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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178
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Daniele Nicolodi <nicolodi@science.unitn.it>
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179 p = param({'covariance', 'The covariance of this noise between input ports for the <i>time-continuous</i> noise model.'}, []);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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180 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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181
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Daniele Nicolodi <nicolodi@science.unitn.it>
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182 p = param({'constant variable names', 'A cell-array of strings of the desired input variable names.'}, {});
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Daniele Nicolodi <nicolodi@science.unitn.it>
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183 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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184
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Daniele Nicolodi <nicolodi@science.unitn.it>
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185 p = param({'constants', 'Array of DC values for the different corresponding inputs.'}, paramValue.DOUBLE_VALUE(zeros(0,1)));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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186 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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187
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Daniele Nicolodi <nicolodi@science.unitn.it>
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188 p = param({'tSteady', 'The settling time used in the calculation, in the same unit as the ssm''s timestep'}, paramValue.DOUBLE_VALUE(10^6) );
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Daniele Nicolodi <nicolodi@science.unitn.it>
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189 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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190
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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191 p = param({'reorganize', 'When set to 0, this means the ssm does not need be modified to match the requested i/o. Faster but dangerous!'}, paramValue.TRUE_FALSE);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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192 pl.append(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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193
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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194 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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195