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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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2 % Test ao/eqmotion for the solution of a torsion pendulum equation of the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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3 % motion
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4 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 % 25-03-2009 L. Ferraioli
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 % CREATION
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7 %
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8 % $Id: test_ao_eqmotion.m,v 1.1 2009/03/27 12:25:15 luigi Exp $
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9 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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10 %% Generate data
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11
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12 % generate signal + white noise
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13 a = ao(plist('tsfcn','20.*sin(2.*pi.*t./800)+randn(size(t))','fs',1,'nsecs',1e5,'yunits','rad'));
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14
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15 %% Solve equation of Motion for the torsion pendulum
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16
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17 % Set pendulum parameters
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18 I = 4.31e-5; % Moment of Inertia
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19 T0 = 563; % Oscillatory period
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20 Q = 2880; % Quality factor
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21 Gam = I*(2*pi/T0)^2;
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22
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23 % building coefficients AO
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24 alpha2 = cdata(I);
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25 alpha2.setYunits(unit('kg').*unit('m').^2./unit('rad'));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 alpha2 = ao(alpha2);
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27
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28 alpha1 = cdata(Gam./(2.*pi.*Q./T0));
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29 alpha1.setYunits(unit('kg').*unit('m').^2./unit('rad')./unit('s'));
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30 alpha1 = ao(alpha1);
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31
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32 alpha0 = cdata(Gam);
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33 alpha0.setYunits(unit('kg').*unit('m').^2./unit('rad')./unit('s').^2);
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34 alpha0 = ao(alpha0);
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35
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36 % Calculate torque output units are defined by the coefficients units
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37 pl1 = plist('ALPHA2',alpha2,'ALPHA1',alpha1,'ALPHA0',alpha0);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38 b1 = eqmotion(a,pl1);
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39 b1.simplifyYunits;
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40 b1.setName;
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41
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42 % Alternative torque calculation set the targunits to get appropiate output
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43 % units
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44 pl2 = plist('ALPHA2',I,'ALPHA1',Gam./(2.*pi.*Q./T0),'ALPHA0',Gam,'TARGETUNITS',unit('kg').*unit('m').^2./unit('s').^2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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45 b2 = eqmotion(a,pl2);
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46 b2.simplifyYunits;
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47 b2.setName;
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48
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49 % plotting
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50 iplot(b1,b2)
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51
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52 %% Extract TF
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53
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54 tf1 = tfe(a,b1,plist('Nfft',1e4));
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55
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56 tf2 = tfe(a,b2,plist('Nfft',1e4));
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57
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58 % Theorethical TF
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59 f = logspace(-4,log10(0.5),300);
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60 f = f.';
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61 s = 1i.*2.*pi.*f;
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62 I = 4.31e-5;
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63 T0 = 563;
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64 Q = 2880;
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65 Gam = I*(2*pi/T0)^2;
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66 TF = I.*s.^2 + (Gam./(2.*pi.*Q./T0)).*s + Gam;
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67 TF = ao(plist('xvals',f,'yvals',TF,'dtype','fsdata','fs',a.fs));
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68 TF.setYunits(tf1.yunits);
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69 TF.setName;
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70
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71 % plot
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72 iplot(TF,tf1,tf2)