triplep_old.m

         % FILENAME:     RM2003May07.m
% DESCRIPTION:  Recycling Mirror Triple Pendulum
% VERSION NO:   RM file version 9


% NOTE:         filename format RM<year><month><date>.m
%               version number to be incremented plus date changed

%%**********************************************************************
%%COMMENTS%%
%% PARAMETERS FOR THE RM SUSPENSION 
%% VERSION HAS NO LEVER_ARM INPUT
%%**********************************************************************

%****************************************************************************
% FILE LOG:
% Written by CIT 7/98                                               Version 1
% Modified by KAS 6/99 (version 0.5.1)                              Version 2
% Modified by PAW for LIGO recycling mirror triple                  Version 3
% Further modified by NAR April 02                                  Version 4
%   top mass is REPRESENTED by a rectangular BLOCK
%   in reality it will be larger and less dense.
% Modified by CAC on 22nd Jan 2003                                  Version 5
%   Update of NAR's TRIPLEP.M model to incorporate features 
%   of PAW's RMfile.m model.
% Modified by CIT on 29th January 2003                              Version 6
% Cleaned up version with new sub-folders
% Modified by CIT on February 3rd 2003 (02/03/03 CIT)               Version 7
% Changed parameters and tidied up lever arm section
% Modified by CIT on February 10th 2003 (02/10/03 CIT)               Version 8
% Changed radius of lower wire, leverarm and added iy&iz to output
%modified by NAR on 4th March 2003                                  Version 9
%modified by CIT on 7th May 2003
%   includes mass and moments from SWorks                            Version 10
%*****************************************************************************

%% coordinates x = longitudinal = u_LIGO roll about this axis
%%             y = transverse   = v_LIGO pitch about this axis
%%             z = vertical     = w_LIGO yaw about this axis

g              = 9.81;

%%%%%%%%%%%%%%%%%%%%%%%%%%% UPPER MASS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%*****1st ATTEMPT*****
%% top mass is REPRESENTED by a rectangular BLOCK
%% in reality it will be larger and less dense.
 %ux	= 0.10;			%dimensions of UPPER MASS (square)
 %uy  =  0.30;
 %uz	= 0.06;
 %den1	= 7000;		%density (steel with holes)
 %m1	= den1* uy* uz* ux;	%mass 
 %I1x	=  m1*( uy^2+ uz^2)/12;	%moment of inertia (transverse roll)
 %I1y	=  m1*( uz^2+ ux^2)/12;	%moment of inertia (longitudinal pitch)
 %I1z	=  m1*( uy^2+ ux^2)/12;	%moment of inertia (yaw)
 %m1_parameters = 'represented by a regtangular block';
 %material1 = 'steel'
%%%%%%%%%%%%%%%%%%%%%%% 
 
%%*****2nd ATTEMPT***** 
%% T-shaped calculated from mofi2.m
% m1             = 12.65;
% I1x            = 8.96e-2;
% I1y            = 2.76e-2;
% I1z            = 8.30e-2;

% m1             = 12.168; %top piece 0.1x0.44x0.017m, bottom piece 0.1x0.116x0.07m NAR 4 Mar 2003
% I1x            = 10.97e-2;  
% I1y            = 1.8613e-2;
% I1z            = 11.137e-2;

% m1_parameters = 'T-shaped calculated from mofi2.m';
% material1 = 'steel';
%%%%%%%%%%%%%%%%%%%%%%% 
 
%%*****3rd ATTEMPT***** 
%% FROM SOLIDWORKS ASSEMBLY OR ACTUAL MASS
 m1 =     12.07;      %Actual shape calculated from SWorks 01/09/02
 I1x =    1.263e-1;   %top plate 100X440X20mm / T-section 96X116X64mm
 I1y =    1.857e-2;
 I1z =    1.274e-1;
 m1_parameters = 'Calculated from SWorks Assem 2003Mar26';
 material1 = 'combination steel+alum';
%%%%%%%%%%%%%%%%%%%%%%%

 pend.m1_parameters = m1_parameters;
 pend.material1 = material1;
 pend.m1 = m1;
 pend.I1x = I1x;
 pend.I1y = I1y;
 pend.I1z = I1z;

%*********************************************************************************
%%%%%%%%%%%%%%%%%%%%INTERMEDIATE MASS%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1st Attempt - NOISE PROTOTYPE
% Silica cylindrical mass
 %ix	    = 0.10;			%dimension of INTERMEDIATE MASS (cylinder)
 %ir	    = 0.1325;

%den2	= 2202;			%density (fused silica)
%m2	    = den2*pi* ir^2* ix	;%intermediate mass
%I2x	= m2*(ir^2/2);		%moment of inertia (transverse roll)
%I2y	= m2*(ir^2/4+ix^2/12);	%moment of inertia (longitudinal pitch)
%I2z	= m2*(ir^2/4+ix^2/12);	%moment of inertia (yaw)
%m2_parameters = 'Noise P-type: Silica Mass';
%material2 = 'silica';

% 2nd Attempt  - CONTROLS PROTOTYPE
% Aluminium "dummy" intermediate mass
% ix             = 0.10;                 %dimensions of INTERMEDIATE MASS (square)
% iy             = 0.265;                %incorporated by CAC 01/2003
% iz             = 0.10;                 %incorporated by CAC 01/2003
% den2           = 4600;                 %combined aluminium and steel to give same mass as m3
% m2             = den2* iy* iz* ix;     %mass     %changed by CIT 01/29/2003
% I2x            =  m2*( iy^2+ iz^2)/12; %moment of inertia (transverse roll)
% I2y            =  m2*( iz^2+ ix^2)/12; %moment of inertia (longitudinal pitch)
% I2z            =  m2*( iy^2+ ix^2)/12; %moment of inertia (yaw)
%m2_parameters = 'Controls P-type: Rectangular block';
%material2 = 'alum with holes + s/steel clamps'; 

% 3rd Attempt  - CONTROLS PROTOTYPE
% Aluminium "dummy" intermediate mass

%ix	    = 0.1;			%dimension of INTERMEDIATE MASS (RECTANGLE)
%iy	    = 0.255; 
%iz      = 0.092;
m2 =    12.214;     %Actual shape calculated from SWorks
I2x =   8.162e-2;   %Dimensions 100X255X92mm   
I2y =   2.035e-2;
I2z =   8.143e-2;
m2_parameters = 'Controls P-type: Calculated from SWorks Assembly';
material2 = 'alum + s/stl inserts + s/stl clamps'; 


pend.m2_parameters = m2_parameters;
 pend.material2 = material2;
 %pend.ix = ix;
 %pend.iy = iy;
 %pend.iz = iz;
 pend.m2 = m2;
 pend.I2x = I2x;
 pend.I2y = I2y;
 pend.I2z = I2z;
 
%*******************************************************************************
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% TEST MASS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1st Attempt - NOISE PROTOTYPE
% Silica cylindrical test mass
 tx             = 0.10;                 %dimensions of TEST MASS (cylinder)
 tr             = 0.1325;
 
  %tx             = 0.10;                 %dimensions of TEST MASS (cylinder)
 %tr             = 0.1425;  %revised size Feb 2007 return to original size
 %April 2007
 
 
 
 
 
 den3	= 2202;			%density (fused silica)
 m3	    = den3*pi*tr^2*tx;	%test mass 
 I3x	= m3*(tr^2/2);		%moment of inertia (transverse roll)
 I3y	= m3*(tr^2/4+tx^2/12);	%moment of inertia (longitudinal pitch)
 I3z	= m3*(tr^2/4+tx^2/12);	%moment of inertia (yaw)
m3_parameters = 'Noise P-type: Silica Mass without flats and ears';
 material3 = 'silica';
 
% 2nd Attempt - CONTROLS PROTOTYPE
% Aluminium "dummy" test mass
%tx             = 0.10;                 
%tr             = 0.265/2;
%m3 =    12.181;     %Actual shape calculated from SWorks 01/09/02
%I3x =   1.051e-1;   % dimensions 100mm thick x 265mm diam
%I3y =   6.277e-2;
%I3z =   6.259e-2;
%m3_parameters = 'Controls P-tpye: Calculated from SWorks Assembly';
%material3 = 'alum with holes, flats + s/stl clamps';


 pend.m3_parameters = m3_parameters;
 pend.material3 = material3;
 pend.tx = tx;
 pend.tr = tr;
 pend.m3 = m3;
 pend.I3x = I3x;
 pend.I3y = I3y;
 pend.I3z = I3z;
 
%***********************************************************************************************


 l1             = 0.20;                 %upper wire length, changed from .25 by PAW 12/2001
 %l2            = 0.234;                %intermediate wire length
 %l2            = 0.25;                 %increased to give good clearance between masses w/ T top mass NAR Apr02

 
 l2             = 0.201;                %intermediate wire length changed from 0.234 by PAW 7/2002
                                        %incorporated by CAC 01/2003
 %l3            = 0.30;                 %lower wire length, changed from .20 by PAW 12/2001
 
 l3             = 0.253;                %lower wire length, changed from 0.30 by PAW 7/2002
                                        %incorporated by CAC 01/2003
pend.l1         = l1;
pend.l2         = l2;
pend.l3         = l3;
%******************************************************************************************


 nw1            =2;                     %number of wires (= number of cantilevers if fitted) per stage (2 or 4)
 nw2            =4;
 nw3            =4;
pend.nw1        = nw1;
pend.nw2        = nw2;
pend.nw3        = nw3;
%***********************************************************************************


 r1             = 300e-6;               %radius of upper wire gives stress 6.3e8 Pa for mass 36.43kg,2 wires
 %r2             = 200e-6;               %radius of intermediate wire 
 
%%CONTROLS PROTOTYPE
 r3_parameters = 'Spring Steel Wires';
 %r3	    = 140e-6;	% radius of lower wire UPDATED 10th FEB CIT, previously 200e-6
 
 r2 = 170e-6; % stress 6.6e8 Pa for mass 24.36 kg, 4 wires May 2007
 r3=120e-6;% stress 6.6e8 Pa for mass 12.15 kg on 4 wires May 2007

%%NOISE PROTOTYPE 
 %r3_parameters = 'Fused-Silica';
%r3	    = ???;	% radius of lower wire
 
 pend.r1 = r1;
 pend.r2 = r2;
 pend.r3_parameters = r3_parameters;
 pend.r3 = r3;



%************************************************************************************

 Y1	= 2.2e11;			%Youngs Modulus of upper wire  (s/steel 302)
                        % Changed to YM for California Steel Wire by CIT 01/09/02, previously 1.65e11
 Y2	= 2.2e11;			%Youngs Modulus of intermediate wire (s/steel 302)
                        % Changed to YM for California Steel Wire  by CIT 01/09/02

%%CONTROLS PROTOTYPE
 Y3_parameters = 'Spring Steel Wires';
 Y3	= 2.2e11;			%Youngs Modulus of lower wire (s/steel 302)
                        % Changed to YM for California Steel Wire  by CIT 01/09/02 
                        
  Y1 = 2.12e11; % number as measured by MB, 11/18/05
  Y2 = 2.12e11; % number as measured by MB, 11/18/05
  Y3 = 2.12e11; % number as measured by MB, 11/18/05
                                        
%%NOISE PROTOTYPE
 %Y3_parameters = 'Fused-Silica Fibres';
 %Y3	    = 7e10;			% Youngs Modulus of lower wire	(fused silica)
                                        
pend.Y1             = Y1;
pend.Y2             = Y2;
pend.Y3_parameters  = Y3_parameters;
pend.Y3             = Y3;

%************************************************************************************************************

% THE opt.m function is used to estimate a cantilever blade in order to get started.
% In order to take the design of a Cantilever blade forward it is necessary to used the EXCEL and ANSYS model.
% It is then necessary to override opt.m with the calculated numbers (an example is shown below on line 196


%blade design - upper blades
 mntb           = (m1 +m2 +m3)/2;         %total per blade
 mnb            = m1/2;                   %uncoupled mass
 
 %[uf,lnb,anb,hnb,stn] = opt(mnb,mntb,8e8,0.28,0.07);
  [uf,lnb,anb,hnb,stn] = opt(mnb,mntb,8e8,0.25,0.065);      %changed by NAR, same length as MC
 
 %ufc1           = uf;
 %pend.l1b       = lnb;
 %pend.a1b       = anb;
 %pend.h1b       = hnb;
 %pend.ufc1      = uf;
%pend.st1       = stn;
 %pend.intmode_1 = 55*hnb*0.37^2/(0.002*lnb^2); %scaled from GEO blade

 
 %*****************************
 %NAR override 
 %Upper blades:length: 25 cm, width: 6.5 cm, thickness: 2.3 mm, max. defl.: 104.8 mm, ufc1: 2.6 Hz (shape factor of 1.36).
 %masses from top to bottom of 12.6, 12.2, and 12.15 kg.
 %ufc1=2.6;          % MIKE PLISSI JAN/29/2003
 %pend.ufc1 = ufc1;
 
  %Note added 17th july 2007 Top mass is now 12.07 kg.
 % blades 25cm x 6.5 cm x 2.3 mm, alpha 1.36 gives freq 2.7 Hz, 
 %alpha 1.55 gives freq 2.52 Hz
  ufc1=2.7;        
 pend.ufc1 = ufc1;
 
 %*******************************************
 
%blade design - lower blades
 mntb           = (m2 +m3)/4;             %total per blade
 mnb            = m2/4;                   %uncoupled mass

 %[uf,lnb,anb,hnb,stn] = opt(mnb,mntb,8e8,0.20,0.05);
 [uf,lnb,anb,hnb,stn] = opt(mnb,mntb,8e8,0.12,0.04);        %changed by NAR, same length as MC
 
 %ufc2           = uf;
 %pend.l2b       = lnb;
 %pend.a2b       = anb;
 %pend.h2b       = hnb;
 %pend.ufc2      = uf;
 %pend.st2       = stn;
 %pend.intmode_2 = 55*hnb*0.37^2/(0.002*lnb^2); %scaled from GEO blade

%********************* 
%NAR override
%Lower blades:length: 12 cm, width: 4.0 cm, thickness: 1.2 mm, max. defl.: 49.9 mm, ufc2: 3.2 Hz (shape factor of 1.55).
%masses from top to bottom of 12.6, 12.2, and 12.15 kg. 
 %ufc2=3.2;              % MIKE PLISSI JAN/29/2003
 %pend.ufc2 = ufc2;
 %Note added 17th July - top mass is now 12.07 kg but makes no difference
 %to these blades
 %Note added 31 Aug 2007. In fact we had changed in 2003 to
 %different size of blades - 32 mm wide, 120 mm long and 1.3 mm thick. This
 %gives essentially same frequency. See file BLADE_RMv2.xls
ufc2 = 3.2;
pend.ufc2 = ufc2;
%**********************************************

 
 d0             = 0.001;                %height of upper wire break-off (above c.of m. upper mass)
 d1             = 0.001;                %height of intermediate wire break-off (below c.of m. upper mass)
 d2             = 0.001;                %height of intermediate wire break-off (above c.of m. of int. mass)
 d3             = 0.001;                %height of lower wire break-off (below c.of m. intermediate mass)
 d4             = 0.001;                %height of lower wire break-off (above c.of m.test mass)
 
 
 
d0             = 0.0036;                %with flexure lengths May 07 
d1             = 0.0024;                %lengths as calc. by MB code
 d2             = 0.0024;                %which allows for angling of wires
 d3             = 0.0021;                
 d4             = 0.0021; 
 
 
 
 
 
 pend.d0        = d0;                   %added CIT PAW 12/2001
 pend.d1        = d1;
 pend.d2        = d2;
 pend.d3        = d3;
 pend.d4        = d4;
 %pend.di = 'all 0.001'; %commented out NAR April02
%******************************************************************************************


% X direction separation


 su             = 0.00;                 % 1/2 separation of upper wires  
 %si             = 0.028;                % 1/2 separation of intermediate wires 
 si             = 0.03;                 %optimise damping of pitch highest mode NAR 4 Mar03
 sl             = 0.005;                % 1/2 separation of lower wires 

 pend.su        = su;
 pend.si        = si;
 pend.sl        = sl;
 %******************************************************************************************
 
%!!!!!!!!!!!!????!! NEED TO LOOK AT THE N's WRT MPL's LAYOUT!!!!!!!!??? 
 
% Y direction separation


%n0            = 0.06;                 % 1/2 separation of upper wires at suspension point
 n0             = 0.077;                % changed by NAR for similar footprint to MC
 n1             = 0.13;                 % 1/2 separation of upper wires at upper mass

                                        % incorporated by CAC 01/2003
%n2             = 0.03;                 % 1/2 separation of intermediate wires at upper mass - TO BE CONFIRMED
                                        % incorporated by CAC 01/2003
 n2             = 0.06;                 % CIT 02/04/03 CIT IN ORDER TO FIT WITH CLEARANCE OF THE 'T'-PIECE
 n2             = 0.07;                  %increased to accommodate wider T piece NAR 4MAr03

 %n3            = ir+0.0065;            % 1/2 separation of intermediate wires at intermediate mass
 %n3            = ir+0.0095;            % increased to give clearance of wire from edge of penultimate mass
 
 %n3             = iy/2+0.0139;          % 1/2 separation of intermediate wires at intermediate mass
                                        % incorporated by CAC 01/2003  
 n3 = 0.1275+0.01;                            % new number from CIT         
 
 n4             = tr+0.0015;            % 1/2 separation of lower wires at intermediate mass
 n4             = tr+0.005;            % allow for breakoff on side of curved mass NAR Feb2007
 %n4 = 0.1275+0.01;                           % new number from CIT
 
 n4 = 0.1455;   %revised number from B Kirsner June 2007, flats removed from mass
 
 n5             = tr+0.0015;            % 1/2 separation of lower wires at test mass
  n5             = tr+0.005;           % allow for breakoff on side of curved mass NAR Feb2007
 %n5 = tr-0.0024+0.0074;                 % new number from CIT
 
 n5 = 0.1455;   %revised number from B Kirsner June 2007, flats removed from mass
 
 pend.n0        = n0;
 pend.n1        = n1;
 pend.n2        = n2;
 pend.n3        = n3;
 pend.n4        = n4;
 pend.n5        = n5;
 
% overall length calculation added by CIT and PAW 12/2001 

% note added 26th Jan 2008. These lengths are recalculated in ssmake3MB
% where tl1 etc are centre to centre of masses and not as below (which
% doesnt include the ds)
% When listing parameters using pend.ref it calls ssmake3MB

pend.tl1        = sqrt(pend.l1^2 - (pend.n0-pend.n1)^2);
pend.tl2        = sqrt(pend.l2^2 - (pend.n2-pend.n3)^2);
pend.tl3        = sqrt(pend.l3^2 - (pend.n4-pend.n5)^2);
%overall length to the centre of mass of the test mass
pend.l_cofm     = pend.tl1+pend.tl2+pend.tl3+pend.d0+pend.d1+pend.d2+pend.d3+pend.d4;   
%overall length including the radius of the test mass
pend.l_total    = pend.tl1+pend.tl2+pend.tl3+pend.d0+pend.d1+pend.d2+pend.d3+pend.d4+pend.tr;




%***********************************************************************************


% represents small loss


 bd             = 0.01;                 % makes phases of open loop plots look nicer

bd=0.0;
 
 
%****************************************************************************************************** 
%IMPORTANT FOR REFERENCE ONLY!!! 
% THE FOLLOWING IS USED TO EXPLAIN THE CALCULATION OF THE NUMBER USED IN THE GAIN TRIANGLE
%Gain triangles in pendn.m

% lever_pitch   = 0.04;                 %PW DEC 02
% lever_yaw     = 0.1;                  %PW DEC 02
% lever_roll    = 0.1;                  %PW DEC 02    %UPDATED 10th FEB 2003 CIT

%% lever_pitch   = 0.03;                %changed by NAR to be same as MC
%% lever_yaw     = 0.08;                %changed by NAR to be same as MC
%% lever_roll    = 0.06;                %changed by NAR to be same as MC              

% pend.lever_pitch = lever_pitch; 
% pend.lever_yaw = lever_yaw; 
% pend.lever_roll = lever_roll;

%gain   = -0.2;                          %PW DEC 02

%% gain = -0.4;                          %changed by NAR to be same as MC  

%Gain triangle = (leverarm)^2 * (no. of coils) * gain


%***Note that gains are linked in different directions due to common coils as below*****
%***If gains in one channel only need to be changed then leverarm can be used***********


%gainzrtrl =gain;       % vertical, z, pitch, rt, roll rl (coils on top of upper mass)
%gaint   = gain.*2;     % transverse, t (coil on one end of upper mass)
%gainlrz = gain;        % longitudinal, l, yaw, rz (coils on long rear side of upper mass) 

%EQUATIONS

%long   = (1)^2             *  2 * gainlrz      = -0.4       incorporated by CAC 01/2003 TO BE CONFIRMED
%pitch  = (lever_pitch)^2   *  2 * gainzrtrl    = -0.00064   incorporated by CAC 01/2003 TO BE CONFIRMED
%vert   = (1)^2             *  3 * gainzrtrl    = -0.6       incorporated by CAC 01/2003 TO BE CONFIRMED
%yaw    = (lever_yaw)^2     *  2 * gainlrz      = -0.004     incorporated by CAC 01/2003 TO BE CONFIRMED
%trans  = (1)^2              *  1 * gaint       = -0.4       incorporated by CAC 01/2003 TO BE CONFIRMED
%roll   = (lever_roll)^2 *  3 * gainzrtrl       = -0.006     incorporated by CAC 01/2003 TO BE CONFIRMED

% NOTE: - NUMBERS ON RHS OF ABOVE EQUATIONS ARE CONSISTENT WITH GAIN AND LEVER ARMS SUPPLIED   %
%  BY PW in Dec 02, AS SHOWN ABOVE                                                              %

%long   = (1)^2             *  2 * gainlrz      = -0.4       
%pitch  = (lever_pitch)^2   *  2 * gainzrtrl    = -0.00081        lever arm 0.045
%vert   = (1)^2             *  3 * gainzrtrl    = -0.6       
%yaw    = (lever_yaw)^2     *  2 * gainlrz      = -0.00256     lever arm 0.08
%trans  = (1)^2              *  1 * gaint       = -0.4       
%roll   = (lever_roll)^2 *  3 * gainzrtrl       = -0.00384     lever arm 0.08

% the above set of numbers with alternative lever arms as shown, gain still -0.2 NAR 4Mar 03

% numbers below correspond to gain = -0.4 and lever arms as shown NAR FEB
% 2007

%long   = (1)^2             *  2 * gainlrz      = -0.8       
%pitch  = (lever_pitch)^2   *  2 * gainzrtrl    = -0.00162        lever arm 0.045
%vert   = (1)^2             *  3 * gainzrtrl    = -1.2       
%yaw    = (lever_yaw)^2     *  2 * gainlrz      = -0.00512     lever arm 0.08
%trans  = (1)^2              *  1 * gaint       = -0.8       
%roll   = (lever_roll)^2 *  3 * gainzrtrl       = -0.00432     lever arm 0.06










%*******************************************************************************************************
%****************************************************************************************************** 

%VIEWER PREFERENCES (under edit on LTI viewer)

%UNITS
%Frequency in Hz using Log scale
%Magnitude in absolute using log scale
%Phase in degrees


%TIME VECTOR
%[0:0.01:50]

%FREQUENCY VECTOR
%logspace(-0.5,1.5,500)