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generateShapedNoise('Ts', 1/Fs, ... %% Sweep Sine gc = 0.1; xi = 0.5; -wn = 2*pi*92.7; +wn = 2*pi*94.3; % Notch filter at the resonance of the APA G_sweep = 0.2*(s^2 + 2*gc*xi*wn*s + wn^2)/(s^2 + 2*xi*wn*s + wn^2); @@ -41,15 +41,6 @@ V_sweep = generateSweepExc('Ts', Ts, ... 'sweep_type', 'log', ... 'V_exc', G_sweep*1/(1 + s/2/pi/500)); -V_sweep_lf = generateSweepExc('Ts', Ts, ... - 'f_start', 0.1, ... - 'f_end', 10, ... - 'V_mean', 3.25, ... - 't_start', Trec_start, ... - 'exc_duration', Trec_dur, ... - 'sweep_type', 'log', ... - 'V_exc', 0.2); - %% High Frequency Shaped Noise [b,a] = cheby1(10, 2, 2*pi*[300 2e3], 'bandpass', 's'); wL = 0.005*tf(b, a); @@ -70,19 +61,6 @@ V_sin = generateSinIncreasingAmpl('Ts', 1/Fs, ... 't_start', Trec_start, ... 'smooth_ends', true); -%% Zero Excitation -% Trec_start = 10; % Start time for Recording [s] -% Trec_dur = 40; % Recording Duration [s] -% -% Tsim = 2*Trec_start + Trec_dur; % Simulation Time [s] - -V_zero = generateShapedNoise('Ts', 1/Fs, ... - 'V_mean', 3.25, ... - 't_start', Trec_start, ... - 'exc_duration', Trec_dur, ... - 'smooth_ends', true, ... - 'V_exc', tf(0)); - %% Select the excitation signal V_exc = timeseries(V_noise(2,:), V_noise(1,:)); @@ -91,12 +69,12 @@ figure; tiledlayout(1, 2, 'TileSpacing', 'Normal', 'Padding', 'None'); ax1 = nexttile; -plot(V_exc.Time, squeeze(V_exc.Data)); +plot(V_exc(1,:), V_exc(2,:)); xlabel('Time [s]'); ylabel('Amplitude [V]'); ax2 = nexttile; -win = hanning(floor(length(squeeze(V_exc.Data))/8)); -[pxx, f] = pwelch(squeeze(V_exc.Data), win, 0, [], Fs); +win = hanning(floor(length(V_exc)/8)); +[pxx, f] = pwelch(V_exc(2,:), win, 0, [], Fs); plot(f, pxx) xlabel('Frequency [Hz]'); ylabel('Power Spectral Density [$V^2/Hz$]'); set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); diff --git a/matlab/test_bench_apa300ml/APA300ML_full_mat_K.CSV b/matlab/mat/APA300ML_full_mat_K.CSV similarity index 100% rename from matlab/test_bench_apa300ml/APA300ML_full_mat_K.CSV rename to matlab/mat/APA300ML_full_mat_K.CSV diff --git a/matlab/test_bench_apa300ml/APA300ML_full_mat_M.CSV b/matlab/mat/APA300ML_full_mat_M.CSV similarity index 100% rename from matlab/test_bench_apa300ml/APA300ML_full_mat_M.CSV rename to matlab/mat/APA300ML_full_mat_M.CSV diff --git a/matlab/test_bench_apa300ml/APA300ML_full_out_nodes_3D.txt b/matlab/mat/APA300ML_full_out_nodes_3D.txt similarity index 100% rename from matlab/test_bench_apa300ml/APA300ML_full_out_nodes_3D.txt rename to matlab/mat/APA300ML_full_out_nodes_3D.txt diff --git a/matlab/APA300ML/APA300ML_mat_K.CSV b/matlab/mat/APA300ML_mat_K.CSV similarity index 100% rename from matlab/APA300ML/APA300ML_mat_K.CSV rename to matlab/mat/APA300ML_mat_K.CSV diff --git a/matlab/APA300ML/APA300ML_mat_M.CSV b/matlab/mat/APA300ML_mat_M.CSV similarity index 100% rename from matlab/APA300ML/APA300ML_mat_M.CSV rename to matlab/mat/APA300ML_mat_M.CSV diff --git a/matlab/APA300ML/APA300ML_out_nodes_3D.txt b/matlab/mat/APA300ML_out_nodes_3D.txt similarity index 100% rename from matlab/APA300ML/APA300ML_out_nodes_3D.txt rename to matlab/mat/APA300ML_out_nodes_3D.txt diff --git a/matlab/mat/full_APA300ML_K.CSV b/matlab/mat/full_APA300ML_K.CSV new file mode 100644 index 0000000..5a09907 --- /dev/null +++ b/matlab/mat/full_APA300ML_K.CSV @@ -0,0 +1,36 @@ 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/dev/null +++ b/matlab/mat/full_APA300ML_out_nodes_3D.txt @@ -0,0 +1,61 @@ + + LIST ALL SELECTED NODES. DSYS= 0 + + *** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 *** + DISTRIBUTED ANSYS Mechanical Enterprise + + 00208316 VERSION=WINDOWS x64 10:10:05 MAR 26, 2021 CP= 2.188 + + Unknown + + + + NODE X Y Z THXY THYZ THZX + 1 0.0000 0.0000 0.28000E-001 0.00 0.00 0.00 + 1228810 0.0000 0.0000 -0.28000E-001 0.00 0.00 0.00 + 1228811 -0.30000E-001 0.0000 0.0000 0.00 0.00 0.00 + 1228812 0.10000E-001 0.0000 0.0000 0.00 0.00 0.00 + 1228813 0.30000E-001 0.0000 0.0000 0.00 0.00 0.00 + + LIST MASTERS ON ALL SELECTED NODES. + CURRENT DOF SET= UX UY UZ ROTX ROTY ROTZ + + *** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 *** + DISTRIBUTED ANSYS Mechanical Enterprise + + 00208316 VERSION=WINDOWS x64 10:10:05 MAR 26, 2021 CP= 2.188 + + Unknown + + + NODE LABEL SUPPORT + 1 UX + 1 UY + 1 UZ + 1 ROTX + 1 ROTY + 1 ROTZ + 1228810 UX + 1228810 UY + 1228810 UZ + 1228810 ROTX + 1228810 ROTY + 1228810 ROTZ + 1228811 UX + 1228811 UY + 1228811 UZ + 1228811 ROTX + 1228811 ROTY + 1228811 ROTZ + 1228812 UX + 1228812 UY + 1228812 UZ + 1228812 ROTX + 1228812 ROTY + 1228812 ROTZ + 1228813 UX + 1228813 UY + 1228813 UZ + 1228813 ROTX + 1228813 ROTY + 1228813 ROTZ diff --git a/matlab/src/initializeAPA.m b/matlab/src/initializeAPA.m new file mode 100644 index 0000000..0013a08 --- /dev/null +++ b/matlab/src/initializeAPA.m @@ -0,0 +1,98 @@ +function [actuator] = initializeAPA(args) +% initializeAPA - +% +% Syntax: [actuator] = initializeAPA(args) +% +% Inputs: +% - args - +% +% Outputs: +% - actuator - + +arguments + args.type char {mustBeMember(args.type,{'2dof', 'flexible frame', 'flexible'})} = '2dof' + + args.Ga (1,1) double {mustBeNumeric} = 0 + args.Gs (1,1) double {mustBeNumeric} = 0 + + % For 2DoF + args.k (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.35e6 + args.ke (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*1.5e6 + args.ka (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*43e6 + + args.c (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*3e1 + args.ce (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*2e1 + args.ca (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*2e1 + + args.Leq (6,1) double {mustBeNumeric} = ones(6,1)*0.056 + + % Force Flexible APA + args.xi (1,1) double {mustBeNumeric, mustBePositive} = 0.5 + + % For Flexible Frame + args.ks (1,1) double {mustBeNumeric, mustBePositive} = 235e6 + args.cs (1,1) double {mustBeNumeric, mustBePositive} = 1e1 +end + +actuator = struct(); + +switch args.type + case '2dof' + actuator.type = 1; + case 'flexible frame' + actuator.type = 2; + case 'flexible' + actuator.type = 3; +end + +if args.Ga == 0 + switch args.type + case '2dof' + actuator.Ga = -46.4; + case 'flexible frame' + actuator.Ga = 1; % TODO + case 'flexible' + actuator.Ga = 23.4; + end +else + actuator.Ga = args.Ga; % Actuator gain [N/V] +end + +if args.Gs == 0 + switch args.type + case '2dof' + actuator.Gs = 0.098; + case 'flexible frame' + actuator.Gs = 1; % TODO + case 'flexible' + actuator.Gs = -4674824; + end +else + actuator.Gs = args.Gs; % Sensor gain [V/m] +end + +actuator.k = args.k; % [N/m] +actuator.ke = args.ke; % [N/m] +actuator.ka = args.ka; % [N/m] + +actuator.c = args.c; % [N/(m/s)] +actuator.ce = args.ce; % [N/(m/s)] +actuator.ca = args.ca; % [N/(m/s)] + +actuator.Leq = args.Leq; % [m] + +switch args.type + case 'flexible frame' + actuator.K = readmatrix('APA300ML_b_mat_K.CSV'); % Stiffness Matrix + actuator.M = readmatrix('APA300ML_b_mat_M.CSV'); % Mass Matrix + actuator.P = extractNodes('APA300ML_b_out_nodes_3D.txt'); % Node coordinates [m] + case 'flexible' + actuator.K = readmatrix('full_APA300ML_K.CSV'); % Stiffness Matrix + actuator.M = readmatrix('full_APA300ML_M.CSV'); % Mass Matrix + actuator.P = extractNodes('full_APA300ML_out_nodes_3D.txt'); % Node coordiantes [m] +end + +actuator.xi = args.xi; % Damping ratio + +actuator.ks = args.ks; % Stiffness of one stack [N/m] +actuator.cs = args.cs; % Damping of one stack [N/m] diff --git a/matlab/src/initializeBotFlexibleJoint.m b/matlab/src/initializeBotFlexibleJoint.m new file mode 100644 index 0000000..95bc1e1 --- /dev/null +++ b/matlab/src/initializeBotFlexibleJoint.m @@ -0,0 +1,45 @@ +function [flex_bot] = initializeBotFlexibleJoint(args) +% initializeBotFlexibleJoint - +% +% Syntax: [flex_bot] = initializeBotFlexibleJoint(args) +% +% Inputs: +% - args - +% +% Outputs: +% - flex_bot - + +arguments + args.type char {mustBeMember(args.type,{'2dof', '3dof', '4dof'})} = '2dof' + + args.kRx (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*5 + args.kRy (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*5 + args.kRz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*260 + args.kz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*1e8 + + args.cRx (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.1 + args.cRy (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.1 + args.cRz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.1 + args.cz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*1e2 +end + +flex_bot = struct(); + +switch args.type + case '2dof' + flex_bot.type = 1; + case '3dof' + flex_bot.type = 2; + case '4dof' + flex_bot.type = 3; +end + +flex_bot.kRx = args.kRx; +flex_bot.kRy = args.kRy; +flex_bot.kRz = args.kRz; +flex_bot.kz = args.kz; + +flex_bot.cRx = args.cRx; +flex_bot.cRy = args.cRy; +flex_bot.cRz = args.cRz; +flex_bot.cz = args.cz; diff --git a/matlab/src/initializeTopFlexibleJoint.m b/matlab/src/initializeTopFlexibleJoint.m new file mode 100644 index 0000000..6e846aa --- /dev/null +++ b/matlab/src/initializeTopFlexibleJoint.m @@ -0,0 +1,45 @@ +function [flex_top] = initializeTopFlexibleJoint(args) +% initializeTopFlexibleJoint - +% +% Syntax: [flex_top] = initializeTopFlexibleJoint(args) +% +% Inputs: +% - args - +% +% Outputs: +% - flex_top - + +arguments + args.type char {mustBeMember(args.type,{'2dof', '3dof', '4dof'})} = '2dof' + + args.kRx (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*5 + args.kRy (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*5 + args.kRz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*260 + args.kz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*1e8 + + args.cRx (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.1 + args.cRy (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.1 + args.cRz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.1 + args.cz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*1e2 +end + +flex_top = struct(); + +switch args.type + case '2dof' + flex_top.type = 1; + case '3dof' + flex_top.type = 2; + case '4dof' + flex_top.type = 3; +end + +flex_top.kRx = args.kRx; +flex_top.kRy = args.kRy; +flex_top.kRz = args.kRz; +flex_top.kz = args.kz; + +flex_top.cRx = args.cRx; +flex_top.cRy = args.cRy; +flex_top.cRz = args.cRz; +flex_top.cz = args.cz; diff --git a/matlab/test_bench_apa300ml.slx b/matlab/test_bench_apa300ml.slx index b907f47..2d41f4c 100644 Binary files a/matlab/test_bench_apa300ml.slx and b/matlab/test_bench_apa300ml.slx differ diff --git a/matlab/test_bench_apa300ml/apa300ml_bot.STEP b/matlab/test_bench_apa300ml/apa300ml_bot.STEP new file mode 100644 index 0000000..e17094b --- /dev/null +++ b/matlab/test_bench_apa300ml/apa300ml_bot.STEP @@ -0,0 +1,1225 @@ +ISO-10303-21; +HEADER; +FILE_DESCRIPTION (( 'STEP AP214' ), + '1' ); +FILE_NAME ('apa300ml_bot.STEP', + '2021-03-26T08:51:52', + ( '' ), + ( '' ), + 'SwSTEP 2.0', + 'SolidWorks 2020', + '' ); +FILE_SCHEMA (( 'AUTOMOTIVE_DESIGN' )); 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Table of Contents

-
-

4.1.1 Without Encoder

+
+

4.1.1 Without Encoder

- +

-
-
4.1.1.1 FRF Identification - Setup
+
+
4.1.1.1 FRF Identification - Setup

The identification is performed in three steps: @@ -2435,8 +2367,8 @@ We get the frequency vector that will be the same for all the frequency domain a

-
-
4.1.1.2 FRF Identification - Displacement
+
+
4.1.1.2 FRF Identification - Displacement

In this section, the dynamics from the excitation voltage \(V_a\) to the interferometer \(d_a\) is identified. @@ -2452,14 +2384,14 @@ We compute the coherence for 2nd and 3rd identification:

-
+

strut_1_frf_dvf_plant_coh.png

Figure 53: Obtained coherence for the plant from \(V_a\) to \(d_a\)

-The transfer function from \(V_a\) to the interferometer measured displacement \(d_a\) is estimated and shown in Figure 54. +The transfer function from \(V_a\) to the interferometer measured displacement \(d_a\) is estimated and shown in Figure 54. 

[dvf_sweep, ~]    = tfestimate(leg_sweep.Va,    leg_sweep.da,    win, [], [], 1/Ts);
@@ -2468,7 +2400,7 @@ The transfer function from \(V_a\) to the interferometer measured displacement \
-
+

strut_1_frf_dvf_plant_tf.png

Figure 54: Estimated FRF for the DVF plant (transfer function from \(V_a\) to the interferometer \(d_a\))

@@ -2476,15 +2408,15 @@ The transfer function from \(V_a\) to the interferometer measured displacement \
-
-
4.1.1.3 FRF Identification - IFF
+
+
4.1.1.3 FRF Identification - IFF

In this section, the dynamics from \(V_a\) to \(V_s\) is identified.

-First the coherence is computed and shown in Figure 55. +First the coherence is computed and shown in Figure 55. The coherence is very nice from 10Hz to 2kHz. It is only dropping near a zeros at 40Hz, and near the resonance at 95Hz (the excitation amplitude being lowered).

@@ -2496,14 +2428,14 @@ It is only dropping near a zeros at 40Hz, and near the resonance at 95Hz (the ex
-
+

strut_1_frf_iff_plant_coh.png

Figure 55: Obtained coherence for the IFF plant

-Then the FRF are estimated and shown in Figure 56 +Then the FRF are estimated and shown in Figure 56 

[iff_sweep, ~] = tfestimate(leg_sweep.Va, leg_sweep.Vs, win, [], [], 1/Ts);
@@ -2512,7 +2444,7 @@ Then the FRF are estimated and shown in Figure 56
-
+

strut_1_frf_iff_plant_tf.png

Figure 56: Identified IFF Plant for the Strut 1

@@ -2521,15 +2453,15 @@ Then the FRF are estimated and shown in Figure 56
-
-

4.1.2 With Encoder

+
+

4.1.2 With Encoder

- +

-
-
4.1.2.1 Measurement Data
+
+
4.1.2.1 Measurement Data
leg_enc_sweep    = load(sprintf('frf_data_leg_coder_badly_align_%i_noise.mat',    1), 't', 'Va', 'Vs', 'de', 'da');
@@ -2539,8 +2471,8 @@ leg_enc_noise_hf = load(sprintf('frf_data_leg_coder_bad
-
-
4.1.2.2 FRF Identification - DVF
+
+
4.1.2.2 FRF Identification - DVF

In this section, the dynamics from \(V_a\) to \(d_e\) is identified. @@ -2556,7 +2488,7 @@ We compute the coherence for 2nd and 3rd identification:

-
+

strut_1_enc_frf_dvf_plant_coh.png

Figure 57: Obtained coherence for the plant from \(V_a\) to \(d_e\)

@@ -2575,14 +2507,14 @@ We compute the coherence for 2nd and 3rd identification:

-The obtained transfer functions are shown in Figure 58. +The obtained transfer functions are shown in Figure 58.

They are all superimposed except for the APA7.

-
+

Why is the APA7 off? We could think that the APA7 is stiffer, but also the mass line is off. @@ -2596,7 +2528,7 @@ Maybe it could be due to the amplifier?

-
+

Why is there a double resonance at around 94Hz?

@@ -2604,7 +2536,7 @@ Why is there a double resonance at around 94Hz?
-
+

strut_1_enc_frf_dvf_plant_tf.png

Figure 58: Estimated FRF for the DVF plant (transfer function from \(V_a\) to the encoder \(d_e\))

@@ -2612,24 +2544,25 @@ Why is there a double resonance at around 94Hz?
-
-
4.1.2.3 Comparison of the Encoder and Interferometer
+
+
4.1.2.3 Comparison of the Encoder and Interferometer

The interferometer could here represent the case where the encoders are fixed to the plates and not the APA.

-The dynamics from \(V_a\) to \(d_e\) and from \(V_a\) to \(d_a\) are compared in Figure 59. +The dynamics from \(V_a\) to \(d_e\) and from \(V_a\) to \(d_a\) are compared in Figure 59.

-
+

strut_1_comp_enc_int.png

+

Figure 59: Comparison of the transfer functions from excitation voltage \(V_a\) to either the encoder \(d_e\) or the interferometer \(d_a\)

-
+

It will clearly be difficult to do something (except some low frequency positioning) with the encoders fixed to the APA.

@@ -2638,17 +2571,18 @@ It will clearly be difficult to do something (except some low frequency position
-
-
4.1.2.4 APA Resonances Frequency
+
+
4.1.2.4 APA Resonances Frequency

-As shown in Figure 60, we can clearly see three spurious resonances at 197Hz, 290Hz and 376Hz. +As shown in Figure 60, we can clearly see three spurious resonances at 197Hz, 290Hz and 376Hz.

-
+

strut_1_spurious_resonances.png

+

Figure 60: Magnitude of the transfer function from excitation voltage \(V_a\) to encoder measurement \(d_e\). The frequency of the resonances are noted.

@@ -2657,33 +2591,33 @@ These resonances correspond to parasitic resonances of the APA itself. They are very close to what was estimated using the FEM:

    -
  • X-bending mode at ~190Hz (Figure 61)
    • -
  • Y-bending mode at ~290Hz (Figure 62)
    • -
  • Z-torsion mode at ~400Hz (Figure 63)
    • +
  • X-bending mode at around 190Hz (Figure 61)
    • +
  • Y-bending mode at around 290Hz (Figure 62)
    • +
  • Z-torsion mode at around 400Hz (Figure 63)
-
+

mode_bending_x.gif

Figure 61: X-bending mode (189Hz)

-
+

mode_bending_y.gif

Figure 62: Y-bending mode (285Hz)

-
+

mode_torsion_z.gif

Figure 63: Z-torsion mode (400Hz)

-
+

The resonances are indeed due to limited stiffness of the APA.

@@ -2692,18 +2626,18 @@ The resonances are indeed due to limited stiffness of the APA.
-
-
4.1.2.5 Estimated Flexible Joint axial stiffness
+
+
4.1.2.5 Estimated Flexible Joint axial stiffness
-
-
4.1.2.6 FRF Identification - IFF
+
+
4.1.2.6 FRF Identification - IFF

In this section, the dynamics from \(V_a\) to \(V_s\) is identified.

-First the coherence is computed and shown in Figure 55. +First the coherence is computed and shown in Figure 55. The coherence is very nice from 10Hz to 2kHz. It is only dropping near a zeros at 40Hz, and near the resonance at 95Hz (the excitation amplitude being lowered).

@@ -2715,14 +2649,14 @@ It is only dropping near a zeros at 40Hz, and near the resonance at 95Hz (the ex
-
+

strut_1_frf_iff_plant_coh.png

Figure 64: Obtained coherence for the IFF plant

-Then the FRF are estimated and shown in Figure 65 +Then the FRF are estimated and shown in Figure 65 

[iff_enc_sweep,    ~] = tfestimate(leg_enc_sweep.Va,    leg_enc_sweep.Vs,    win, [], [], 1/Ts);
@@ -2731,23 +2665,23 @@ Then the FRF are estimated and shown in Figure 65
-
+

strut_1_enc_frf_iff_plant_tf.png

Figure 65: Identified IFF Plant

-Let’s now compare the IFF plants whether the encoders are fixed to the APA or not (Figure 66). +Let’s now compare the IFF plants whether the encoders are fixed to the APA or not (Figure 66).

-
+

strut_1_frf_iff_effect_enc.png

Figure 66: Effect of the encoder on the IFF plant

-
+

We can see that the IFF does not change whether of not the encoder are fixed to the struts.

@@ -2758,18 +2692,18 @@ We can see that the IFF does not change whether of not the encoder are fixed to
-
-

4.2 Comparison of all the Struts

+
+

4.2 Comparison of all the Struts

- +

Now all struts are measured using the same procedure and test bench.

-
-

4.2.1 FRF Identification - Setup

+
+

4.2.1 FRF Identification - Setup

The identification is performed in two steps: @@ -2843,8 +2777,8 @@ We get the frequency vector that will be the same for all the frequency domain a

-
-

4.2.2 FRF Identification - DVF

+
+

4.2.2 FRF Identification - DVF

In this section, the dynamics from \(V_a\) to \(d_e\) is identified. @@ -2870,12 +2804,12 @@ coh_noise_hf = zeros(length(f), length(leg_nums));

-The coherence is shown in Figure 67. +The coherence is shown in Figure 67. It is clear that the Noise sine gives good coherence up to 400Hz and that the high frequency noise excitation signal helps increasing a little bit the coherence at high frequency.

-
+

struts_frf_dvf_plant_coh.png

Figure 67: Obtained coherence for the plant from \(V_a\) to \(d_e\)

@@ -2902,22 +2836,22 @@ dvf_noise_hf = zeros(length(f), length(leg_nums));

-The obtained transfer functions are shown in Figure 68. +The obtained transfer functions are shown in Figure 68.

They are all superimposed except for the LEG7.

-
+

struts_frf_dvf_plant_tf.png

Figure 68: Estimated FRF for the DVF plant (transfer function from \(V_a\) to the encoder \(d_e\))

-
+

-Depending on how the APA are mounted with the flexible joints, the dynamics can change a lot as shown in Figure 68. +Depending on how the APA are mounted with the flexible joints, the dynamics can change a lot as shown in Figure 68. In the future, a “pin” will be used to better align the APA with the flexible joints. We can expect the amplitude of the spurious resonances to decrease.

@@ -2926,8 +2860,8 @@ We can expect the amplitude of the spurious resonances to decrease.
-
-

4.2.3 FRF Identification - DVF with interferometer

+
+

4.2.3 FRF Identification - DVF with interferometer

In this section, the dynamics from \(V_a\) to \(d_a\) is identified. @@ -2953,11 +2887,11 @@ coh_noise_hf = zeros(length(f), length(leg_nums));

-The coherence is shown in Figure 69. +The coherence is shown in Figure 69. It is clear that the Noise sine gives good coherence up to 400Hz and that the high frequency noise excitation signal helps increasing a little bit the coherence at high frequency.

-
+

struts_frf_int_plant_coh.png

Figure 69: Obtained coherence for the plant from \(V_a\) to \(d_e\)

@@ -2983,7 +2917,7 @@ dvf_a_noise_hf = zeros(length(f), length(leg_nums));

-The obtained transfer functions are shown in Figure 70. +The obtained transfer functions are shown in Figure 70.

@@ -2991,7 +2925,7 @@ They are all superimposed except for the LEG7.

-
+

struts_frf_int_plant_tf.png

Figure 70: Estimated FRF for the DVF plant (transfer function from \(V_a\) to the encoder \(d_e\))

@@ -2999,15 +2933,15 @@ They are all superimposed except for the LEG7.
-
-

4.2.4 FRF Identification - IFF

+
+

4.2.4 FRF Identification - IFF

In this section, the dynamics from \(V_a\) to \(V_s\) is identified.

-First the coherence is computed and shown in Figure 71. +First the coherence is computed and shown in Figure 71. The coherence is very nice from 10Hz to 2kHz. It is only dropping near a zeros at 40Hz, and near the resonance at 95Hz (the excitation amplitude being lowered).

@@ -3029,14 +2963,14 @@ coh_noise_hf = zeros(length(f), length(leg_nums));
-
+

struts_frf_iff_plant_coh.png

Figure 71: Obtained coherence for the IFF plant

-Then the FRF are estimated and shown in Figure 72 +Then the FRF are estimated and shown in Figure 72 

%% FRF estimation of the transfer function from Va to Vs
@@ -3055,7 +2989,7 @@ iff_noise_hf = zeros(length(f), length(leg_nums));
-
+

struts_frf_iff_plant_tf.png

Figure 72: Identified IFF Plant

@@ -3065,90 +2999,38 @@ iff_noise_hf = zeros(length(f), length(leg_nums));
-
-

5 Test Bench APA300ML - Simscape Model

+
+

5 Test Bench APA300ML - Simscape Model

-
-

5.1 Introduction

+
+

5.1 Introduction

+
+

+A simscape model (Figure 73) of the measurement bench is used. +

+ + +
+

model_bench_apa.png +

+

Figure 73: Screenshot of the Simscape model

-
-

5.2 Nano Hexapod object

+
+
+ +
+

5.2 First Identification

+

+The APA is first initialized with default parameters and the transfer function from excitation voltage \(V_a\) (before the amplification of 20 due to the PD200 amplifier) to the sensor stack voltage \(V_s\), encoder \(d_L\) and interferometer \(z\) is identified. +

n_hexapod = struct();
+n_hexapod.actuator = initializeAPA('type', '2dof');
-
-
-

5.2.1 APA - 2 DoF

-
-
-
n_hexapod.actuator = struct();
-
-n_hexapod.actuator.type = 1;
-
-n_hexapod.actuator.k  = ones(6,1)*0.35e6; % [N/m]
-n_hexapod.actuator.ke = ones(6,1)*1.5e6; % [N/m]
-n_hexapod.actuator.ka = ones(6,1)*43e6; % [N/m]
-
-n_hexapod.actuator.c  = ones(6,1)*3e1; % [N/(m/s)]
-n_hexapod.actuator.ce = ones(6,1)*1e1; % [N/(m/s)]
-n_hexapod.actuator.ca = ones(6,1)*1e1; % [N/(m/s)]
-
-n_hexapod.actuator.Leq = ones(6,1)*0.056; % [m]
-
-n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V]
-n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m]
-
-
-
-
- -
-

5.2.2 APA - Flexible Frame

-
-
-
n_hexapod.actuator.type = 2;
-
-n_hexapod.actuator.K = readmatrix('APA300ML_b_mat_K.CSV'); % Stiffness Matrix
-n_hexapod.actuator.M = readmatrix('APA300ML_b_mat_M.CSV'); % Mass Matrix
-n_hexapod.actuator.xi = 0.01; % Damping ratio
-n_hexapod.actuator.P = extractNodes('APA300ML_b_out_nodes_3D.txt'); % Node coordinates [m]
-
-n_hexapod.actuator.ks = 235e6; % Stiffness of one stack [N/m]
-n_hexapod.actuator.cs = 1e1; % Stiffness of one stack [N/m]
-
-n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V]
-n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m]
-
-
-
-
- -
-

5.2.3 APA - Fully Flexible

-
-
-
n_hexapod.actuator.type = 3;
-
-n_hexapod.actuator.K = readmatrix('APA300ML_full_mat_K.CSV'); % Stiffness Matrix
-n_hexapod.actuator.M = readmatrix('APA300ML_full_mat_M.CSV'); % Mass Matrix
-n_hexapod.actuator.xi = 0.01; % Damping ratio
-n_hexapod.actuator.P = extractNodes('APA300ML_full_out_nodes_3D.txt'); % Node coordiantes [m]
-
-n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V]
-n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m]
-
-
-
-
-
- -
-

5.3 Identification

-
%% Options for Linearized
 options = linearizeOptions;
@@ -3170,225 +3052,181 @@ Ga.InputName  = {'Va'};
 Ga.OutputName = {'Vs', 'dL', 'z'};
+ +

+The obtain dynamics are shown in Figure 74 and 75. +

+ + +
+

apa_model_bench_bode_vs.png +

+

Figure 74: Bode plot of the transfer function from \(V_a\) to \(V_s\)

+
+ + +
+

apa_model_bench_bode_dl_z.png +

+

Figure 75: Bode plot of the transfer function from \(V_a\) to \(d_L\) and to \(z\)

+
-
-

5.4 Compare 2-DoF with flexible

-
+ +
+

5.3 Identify Sensor/Actuator constants and compare with measured FRF

+
-
-

5.4.1 APA - 2 DoF

-
+
+

5.3.1 How to identify these constants?

+
+
+
+
5.3.1.1 Piezoelectric Actuator Constant
+
+

+Using the measurement test-bench, it is rather easy the determine the static gain between the applied voltage \(V_a\) to the induced displacement \(d\). +

+\begin{equation} + d = g_{d/V_a} \cdot V_a +\end{equation} + +

+Using the Simscape model of the APA, it is possible to determine the static gain between the actuator force \(F_a\) to the induced displacement \(d\): +

+\begin{equation} + d = g_{d/F_a} \cdot F_a +\end{equation} + +

+From the two gains, it is then easy to determine \(g_a\): +

+\begin{equation} + g_a = \frac{F_a}{V_a} = \frac{F_a}{d} \cdot \frac{d}{V_a} = \frac{g_{d/V_a}}{g_{d/F_a}} +\end{equation} +
+
+ +
+
5.3.1.2 Piezoelectric Sensor Constant
+
+

+Similarly, it is easy to determine the gain from the excitation voltage \(V_a\) to the voltage generated by the sensor stack \(V_s\): +

+\begin{equation} + V_s = g_{V_s/V_a} V_a +\end{equation} + +

+Note here that there is an high pass filter formed by the piezo capacitor and parallel resistor. +

+ +

+The gain can be computed from the dynamical identification and taking the gain at the wanted frequency (above the first resonance). +

+ +

+Using the simscape model, compute the gain at the same frequency from the actuator force \(F_a\) to the strain of the sensor stack \(dl\): +

+\begin{equation} + dl = g_{dl/F_a} F_a +\end{equation} + +

+Then, the “sensor” constant is: +

+\begin{equation} + g_s = \frac{V_s}{dl} = \frac{V_s}{V_a} \cdot \frac{V_a}{F_a} \cdot \frac{F_a}{dl} = \frac{g_{V_s/V_a}}{g_a \cdot g_{dl/F_a}} +\end{equation} +
+
+
+ +
+

5.3.2 Identification Data

+
-
n_hexapod = struct();
+
leg_sweep    = load(sprintf('frf_data_%i_sweep.mat',    1), 't', 'Va', 'Vs', 'de', 'da');
+leg_noise_hf = load(sprintf('frf_data_%i_noise_hf.mat', 1), 't', 'Va', 'Vs', 'de', 'da');
+

+
-n_hexapod.actuator = struct(); +

+The time is the same for all measurements. +

+
+
%% Time vector
+t = leg_sweep.t - leg_sweep.t(1) ; % Time vector [s]
 
-n_hexapod.actuator.type = 1;
+%% Sampling
+Ts = (t(end) - t(1))/(length(t)-1); % Sampling Time [s]
+Fs = 1/Ts; % Sampling Frequency [Hz]
+
+
-n_hexapod.actuator.k = ones(6,1)*0.35e6; % [N/m] -n_hexapod.actuator.ke = ones(6,1)*1.5e6; % [N/m] -n_hexapod.actuator.ka = ones(6,1)*43e6; % [N/m] +

+Then we defined a “Hanning” windows that will be used for the spectral analysis: +

+
+
win = hanning(ceil(0.5*Fs)); % Hannning Windows
+
+
-n_hexapod.actuator.c = ones(6,1)*3e1; % [N/(m/s)] -n_hexapod.actuator.ce = ones(6,1)*1e1; % [N/(m/s)] -n_hexapod.actuator.ca = ones(6,1)*1e1; % [N/(m/s)] - -n_hexapod.actuator.Leq = ones(6,1)*0.056; % [m] - -n_hexapod.actuator.Ga = ones(6,1)*-2.15; % Actuator gain [N/V] -n_hexapod.actuator.Gs = ones(6,1)*2.305e-08; % Sensor gain [V/m] +

+We get the frequency vector that will be the same for all the frequency domain analysis. +

+
+
% Only used to have the frequency vector "f"
+[~, f] = tfestimate(leg_sweep.Va, leg_sweep.de, win, [], [], 1/Ts);
-
G_2dof = linearize(mdl, io, 0.0, options);
-G_2dof.InputName  = {'Va'};
-G_2dof.OutputName = {'Vs', 'dL', 'z'};
+
[dvf_sweep, ~]    = tfestimate(leg_sweep.Va,    leg_sweep.da,    win, [], [], 1/Ts);
+[dvf_noise_hf, ~] = tfestimate(leg_noise_hf.Va, leg_noise_hf.da, win, [], [], 1/Ts);
+

+
+ +
+
[iff_sweep, ~] = tfestimate(leg_sweep.Va, leg_sweep.Vs, win, [], [], 1/Ts);
+[iff_noise_hf, ~] = tfestimate(leg_noise_hf.Va, leg_noise_hf.Vs, win, [], [], 1/Ts);
+
+
+ +
+
freqs = 2*logspace(0, 3, 1000);
-
-

5.4.2 APA - Fully Flexible

-
-
-
n_hexapod = struct();
-
-n_hexapod.actuator.type = 3;
-
-n_hexapod.actuator.K = readmatrix('APA300ML_full_mat_K.CSV'); % Stiffness Matrix
-n_hexapod.actuator.M = readmatrix('APA300ML_full_mat_M.CSV'); % Mass Matrix
-n_hexapod.actuator.xi = 0.01; % Damping ratio
-n_hexapod.actuator.P = extractNodes('APA300ML_full_out_nodes_3D.txt'); % Node coordiantes [m]
-
-n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V]
-n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m]
-
+
+

5.3.3 2DoF APA

+
- +
+
5.3.3.1 2DoF APA
+
-
G_flex = linearize(mdl, io, 0.0, options);
-G_flex.InputName  = {'Va'};
-G_flex.OutputName = {'Vs', 'dL', 'z'};
+
n_hexapod.actuator = initializeAPA('type', '2dof', 'ga', 1, 'gs', 1);
-
-

5.4.3 Comparison

-
-
-
- -
-

6 Test Bench Struts - Simscape Model

-
-
-
-

6.1 Introduction

-
-
-

6.2 Nano Hexapod object

-
+
+
5.3.3.2 Identification without actuator or sensor constants
+
-
n_hexapod = struct();
-
-
-
- -
-

6.2.1 Flexible Joint - Bot

-
-
-
n_hexapod.flex_bot = struct();
-
-n_hexapod.flex_bot.type = 1; % 1: 2dof / 2: 3dof / 3: 4dof
-
-n_hexapod.flex_bot.kRx = ones(6,1)*5; % X bending stiffness [Nm/rad]
-n_hexapod.flex_bot.kRy = ones(6,1)*5; % Y bending stiffness [Nm/rad]
-n_hexapod.flex_bot.kRz = ones(6,1)*260; % Torsionnal stiffness [Nm/rad]
-n_hexapod.flex_bot.kz  = ones(6,1)*1e8; % Axial stiffness [N/m]
-
-n_hexapod.flex_bot.cRx = ones(6,1)*0.1; % [Nm/(rad/s)]
-n_hexapod.flex_bot.cRy = ones(6,1)*0.1; % [Nm/(rad/s)]
-n_hexapod.flex_bot.cRz = ones(6,1)*0.1; % [Nm/(rad/s)]
-n_hexapod.flex_bot.cz  = ones(6,1)*1e2; %[N/(m/s)]
-
-
-
-
- -
-

6.2.2 Flexible Joint - Top

-
-
-
n_hexapod.flex_top = struct();
-
-n_hexapod.flex_top.type = 2; % 1: 2dof / 2: 3dof / 3: 4dof
-
-n_hexapod.flex_top.kRx = ones(6,1)*5; % X bending stiffness [Nm/rad]
-n_hexapod.flex_top.kRy = ones(6,1)*5; % Y bending stiffness [Nm/rad]
-n_hexapod.flex_top.kRz = ones(6,1)*260; % Torsionnal stiffness [Nm/rad]
-n_hexapod.flex_top.kz  = ones(6,1)*1e8; % Axial stiffness [N/m]
-
-n_hexapod.flex_top.cRx = ones(6,1)*0.1; % [Nm/(rad/s)]
-n_hexapod.flex_top.cRy = ones(6,1)*0.1; % [Nm/(rad/s)]
-n_hexapod.flex_top.cRz = ones(6,1)*0.1; % [Nm/(rad/s)]
-n_hexapod.flex_top.cz  = ones(6,1)*1e2; %[N/(m/s)]
-
-
-
-
- -
-

6.2.3 APA - 2 DoF

-
-
-
n_hexapod.actuator = struct();
-
-n_hexapod.actuator.type = 1;
-
-n_hexapod.actuator.k  = ones(6,1)*0.35e6; % [N/m]
-n_hexapod.actuator.ke = ones(6,1)*1.5e6; % [N/m]
-n_hexapod.actuator.ka = ones(6,1)*43e6; % [N/m]
-
-n_hexapod.actuator.c  = ones(6,1)*3e1; % [N/(m/s)]
-n_hexapod.actuator.ce = ones(6,1)*1e1; % [N/(m/s)]
-n_hexapod.actuator.ca = ones(6,1)*1e1; % [N/(m/s)]
-
-n_hexapod.actuator.Leq = ones(6,1)*0.056; % [m]
-
-n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V]
-n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m]
-
-
-
-
- -
-

6.2.4 APA - Flexible Frame

-
-
-
n_hexapod.actuator.type = 2;
-
-n_hexapod.actuator.K = readmatrix('APA300ML_b_mat_K.CSV'); % Stiffness Matrix
-n_hexapod.actuator.M = readmatrix('APA300ML_b_mat_M.CSV'); % Mass Matrix
-n_hexapod.actuator.xi = 0.01; % Damping ratio
-n_hexapod.actuator.P = extractNodes('APA300ML_b_out_nodes_3D.txt'); % Node coordinates [m]
-
-n_hexapod.actuator.ks = 235e6; % Stiffness of one stack [N/m]
-n_hexapod.actuator.cs = 1e1; % Stiffness of one stack [N/m]
-
-n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V]
-n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m]
-
-
-
-
- -
-

6.2.5 APA - Fully Flexible

-
-
-
n_hexapod.actuator.type = 3;
-
-n_hexapod.actuator.K = readmatrix('APA300ML_full_mat_K.CSV'); % Stiffness Matrix
-n_hexapod.actuator.M = readmatrix('APA300ML_full_mat_M.CSV'); % Mass Matrix
-n_hexapod.actuator.xi = 0.01; % Damping ratio
-n_hexapod.actuator.P = extractNodes('APA300ML_full_out_nodes_3D.txt'); % Node coordiantes [m]
-
-n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V]
-n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m]
-
-
-
-
-
- - -
-

6.3 Identification

-
-
-
%% Options for Linearized
-options = linearizeOptions;
-options.SampleTime = 0;
-
-%% Name of the Simulink File
-mdl = 'test_bench_struts';
-
-%% Input/Output definition
+
%% Input/Output definition
 clear io; io_i = 1;
 io(io_i) = linio([mdl, '/Va'],  1, 'openinput');  io_i = io_i + 1; % Actuator Voltage
 io(io_i) = linio([mdl, '/Vs'],  1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage
 io(io_i) = linio([mdl, '/dL'],  1, 'openoutput'); io_i = io_i + 1; % Relative Motion Outputs
 io(io_i) = linio([mdl, '/z'],   1, 'openoutput'); io_i = io_i + 1; % Vertical Motion
 
-%% Run the linearization
+%% Identification
 Gs = linearize(mdl, io, 0.0, options);
 Gs.InputName  = {'Va'};
 Gs.OutputName = {'Vs', 'dL', 'z'};
@@ -3397,102 +3235,799 @@ Gs.OutputName = {'Vs',
-
-

6.4 Compare flexible joints

-
-
-
-

6.4.1 Perfect

-
+
+
5.3.3.3 Actuator Constant
+
-
n_hexapod.flex_bot.type = 1; % 1: 2dof / 2: 3dof / 3: 4dof
-n_hexapod.flex_top.type = 2; % 1: 2dof / 2: 3dof / 3: 4dof
+
ga = -mean(abs(dvf_sweep(f>10 & f<20)))./dcgain(Gs('dL', 'Va')); % [N/V]
+

+
+ +
+ga = -46.4 [N/V]
+
+ + +
+
n_hexapod.actuator.Ga = ones(6,1)*ga; % Actuator gain [N/V]
+
+
+
+
+ +
+
5.3.3.4 Sensor Constant
+
+
+
gs = -mean(abs(iff_sweep(f>400 & f<500)))./(ga*abs(squeeze(freqresp(Gs('Vs', 'Va'), 1e3, 'Hz')))); % [V/m]
+
+
+ +
+gs = 0.098 [V/m]
+
+ + +
+
n_hexapod.actuator.Gs = ones(6,1)*gs; % Sensor gain [V/m]
+
+
+
+
+ +
+
5.3.3.5 Comparison
+
+

+Identify the dynamics with included constants. +

+
+
Gs = linearize(mdl, io, 0.0, options);
+Gs = Gs*exp(-Ts*s);
+Gs.InputName  = {'Va'};
+Gs.OutputName = {'Vs', 'dL', 'z'};
+
+
+ + +
+

apa_act_constant_comp.png +

+

Figure 76: Comparison of the experimental data and Simscape model (\(V_a\) to \(d_e\))

+
+ + +
+

apa_sens_constant_comp.png +

+

Figure 77: Comparison of the experimental data and Simscape model (\(V_a\) to \(V_s\))

+
+
+
+
+ +
+

5.3.4 Flexible APA

+
+
+
+
5.3.4.1 Flexible APA
+
+
+
n_hexapod.actuator = initializeAPA('type', 'flexible', 'ga', 1, 'gs', 1);
+
+
+
+
+ +
+
5.3.4.2 Identification without actuator or sensor constants
+
+
+
Gs = linearize(mdl, io, 0.0, options);
+Gs.InputName  = {'Va'};
+Gs.OutputName = {'Vs', 'dL', 'z'};
+
+
+
+
+ +
+
5.3.4.3 Actuator Constant
+
+
+
ga = -mean(abs(dvf_sweep(f>10 & f<20)))./dcgain(Gs('dL', 'Va')); % [N/V]
+
+
+ +
+ga = 23.4 [N/V]
+
+ + +
+
n_hexapod.actuator.Ga = ones(6,1)*ga; % Actuator gain [N/V]
+
+
+
+
+ +
+
5.3.4.4 Sensor Constant
+
+
+
gs = -mean(abs(iff_sweep(f>400 & f<500)))./(ga*abs(squeeze(freqresp(Gs('Vs', 'Va'), 1e3, 'Hz')))); % [V/m]
+
+
+ +
+gs = -4674824.519 [V/m]
+
+ + +
+
n_hexapod.actuator.Gs = ones(6,1)*gs; % Sensor gain [V/m]
+
+
+
+
+ +
+
5.3.4.5 Comparison
+
+
+
Gs = linearize(mdl, io, 0.0, options);
+Gs = Gs*exp(-Ts*s);
+Gs.InputName  = {'Va'};
+Gs.OutputName = {'Vs', 'dL', 'z'};
+
+
+ + +
+

apa_act_constant_comp_flex.png +

+

Figure 78: Comparison of the experimental data and Simscape model (\(V_a\) to \(d_e\))

+
+ + +
+

apa_sens_constant_comp_flex.png +

+

Figure 79: Comparison of the experimental data and Simscape model (\(V_a\) to \(V_s\))

+
+
+
+
+
+ +
+

5.4 Compare 2-DoF with flexible

+
+

+APA - 2 DoF +

+
+
n_hexapod.actuator = initializeAPA('type', '2dof');
+
+G_2dof = linearize(mdl, io, 0.0, options);
+G_2dof.InputName  = {'Va'};
+G_2dof.OutputName = {'Vs', 'dL', 'z'};
+
+
+ +

+APA - Fully Flexible +

+
+
n_hexapod.actuator = initializeAPA('type', 'flexible');
+
+G_flex = linearize(mdl, io, 0.0, options);
+G_flex.InputName  = {'Va'};
+G_flex.OutputName = {'Vs', 'dL', 'z'};
+
+
+ +

+Comparison +

+ +
+

apa_effect_joint_comp_vs.png +

+

Figure 80: Effect of the joint’s flexibility on the transfer function from \(V_a\) to \(V_s\)

+
+ + +
+

apa_effect_joint_comp_dl.png +

+

Figure 81: Effect of the joint’s flexibility on the transfer function from \(V_a\) to \(d_L\) (encoder)

+
+ + +
+

apa_effect_joint_comp_z.png +

+

Figure 82: Effect of the joint’s flexibility on the transfer function from \(V_a\) to \(z\) (interferometer)

+
+
+
+
+ +
+

6 Test Bench Struts - Simscape Model

+
+
+
+

6.1 Introduction

+
+
+

6.2 First Identification

+
+

+The object containing all the data is created. +

+
+
n_hexapod = struct();
+n_hexapod.flex_bot = initializeBotFlexibleJoint('type', '2dof');
+n_hexapod.flex_top = initializeTopFlexibleJoint('type', '2dof');
+n_hexapod.actuator = initializeAPA('type', '2dof');
-
Gp = linearize(mdl, io, 0.0, options);
+
%% Input/Output definition
+clear io; io_i = 1;
+io(io_i) = linio([mdl, '/Va'],  1, 'openinput');  io_i = io_i + 1; % Actuator Voltage
+io(io_i) = linio([mdl, '/Vs'],  1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage
+io(io_i) = linio([mdl, '/dL'],  1, 'openoutput'); io_i = io_i + 1; % Relative Motion Outputs
+io(io_i) = linio([mdl, '/z'],   1, 'openoutput'); io_i = io_i + 1; % Vertical Motion
+

+
+ +
+
%% Run the linearization
+Gs = linearize(mdl, io, 0.0, options);
+Gs.InputName  = {'Va'};
+Gs.OutputName = {'Vs', 'dL', 'z'};
+
+
+ + +
+

strut_bench_model_iff_bode.png +

+

Figure 83: Identified transfer function from \(V_a\) to \(V_s\)

+
+ + +
+

strut_bench_model_dvf_bode.png +

+

Figure 84: Identified transfer function from \(V_a\) to \(d_L\)

+
+
+
+ +
+

6.3 Effect of flexible joints

+
+

+Perfect +

+
+
n_hexapod.flex_bot = initializeBotFlexibleJoint('type', '2dof');
+n_hexapod.flex_top = initializeTopFlexibleJoint('type', '3dof');
+
+Gp = linearize(mdl, io, 0.0, options);
 Gp.InputName  = {'Va'};
 Gp.OutputName = {'Vs', 'dL', 'z'};
-
-
-
-

6.4.2 Top Flexible

-
+

+Top Flexible +

-
n_hexapod.flex_bot.type = 1; % 1: 2dof / 2: 3dof / 3: 4dof
-n_hexapod.flex_top.type = 3; % 1: 2dof / 2: 3dof / 3: 4dof
-
-
+
n_hexapod.flex_bot = initializeBotFlexibleJoint('type', '2dof');
+n_hexapod.flex_top = initializeTopFlexibleJoint('type', '4dof');
 
-

-
Gt = linearize(mdl, io, 0.0, options);
+Gt = linearize(mdl, io, 0.0, options);
 Gt.InputName  = {'Va'};
 Gt.OutputName = {'Vs', 'dL', 'z'};
 

 

-
-
-
-

6.4.3 Bottom Flexible

-
+

+Bottom Flexible +

-
n_hexapod.flex_bot.type = 3; % 1: 2dof / 2: 3dof / 3: 4dof
-n_hexapod.flex_top.type = 2; % 1: 2dof / 2: 3dof / 3: 4dof
-
-
+
n_hexapod.flex_bot = initializeBotFlexibleJoint('type', '4dof');
+n_hexapod.flex_top = initializeTopFlexibleJoint('type', '3dof');
 
-

-
Gb = linearize(mdl, io, 0.0, options);
+Gb = linearize(mdl, io, 0.0, options);
 Gb.InputName  = {'Va'};
 Gb.OutputName = {'Vs', 'dL', 'z'};
 

 

-
-
-
-

6.4.4 Both Flexible

-
+

+Both Flexible +

-
n_hexapod.flex_bot.type = 3; % 1: 2dof / 2: 3dof / 3: 4dof
-n_hexapod.flex_top.type = 3; % 1: 2dof / 2: 3dof / 3: 4dof
-
-
+
n_hexapod.flex_bot = initializeBotFlexibleJoint('type', '4dof');
+n_hexapod.flex_top = initializeTopFlexibleJoint('type', '4dof');
 
-

-
Gf = linearize(mdl, io, 0.0, options);
+Gf = linearize(mdl, io, 0.0, options);
 Gf.InputName  = {'Va'};
 Gf.OutputName = {'Vs', 'dL', 'z'};
 

+

+
+

+Comparison in Figures 85, 86 and 87.
+

+
+
+

+
strut_effect_joint_comp_vs.png
+

+
Figure 85: Effect of the joint’s flexibility on the transfer function from \(V_a\) to \(V_s\)

+

+
+
+

+
strut_effect_joint_comp_dl.png
+

+
Figure 86: Effect of the joint’s flexibility on the transfer function from \(V_a\) to \(d_L\) (encoder)

+

+
+
+

+
strut_effect_joint_comp_z.png
+

+
Figure 87: Effect of the joint’s flexibility on the transfer function from \(V_a\) to \(z\) (interferometer)

+

+
+

+

+Imperfection of the flexible joints has the largest impact on the transfer function from \(V_a\) to \(d_L\).
+However, it has relatively small impact on the transfer functions from \(V_a\) to \(V_s\) and to \(z\).
+

+
-
-

6.4.5 Comparison

+
+

6.4 Integral Force Feedback

+
+
+
+

6.4.1 Initialize the system

+
+
+
n_hexapod = struct();
+n_hexapod.flex_bot = initializeBotFlexibleJoint('type', '2dof');
+n_hexapod.flex_top = initializeTopFlexibleJoint('type', '3dof');
+n_hexapod.actuator = initializeAPA('type', '2dof');
+
-
-

7 Function

+ +
+

6.4.2 Plant Identification

+
+
+
G = linearize(mdl, io, 0.0, options);
+G.InputName  = {'Va'};
+G.OutputName = {'Vs', 'dL', 'z'};
+
+
+ +
+
Giff = G('Vs', 'Va');
+
+
+
+
+ +
+

6.4.3 Root Locus

+
+\begin{equation} +K_{\text{IFF}} = \frac{g}{s + \omega_c} +\end{equation} + +
+
wc = 2*pi*20;
+
+
+
+
+
+
+ +
+

7 Function

-
-

7.1 generateSweepExc: Generate sweep sinus excitation

+
+

7.1 initializeBotFlexibleJoint - Initialize Flexible Joint

- +

-
-

Function description

-
+
+

Function description

+
+
+
function [flex_bot] = initializeBotFlexibleJoint(args)
+% initializeBotFlexibleJoint -
+%
+% Syntax: [flex_bot] = initializeBotFlexibleJoint(args)
+%
+% Inputs:
+%    - args -
+%
+% Outputs:
+%    - flex_bot -
+
+
+
+
+ +
+

Optional Parameters

+
+
+
arguments
+    args.type      char   {mustBeMember(args.type,{'2dof', '3dof', '4dof'})} = '2dof'
+
+    args.kRx (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*5
+    args.kRy (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*5
+    args.kRz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*260
+    args.kz  (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*1e8
+
+    args.cRx (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.1
+    args.cRy (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.1
+    args.cRz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.1
+    args.cz  (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*1e2
+end
+
+
+
+
+ +
+

Initialize the structure

+
+
+
flex_bot = struct();
+
+
+
+
+ +
+

Set the Joint’s type

+
+
+
switch args.type
+  case '2dof'
+    flex_bot.type = 1;
+  case '3dof'
+    flex_bot.type = 2;
+  case '4dof'
+    flex_bot.type = 3;
+end
+
+
+
+
+ +
+

Set parameters

+
+
+
flex_bot.kRx = args.kRx;
+flex_bot.kRy = args.kRy;
+flex_bot.kRz = args.kRz;
+flex_bot.kz  = args.kz;
+
+
+ +
+
flex_bot.cRx = args.cRx;
+flex_bot.cRy = args.cRy;
+flex_bot.cRz = args.cRz;
+flex_bot.cz  = args.cz;
+
+
+
+
+
+ +
+

7.2 initializeTopFlexibleJoint - Initialize Flexible Joint

+
+

+ +

+
+ +
+

Function description

+
+
+
function [flex_top] = initializeTopFlexibleJoint(args)
+% initializeTopFlexibleJoint -
+%
+% Syntax: [flex_top] = initializeTopFlexibleJoint(args)
+%
+% Inputs:
+%    - args -
+%
+% Outputs:
+%    - flex_top -
+
+
+
+
+ +
+

Optional Parameters

+
+
+
arguments
+    args.type      char   {mustBeMember(args.type,{'2dof', '3dof', '4dof'})} = '2dof'
+
+    args.kRx (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*5
+    args.kRy (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*5
+    args.kRz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*260
+    args.kz  (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*1e8
+
+    args.cRx (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.1
+    args.cRy (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.1
+    args.cRz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.1
+    args.cz  (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*1e2
+end
+
+
+
+
+ +
+

Initialize the structure

+
+
+
flex_top = struct();
+
+
+
+
+ +
+

Set the Joint’s type

+
+
+
switch args.type
+  case '2dof'
+    flex_top.type = 1;
+  case '3dof'
+    flex_top.type = 2;
+  case '4dof'
+    flex_top.type = 3;
+end
+
+
+
+
+ +
+

Set parameters

+
+
+
flex_top.kRx = args.kRx;
+flex_top.kRy = args.kRy;
+flex_top.kRz = args.kRz;
+flex_top.kz  = args.kz;
+
+
+ +
+
flex_top.cRx = args.cRx;
+flex_top.cRy = args.cRy;
+flex_top.cRz = args.cRz;
+flex_top.cz  = args.cz;
+
+
+
+
+
+ +
+

7.3 initializeAPA - Initialize APA

+
+

+ +

+
+ +
+

Function description

+
+
+
function [actuator] = initializeAPA(args)
+% initializeAPA -
+%
+% Syntax: [actuator] = initializeAPA(args)
+%
+% Inputs:
+%    - args -
+%
+% Outputs:
+%    - actuator -
+
+
+
+
+ +
+

Optional Parameters

+
+
+
arguments
+    args.type      char   {mustBeMember(args.type,{'2dof', 'flexible frame', 'flexible'})} = '2dof'
+
+    args.Ga  (1,1) double {mustBeNumeric} = 0
+    args.Gs  (1,1) double {mustBeNumeric} = 0
+
+    % For 2DoF
+    args.k   (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.35e6
+    args.ke  (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*1.5e6
+    args.ka  (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*43e6
+
+    args.c   (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*3e1
+    args.ce  (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*2e1
+    args.ca  (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*2e1
+
+    args.Leq (6,1) double {mustBeNumeric} = ones(6,1)*0.056
+
+    % Force Flexible APA
+    args.xi (1,1) double {mustBeNumeric, mustBePositive} = 0.5
+
+    % For Flexible Frame
+    args.ks (1,1) double {mustBeNumeric, mustBePositive} = 235e6
+    args.cs (1,1) double {mustBeNumeric, mustBePositive} = 1e1
+end
+
+
+
+
+ +
+

Initialize Structure

+
+
+
actuator = struct();
+
+
+
+
+ +
+

Type

+
+
+
switch args.type
+  case '2dof'
+    actuator.type = 1;
+  case 'flexible frame'
+    actuator.type = 2;
+  case 'flexible'
+    actuator.type = 3;
+end
+
+
+
+
+ +
+

Actuator/Sensor Constants

+
+
+
if args.Ga == 0
+    switch args.type
+      case '2dof'
+        actuator.Ga = -46.4;
+      case 'flexible frame'
+        actuator.Ga = 1; % TODO
+      case 'flexible'
+        actuator.Ga = 23.4;
+    end
+else
+    actuator.Ga = args.Ga; % Actuator gain [N/V]
+end
+
+
+ +
+
if args.Gs == 0
+    switch args.type
+      case '2dof'
+        actuator.Gs = 0.098;
+      case 'flexible frame'
+        actuator.Gs = 1; % TODO
+      case 'flexible'
+        actuator.Gs = -4674824;
+    end
+else
+    actuator.Gs = args.Gs; % Sensor gain [V/m]
+end
+
+
+
+
+ +
+

2DoF parameters

+
+
+
actuator.k  = args.k;  % [N/m]
+actuator.ke = args.ke; % [N/m]
+actuator.ka = args.ka; % [N/m]
+
+actuator.c  = args.c;  % [N/(m/s)]
+actuator.ce = args.ce; % [N/(m/s)]
+actuator.ca = args.ca; % [N/(m/s)]
+
+actuator.Leq = args.Leq; % [m]
+
+
+
+
+ +
+

Flexible frame and fully flexible

+
+
+
switch args.type
+  case 'flexible frame'
+    actuator.K = readmatrix('APA300ML_b_mat_K.CSV'); % Stiffness Matrix
+    actuator.M = readmatrix('APA300ML_b_mat_M.CSV'); % Mass Matrix
+    actuator.P = extractNodes('APA300ML_b_out_nodes_3D.txt'); % Node coordinates [m]
+  case 'flexible'
+    actuator.K = readmatrix('full_APA300ML_K.CSV'); % Stiffness Matrix
+    actuator.M = readmatrix('full_APA300ML_M.CSV'); % Mass Matrix
+    actuator.P = extractNodes('full_APA300ML_out_nodes_3D.txt'); % Node coordiantes [m]
+end
+
+actuator.xi = args.xi; % Damping ratio
+
+actuator.ks = args.ks; % Stiffness of one stack [N/m]
+actuator.cs = args.cs; % Damping of one stack [N/m]
+
+
+
+
+
+ +
+

7.4 generateSweepExc: Generate sweep sinus excitation

+
+

+ +

+
+ +
+

Function description

+
function [U_exc] = generateSweepExc(args)
 % generateSweepExc - Generate a Sweep Sine excitation signal
@@ -3515,9 +4050,9 @@ Gf.OutputName = {'Vs',
-
-

Optional Parameters

-
+
+

Optional Parameters

+
arguments
     args.Ts              (1,1) double  {mustBeNumeric, mustBePositive} = 1e-4
@@ -3535,9 +4070,9 @@ Gf.OutputName = {'Vs',
-
-

Sweep Sine part

-
+
+

Sweep Sine part

+
t_sweep = 0:args.Ts:args.exc_duration;
 
@@ -3566,9 +4101,9 @@ Gf.OutputName = {'Vs',
-
-

Smooth Ends

-
+
+

Smooth Ends

+
if args.t_start > 0
     t_smooth_start = args.Ts:args.Ts:args.t_start;
@@ -3597,9 +4132,9 @@ Gf.OutputName = {'Vs',
-
-

Combine Excitation signals

-
+
+

Combine Excitation signals

+
V_exc = [V_smooth_start, V_sweep, V_smooth_end];
 t_exc = args.Ts*[0:1:length(V_exc)-1];
@@ -3614,17 +4149,17 @@ t_exc = args.Ts*[0:1
-
-

7.2 generateShapedNoise: Generate Shaped Noise excitation

-
+
+

7.5 generateShapedNoise: Generate Shaped Noise excitation

+

- +

-
-

Function description

-
+
+

Function description

+
function [U_exc] = generateShapedNoise(args)
 % generateShapedNoise - Generate a Shaped Noise excitation signal
@@ -3644,9 +4179,9 @@ t_exc = args.Ts*[0:1
-
-

Optional Parameters

-
+
+

Optional Parameters

+
arguments
     args.Ts              (1,1) double  {mustBeNumeric, mustBePositive} = 1e-4
@@ -3661,9 +4196,9 @@ t_exc = args.Ts*[0:1
-
-

Shaped Noise

-
+
+

Shaped Noise

+
t_noise = 0:args.Ts:args.exc_duration;
 
@@ -3681,9 +4216,9 @@ t_exc = args.Ts*[0:1
-
-

Smooth Ends

-
+
+

Smooth Ends

+
t_smooth_start = args.Ts:args.Ts:args.t_start;
 
@@ -3707,9 +4242,9 @@ V_smooth_end   = zeros(size(t_smooth_start));
-
-

Combine Excitation signals

-
+
+

Combine Excitation signals

+
V_exc = [V_smooth_start, V_noise, V_smooth_end];
 t_exc = args.Ts*[0:1:length(V_exc)-1];
@@ -3724,17 +4259,17 @@ t_exc = args.Ts*[0:1
-
-

7.3 generateSinIncreasingAmpl: Generate Sinus with increasing amplitude

-
+
+

7.6 generateSinIncreasingAmpl: Generate Sinus with increasing amplitude

+

- +

-
-

Function description

-
+
+

Function description

+
function [U_exc] = generateSinIncreasingAmpl(args)
 % generateSinIncreasingAmpl - Generate Sinus with increasing amplitude
@@ -3755,9 +4290,9 @@ t_exc = args.Ts*[0:1
-
-

Optional Parameters

-
+
+

Optional Parameters

+
arguments
     args.Ts              (1,1) double  {mustBeNumeric, mustBePositive} = 1e-4
@@ -3773,9 +4308,9 @@ t_exc = args.Ts*[0:1
-
-

Sinus excitation

-
+
+

Sinus excitation

+
t_noise = 0:args.Ts:args.sin_period*args.sin_num;
 sin_exc = [];
@@ -3791,9 +4326,9 @@ sin_exc = [];
-
-

Smooth Ends

-
+
+

Smooth Ends

+
t_smooth_start = args.Ts:args.Ts:args.t_start;
 
@@ -3817,9 +4352,9 @@ V_smooth_end   = zeros(size(t_smooth_start));
-
-

Combine Excitation signals

-
+
+

Combine Excitation signals

+
V_exc = [V_smooth_start, sin_exc, V_smooth_end];
 t_exc = args.Ts*[0:1:length(V_exc)-1];
@@ -3842,7 +4377,7 @@ t_exc = args.Ts*[0:1

Author: Dehaeze Thomas

-

Created: 2021-06-04 ven. 12:04

+

Created: 2021-06-07 lun. 18:42

diff --git a/test-bench-apa300ml.org b/test-bench-apa300ml.org index 4f4d4b2..eb7e2f6 100644 --- a/test-bench-apa300ml.org +++ b/test-bench-apa300ml.org @@ -1274,6 +1274,10 @@ exportFig('figs/apa_1_frf_dvf.pdf', 'width', 'wide', 'height', 'tall'); #+RESULTS: [[file:figs/apa_1_frf_dvf.png]] +#+begin_important +It seems that using the interferometer, we have a lot more time delay than when using the encoder. +#+end_important + *** FRF Identification - Force Sensor Now the dynamics from excitation voltage $V_a$ to the force sensor stack voltage $V_s$ is identified. @@ -1343,77 +1347,6 @@ exportFig('figs/apa_1_frf_iff.pdf', 'width', 'wide', 'height', 'tall'); #+RESULTS: [[file:figs/apa_1_frf_iff.png]] -*** TODO Extract Parameters (Actuator/Sensor constants) -**** Piezoelectric Actuator Constant - -Using the measurement test-bench, it is rather easy the determine the static gain between the applied voltage $V_a$ to the induced displacement $d$. -Use a quasi static (1Hz) excitation signal $V_a$ on the piezoelectric stack and measure the vertical displacement $d$. -Perform a linear regression to obtain: -\begin{equation} - d = g_{d/V_a} \cdot V_a -\end{equation} - -Using the Simscape model of the APA, it is possible to determine the static gain between the actuator force $F_a$ to the induced displacement $d$: -\begin{equation} - d = g_{d/F_a} \cdot F_a -\end{equation} - -From the two gains, it is then easy to determine $g_a$: -\begin{equation} - g_a = \frac{F_a}{V_a} = \frac{F_a}{d} \cdot \frac{d}{V_a} = \frac{g_{d/V_a}}{g_{d/F_a}} -\end{equation} - -**** Piezoelectric Sensor Constant - -From a quasi static excitation of the piezoelectric stack, measure the gain from $V_a$ to $V_s$: -\begin{equation} - V_s = g_{V_s/V_a} V_a -\end{equation} - -Note here that there is an high pass filter formed by the piezo capacitor and parallel resistor. -The excitation frequency should then be in between the cut-off frequency of this high pass filter and the first resonance. - -Alternatively, the gain can be computed from the dynamical identification and taking the gain at the wanted frequency. - -Using the simscape model, compute the static gain from the actuator force $F_a$ to the strain of the sensor stack $dl$: -\begin{equation} - dl = g_{dl/F_a} F_a -\end{equation} - -Then, the static gain from the sensor stack strain $dl$ to the general voltage $V_s$ is: -\begin{equation} - g_s = \frac{V_s}{dl} = \frac{V_s}{V_a} \cdot \frac{V_a}{F_a} \cdot \frac{F_a}{dl} = \frac{g_{V_s/V_a}}{g_a \cdot g_{dl/F_a}} -\end{equation} - -Alternatively, we could impose an external force to add strain in the APA that should be equally present in all the 3 stacks and equal to 1/5 of the vertical strain. -This external force can be some weight added, or a piezo in parallel. - -**** Results - -Quasi static gain between $d$ and $V_a$: -#+begin_src matlab -g_d_Va = mean(abs(dvf_sweep(f > 10 & f < 15))); -#+end_src - -#+begin_src matlab :results value replace :exports results -sprintf('g_d_Va = %.1e [m/V]', g_d_Va) -#+end_src - -#+RESULTS: -: g_d_Va = 1.7e-05 [m/V] - -Quasi static gain between $V_s$ and $V_a$: -#+begin_src matlab -g_Vs_Va = mean(abs(iff_sweep(f > 10 & f < 15))); -#+end_src - -#+begin_src matlab :results value replace :exports results -sprintf('g_Vs_Va = %.1e [V/V]', g_Vs_Va) -#+end_src - -#+RESULTS: -: g_Vs_Va = 5.7e-01 [V/V] - *** Hysteresis We here wish to visually see the amount of hysteresis present in the APA. @@ -4099,7 +4032,15 @@ It is the expected behavior as shown in the Figure [[fig:souleille18_results]] ( * Test Bench APA300ML - Simscape Model ** Introduction -** Matlab Init :noexport:ignore: + +A simscape model (Figure [[fig:model_bench_apa]]) of the measurement bench is used. + +#+name: fig:model_bench_apa +#+caption: Screenshot of the Simscape model +#+attr_latex: :width 0.5\linewidth +[[file:figs/model_bench_apa.png]] + +** Matlab Init :noexport:ignore: #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) <> #+end_src @@ -4109,72 +4050,39 @@ It is the expected behavior as shown in the Figure [[fig:souleille18_results]] ( #+end_src #+begin_src matlab :tangle no +addpath('matlab/'); addpath('matlab/test_bench_apa300ml/'); +addpath('matlab/mat/'); +addpath('matlab/src/'); +addpath('matlab/png/'); #+end_src #+begin_src matlab :eval no addpath('test_bench_apa300ml/'); +addpath('png/'); +addpath('mat/'); +addpath('src/'); #+end_src #+begin_src matlab -open('test_bench_apa300ml.slx') +%% Options for Linearized +options = linearizeOptions; +options.SampleTime = 0; + +%% Name of the Simulink File +mdl = 'test_bench_apa300ml'; + +%% Open the Simulink File +open([mdl, '.slx']) #+end_src -** Nano Hexapod object +** First Identification +The APA is first initialized with default parameters and the transfer function from excitation voltage $V_a$ (before the amplification of 20 due to the PD200 amplifier) to the sensor stack voltage $V_s$, encoder $d_L$ and interferometer $z$ is identified. #+begin_src matlab n_hexapod = struct(); +n_hexapod.actuator = initializeAPA('type', '2dof'); #+end_src -*** APA - 2 DoF -#+begin_src matlab -n_hexapod.actuator = struct(); - -n_hexapod.actuator.type = 1; - -n_hexapod.actuator.k = ones(6,1)*0.35e6; % [N/m] -n_hexapod.actuator.ke = ones(6,1)*1.5e6; % [N/m] -n_hexapod.actuator.ka = ones(6,1)*43e6; % [N/m] - -n_hexapod.actuator.c = ones(6,1)*3e1; % [N/(m/s)] -n_hexapod.actuator.ce = ones(6,1)*1e1; % [N/(m/s)] -n_hexapod.actuator.ca = ones(6,1)*1e1; % [N/(m/s)] - -n_hexapod.actuator.Leq = ones(6,1)*0.056; % [m] - -n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V] -n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m] -#+end_src - -*** APA - Flexible Frame -#+begin_src matlab -n_hexapod.actuator.type = 2; - -n_hexapod.actuator.K = readmatrix('APA300ML_b_mat_K.CSV'); % Stiffness Matrix -n_hexapod.actuator.M = readmatrix('APA300ML_b_mat_M.CSV'); % Mass Matrix -n_hexapod.actuator.xi = 0.01; % Damping ratio -n_hexapod.actuator.P = extractNodes('APA300ML_b_out_nodes_3D.txt'); % Node coordinates [m] - -n_hexapod.actuator.ks = 235e6; % Stiffness of one stack [N/m] -n_hexapod.actuator.cs = 1e1; % Stiffness of one stack [N/m] - -n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V] -n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m] -#+end_src - -*** APA - Fully Flexible -#+begin_src matlab -n_hexapod.actuator.type = 3; - -n_hexapod.actuator.K = readmatrix('APA300ML_full_mat_K.CSV'); % Stiffness Matrix -n_hexapod.actuator.M = readmatrix('APA300ML_full_mat_M.CSV'); % Mass Matrix -n_hexapod.actuator.xi = 0.01; % Damping ratio -n_hexapod.actuator.P = extractNodes('APA300ML_full_out_nodes_3D.txt'); % Node coordiantes [m] - -n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V] -n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m] -#+end_src - -** Identification #+begin_src matlab %% Options for Linearized options = linearizeOptions; @@ -4196,6 +4104,8 @@ Ga.InputName = {'Va'}; Ga.OutputName = {'Vs', 'dL', 'z'}; #+end_src +The obtain dynamics are shown in Figure [[fig:apa_model_bench_bode_vs]] and [[fig:apa_model_bench_bode_dl_z]]. + #+begin_src matlab :exports none freqs = logspace(1, 3, 1000); @@ -4204,25 +4114,33 @@ tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); ax1 = nexttile([2,1]); hold on; -plot(freqs, abs(squeeze(freqresp(Ga('Vs', 'Va'), freqs, 'Hz'))), 'DisplayName', '') +plot(freqs, abs(squeeze(freqresp(Ga('Vs', 'Va'), freqs, 'Hz'))), 'k-') hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]); hold off; -legend('location', 'southwest'); ax2 = nexttile; hold on; -plot(freqs, 180/pi*angle(squeeze(freqresp(Ga('Vs', 'Va'), freqs, 'Hz')))) +plot(freqs, 180/pi*angle(squeeze(freqresp(Ga('Vs', 'Va'), freqs, 'Hz'))), 'k-') set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); hold off; yticks(-360:45:360); -ylim([-180, 180]) +ylim([0, 180]) linkaxes([ax1,ax2],'x'); #+end_src +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/apa_model_bench_bode_vs.pdf', 'width', 'wide', 'height', 'normal'); +#+end_src + +#+name: fig:apa_model_bench_bode_vs +#+caption: Bode plot of the transfer function from $V_a$ to $V_s$ +#+RESULTS: +[[file:figs/apa_model_bench_bode_vs.png]] + #+begin_src matlab :exports none freqs = logspace(1, 3, 1000); @@ -4252,58 +4170,388 @@ ylim([-180, 180]) linkaxes([ax1,ax2],'x'); #+end_src -** Compare 2-DoF with flexible -*** APA - 2 DoF +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/apa_model_bench_bode_dl_z.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:apa_model_bench_bode_dl_z +#+caption: Bode plot of the transfer function from $V_a$ to $d_L$ and to $z$ +#+RESULTS: +[[file:figs/apa_model_bench_bode_dl_z.png]] + + +** Identify Sensor/Actuator constants and compare with measured FRF +*** How to identify these constants? +**** Piezoelectric Actuator Constant + +Using the measurement test-bench, it is rather easy the determine the static gain between the applied voltage $V_a$ to the induced displacement $d$. +\begin{equation} + d = g_{d/V_a} \cdot V_a +\end{equation} + +Using the Simscape model of the APA, it is possible to determine the static gain between the actuator force $F_a$ to the induced displacement $d$: +\begin{equation} + d = g_{d/F_a} \cdot F_a +\end{equation} + +From the two gains, it is then easy to determine $g_a$: +\begin{equation} + g_a = \frac{F_a}{V_a} = \frac{F_a}{d} \cdot \frac{d}{V_a} = \frac{g_{d/V_a}}{g_{d/F_a}} +\end{equation} + +**** Piezoelectric Sensor Constant + +Similarly, it is easy to determine the gain from the excitation voltage $V_a$ to the voltage generated by the sensor stack $V_s$: +\begin{equation} + V_s = g_{V_s/V_a} V_a +\end{equation} + +Note here that there is an high pass filter formed by the piezo capacitor and parallel resistor. + +The gain can be computed from the dynamical identification and taking the gain at the wanted frequency (above the first resonance). + +Using the simscape model, compute the gain at the same frequency from the actuator force $F_a$ to the strain of the sensor stack $dl$: +\begin{equation} + dl = g_{dl/F_a} F_a +\end{equation} + +Then, the "sensor" constant is: +\begin{equation} + g_s = \frac{V_s}{dl} = \frac{V_s}{V_a} \cdot \frac{V_a}{F_a} \cdot \frac{F_a}{dl} = \frac{g_{V_s/V_a}}{g_a \cdot g_{dl/F_a}} +\end{equation} + +*** Identification Data #+begin_src matlab -n_hexapod = struct(); +leg_sweep = load(sprintf('frf_data_%i_sweep.mat', 1), 't', 'Va', 'Vs', 'de', 'da'); +leg_noise_hf = load(sprintf('frf_data_%i_noise_hf.mat', 1), 't', 'Va', 'Vs', 'de', 'da'); +#+end_src -n_hexapod.actuator = struct(); +The time is the same for all measurements. +#+begin_src matlab +%% Time vector +t = leg_sweep.t - leg_sweep.t(1) ; % Time vector [s] -n_hexapod.actuator.type = 1; +%% Sampling +Ts = (t(end) - t(1))/(length(t)-1); % Sampling Time [s] +Fs = 1/Ts; % Sampling Frequency [Hz] +#+end_src -n_hexapod.actuator.k = ones(6,1)*0.35e6; % [N/m] -n_hexapod.actuator.ke = ones(6,1)*1.5e6; % [N/m] -n_hexapod.actuator.ka = ones(6,1)*43e6; % [N/m] +Then we defined a "Hanning" windows that will be used for the spectral analysis: +#+begin_src matlab +win = hanning(ceil(0.5*Fs)); % Hannning Windows +#+end_src -n_hexapod.actuator.c = ones(6,1)*3e1; % [N/(m/s)] -n_hexapod.actuator.ce = ones(6,1)*1e1; % [N/(m/s)] -n_hexapod.actuator.ca = ones(6,1)*1e1; % [N/(m/s)] - -n_hexapod.actuator.Leq = ones(6,1)*0.056; % [m] - -n_hexapod.actuator.Ga = ones(6,1)*-2.15; % Actuator gain [N/V] -n_hexapod.actuator.Gs = ones(6,1)*2.305e-08; % Sensor gain [V/m] +We get the frequency vector that will be the same for all the frequency domain analysis. +#+begin_src matlab +% Only used to have the frequency vector "f" +[~, f] = tfestimate(leg_sweep.Va, leg_sweep.de, win, [], [], 1/Ts); #+end_src #+begin_src matlab +[dvf_sweep, ~] = tfestimate(leg_sweep.Va, leg_sweep.da, win, [], [], 1/Ts); +[dvf_noise_hf, ~] = tfestimate(leg_noise_hf.Va, leg_noise_hf.da, win, [], [], 1/Ts); +#+end_src + +#+begin_src matlab +[iff_sweep, ~] = tfestimate(leg_sweep.Va, leg_sweep.Vs, win, [], [], 1/Ts); +[iff_noise_hf, ~] = tfestimate(leg_noise_hf.Va, leg_noise_hf.Vs, win, [], [], 1/Ts); +#+end_src + +#+begin_src matlab +freqs = 2*logspace(0, 3, 1000); +#+end_src + +*** 2DoF APA +**** 2DoF APA +#+begin_src matlab +n_hexapod.actuator = initializeAPA('type', '2dof', 'ga', 1, 'gs', 1); +#+end_src + +**** Identification without actuator or sensor constants +#+begin_src matlab +%% Input/Output definition +clear io; io_i = 1; +io(io_i) = linio([mdl, '/Va'], 1, 'openinput'); io_i = io_i + 1; % Actuator Voltage +io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage +io(io_i) = linio([mdl, '/dL'], 1, 'openoutput'); io_i = io_i + 1; % Relative Motion Outputs +io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1; % Vertical Motion + +%% Identification +Gs = linearize(mdl, io, 0.0, options); +Gs.InputName = {'Va'}; +Gs.OutputName = {'Vs', 'dL', 'z'}; +#+end_src + +**** Actuator Constant +#+begin_src matlab +ga = -mean(abs(dvf_sweep(f>10 & f<20)))./dcgain(Gs('dL', 'Va')); % [N/V] +#+end_src + +#+begin_src matlab :results value replace :exports results :tangle no +sprintf('ga = %.1f [N/V]', ga); +#+end_src + +#+RESULTS: +: ga = -46.4 [N/V] + +#+begin_src matlab +n_hexapod.actuator.Ga = ones(6,1)*ga; % Actuator gain [N/V] +#+end_src + +**** Sensor Constant +#+begin_src matlab +gs = -mean(abs(iff_sweep(f>400 & f<500)))./(ga*abs(squeeze(freqresp(Gs('Vs', 'Va'), 1e3, 'Hz')))); % [V/m] +#+end_src + +#+begin_src matlab :results value replace :exports results :tangle no +sprintf('gs = %.3f [V/m]', gs); +#+end_src + +#+RESULTS: +: gs = 0.098 [V/m] + +#+begin_src matlab +n_hexapod.actuator.Gs = ones(6,1)*gs; % Sensor gain [V/m] +#+end_src + +**** Comparison +Identify the dynamics with included constants. +#+begin_src matlab +Gs = linearize(mdl, io, 0.0, options); +Gs = Gs*exp(-Ts*s); +Gs.InputName = {'Va'}; +Gs.OutputName = {'Vs', 'dL', 'z'}; +#+end_src + +#+begin_src matlab :exports none +figure; +tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +plot(f(f> 350), abs(dvf_noise_hf(f> 350)), 'k-'); +plot(f(f<=350), abs(dvf_sweep( f<=350)), 'k-'); +plot(freqs, abs(squeeze(freqresp(Gs('dL', 'Va'), freqs, 'Hz')))) +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude $d_e/V_a$ [m/V]'); set(gca, 'XTickLabel',[]); +hold off; +ylim([1e-9, 1e-3]); + +ax2 = nexttile; +hold on; +plot(f(f> 350), 180/pi*angle(dvf_noise_hf(f> 350)), 'k-'); +plot(f(f<=350), 180/pi*angle(dvf_sweep( f<=350)), 'k-'); +plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('dL', 'Va'), freqs, 'Hz')))) +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +hold off; +yticks(-360:90:360); ylim([-180, 180]); + +linkaxes([ax1,ax2],'x'); +xlim([10, 2e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/apa_act_constant_comp.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:apa_act_constant_comp +#+caption: Comparison of the experimental data and Simscape model ($V_a$ to $d_e$) +#+RESULTS: +[[file:figs/apa_act_constant_comp.png]] + +#+begin_src matlab :exports none +figure; +tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +plot(f(f> 350), abs(iff_noise_hf(f> 350)), 'k-'); +plot(f(f<=350), abs(iff_sweep( f<=350)), 'k-'); +plot(freqs, abs(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz')))) +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]); +hold off; +ylim([1e-2, 1e2]); + +ax2 = nexttile; +hold on; +plot(f(f> 350), 180/pi*angle(iff_noise_hf(f> 350)), 'k-'); +plot(f(f<=350), 180/pi*angle(iff_sweep( f<=350)), 'k-'); +plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz')))) +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +hold off; +yticks(-360:90:360); ylim([-180, 180]); + +linkaxes([ax1,ax2],'x'); +xlim([10, 2e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/apa_sens_constant_comp.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:apa_sens_constant_comp +#+caption: Comparison of the experimental data and Simscape model ($V_a$ to $V_s$) +#+RESULTS: +[[file:figs/apa_sens_constant_comp.png]] + +*** Flexible APA +**** Flexible APA +#+begin_src matlab +n_hexapod.actuator = initializeAPA('type', 'flexible', 'ga', 1, 'gs', 1); +#+end_src + +**** Identification without actuator or sensor constants +#+begin_src matlab +Gs = linearize(mdl, io, 0.0, options); +Gs.InputName = {'Va'}; +Gs.OutputName = {'Vs', 'dL', 'z'}; +#+end_src + +**** Actuator Constant +#+begin_src matlab +ga = -mean(abs(dvf_sweep(f>10 & f<20)))./dcgain(Gs('dL', 'Va')); % [N/V] +#+end_src + +#+begin_src matlab :results value replace :exports results :tangle no +sprintf('ga = %.1f [N/V]', ga); +#+end_src + +#+RESULTS: +: ga = 23.4 [N/V] + +#+begin_src matlab +n_hexapod.actuator.Ga = ones(6,1)*ga; % Actuator gain [N/V] +#+end_src + +**** Sensor Constant +#+begin_src matlab +gs = -mean(abs(iff_sweep(f>400 & f<500)))./(ga*abs(squeeze(freqresp(Gs('Vs', 'Va'), 1e3, 'Hz')))); % [V/m] +#+end_src + +#+begin_src matlab :results value replace :exports results :tangle no +sprintf('gs = %.3f [V/m]', gs); +#+end_src + +#+RESULTS: +: gs = -4674824.519 [V/m] + +#+begin_src matlab +n_hexapod.actuator.Gs = ones(6,1)*gs; % Sensor gain [V/m] +#+end_src + +**** Comparison +#+begin_src matlab +Gs = linearize(mdl, io, 0.0, options); +Gs = Gs*exp(-Ts*s); +Gs.InputName = {'Va'}; +Gs.OutputName = {'Vs', 'dL', 'z'}; +#+end_src + +#+begin_src matlab :exports none +figure; +tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +plot(f(f> 350), abs(dvf_noise_hf(f> 350)), 'k-'); +plot(f(f<=350), abs(dvf_sweep( f<=350)), 'k-'); +plot(freqs, abs(squeeze(freqresp(Gs('dL', 'Va'), freqs, 'Hz')))) +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude $d_e/V_a$ [m/V]'); set(gca, 'XTickLabel',[]); +hold off; +ylim([1e-9, 1e-3]); + +ax2 = nexttile; +hold on; +plot(f(f> 350), 180/pi*angle(dvf_noise_hf(f> 350)), 'k-'); +plot(f(f<=350), 180/pi*angle(dvf_sweep( f<=350)), 'k-'); +plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('dL', 'Va'), freqs, 'Hz')))) +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +hold off; +yticks(-360:90:360); ylim([-180, 180]); + +linkaxes([ax1,ax2],'x'); +xlim([10, 2e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/apa_act_constant_comp_flex.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:apa_act_constant_comp_flex +#+caption: Comparison of the experimental data and Simscape model ($V_a$ to $d_e$) +#+RESULTS: +[[file:figs/apa_act_constant_comp_flex.png]] + +#+begin_src matlab :exports none +figure; +tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +plot(f(f> 350), abs(iff_noise_hf(f> 350)), 'k-'); +plot(f(f<=350), abs(iff_sweep( f<=350)), 'k-'); +plot(freqs, abs(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz')))) +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]); +hold off; +ylim([1e-2, 1e2]); + +ax2 = nexttile; +hold on; +plot(f(f> 350), 180/pi*angle(iff_noise_hf(f> 350)), 'k-'); +plot(f(f<=350), 180/pi*angle(iff_sweep( f<=350)), 'k-'); +plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz')))) +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); +xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); +hold off; +yticks(-360:90:360); ylim([-180, 180]); + +linkaxes([ax1,ax2],'x'); +xlim([10, 2e3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/apa_sens_constant_comp_flex.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:apa_sens_constant_comp_flex +#+caption: Comparison of the experimental data and Simscape model ($V_a$ to $V_s$) +#+RESULTS: +[[file:figs/apa_sens_constant_comp_flex.png]] + +** Compare 2-DoF with flexible +APA - 2 DoF +#+begin_src matlab +n_hexapod.actuator = initializeAPA('type', '2dof'); + G_2dof = linearize(mdl, io, 0.0, options); G_2dof.InputName = {'Va'}; G_2dof.OutputName = {'Vs', 'dL', 'z'}; #+end_src -*** APA - Fully Flexible +APA - Fully Flexible #+begin_src matlab -n_hexapod = struct(); +n_hexapod.actuator = initializeAPA('type', 'flexible'); -n_hexapod.actuator.type = 3; - -n_hexapod.actuator.K = readmatrix('APA300ML_full_mat_K.CSV'); % Stiffness Matrix -n_hexapod.actuator.M = readmatrix('APA300ML_full_mat_M.CSV'); % Mass Matrix -n_hexapod.actuator.xi = 0.01; % Damping ratio -n_hexapod.actuator.P = extractNodes('APA300ML_full_out_nodes_3D.txt'); % Node coordiantes [m] - -n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V] -n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m] -#+end_src - -#+begin_src matlab G_flex = linearize(mdl, io, 0.0, options); G_flex.InputName = {'Va'}; G_flex.OutputName = {'Vs', 'dL', 'z'}; #+end_src -*** Comparison - +Comparison #+begin_src matlab :exports none freqs = logspace(1, 4, 1000); @@ -4312,13 +4560,13 @@ tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); ax1 = nexttile([2,1]); hold on; -plot(freqs, abs(squeeze(freqresp(G_2dof('Vs', 'Va'), freqs, 'Hz'))), 'DisplayName', '$G_a$') -plot(freqs, abs(squeeze(freqresp(G_flex('Vs', 'Va'), freqs, 'Hz'))), 'DisplayName', '$G_s$') +plot(freqs, abs(squeeze(freqresp(G_2dof('Vs', 'Va'), freqs, 'Hz'))), 'DisplayName', '2DoF') +plot(freqs, abs(squeeze(freqresp(G_flex('Vs', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Flexible') hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]); hold off; -legend('location', 'southwest'); +legend('location', 'southeast'); ax2 = nexttile; hold on; @@ -4333,6 +4581,15 @@ ylim([-180, 180]) linkaxes([ax1,ax2],'x'); #+end_src +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/apa_effect_joint_comp_vs.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:apa_effect_joint_comp_vs +#+caption: Effect of the joint's flexibility on the transfer function from $V_a$ to $V_s$ +#+RESULTS: +[[file:figs/apa_effect_joint_comp_vs.png]] + #+begin_src matlab :exports none freqs = logspace(1, 4, 1000); @@ -4341,8 +4598,8 @@ tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); ax1 = nexttile([2,1]); hold on; -plot(freqs, abs(squeeze(freqresp(G_2dof('dL', 'Va'), freqs, 'Hz'))), 'DisplayName', '$G_a$') -plot(freqs, abs(squeeze(freqresp(G_flex('dL', 'Va'), freqs, 'Hz'))), 'DisplayName', '$G_s$') +plot(freqs, abs(squeeze(freqresp(G_2dof('dL', 'Va'), freqs, 'Hz'))), 'DisplayName', '2DoF') +plot(freqs, abs(squeeze(freqresp(G_flex('dL', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Flexible') hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); ylabel('Amplitude $d_L/V_a$ [m/V]'); set(gca, 'XTickLabel',[]); @@ -4362,6 +4619,15 @@ ylim([-180, 180]) linkaxes([ax1,ax2],'x'); #+end_src +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/apa_effect_joint_comp_dl.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:apa_effect_joint_comp_dl +#+caption: Effect of the joint's flexibility on the transfer function from $V_a$ to $d_L$ (encoder) +#+RESULTS: +[[file:figs/apa_effect_joint_comp_dl.png]] + #+begin_src matlab :exports none freqs = logspace(1, 4, 1000); @@ -4370,8 +4636,8 @@ tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); ax1 = nexttile([2,1]); hold on; -plot(freqs, abs(squeeze(freqresp(G_2dof('z', 'Va'), freqs, 'Hz'))), 'DisplayName', '$G_a$') -plot(freqs, abs(squeeze(freqresp(G_flex('z', 'Va'), freqs, 'Hz'))), 'DisplayName', '$G_s$') +plot(freqs, abs(squeeze(freqresp(G_2dof('z', 'Va'), freqs, 'Hz'))), 'DisplayName', '2DoF') +plot(freqs, abs(squeeze(freqresp(G_flex('z', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Flexible') hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); ylabel('Amplitude $z/V_a$ [m/V]'); set(gca, 'XTickLabel',[]); @@ -4391,6 +4657,15 @@ ylim([-180, 180]) linkaxes([ax1,ax2],'x'); #+end_src +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/apa_effect_joint_comp_z.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:apa_effect_joint_comp_z +#+caption: Effect of the joint's flexibility on the transfer function from $V_a$ to $z$ (interferometer) +#+RESULTS: +[[file:figs/apa_effect_joint_comp_z.png]] + * Test Bench Struts - Simscape Model ** Introduction ** Matlab Init :noexport:ignore: @@ -4405,108 +4680,18 @@ linkaxes([ax1,ax2],'x'); #+begin_src matlab :tangle no addpath('matlab/'); addpath('matlab/test_bench_struts/'); +addpath('matlab/mat/'); +addpath('matlab/src/'); addpath('matlab/png/'); #+end_src #+begin_src matlab :eval no addpath('test_bench_struts/'); addpath('png/'); +addpath('mat/'); +addpath('src/'); #+end_src -#+begin_src matlab -open('test_bench_struts.slx') -#+end_src - -** Nano Hexapod object -#+begin_src matlab -n_hexapod = struct(); -#+end_src - -*** Flexible Joint - Bot -#+begin_src matlab -n_hexapod.flex_bot = struct(); - -n_hexapod.flex_bot.type = 1; % 1: 2dof / 2: 3dof / 3: 4dof - -n_hexapod.flex_bot.kRx = ones(6,1)*5; % X bending stiffness [Nm/rad] -n_hexapod.flex_bot.kRy = ones(6,1)*5; % Y bending stiffness [Nm/rad] -n_hexapod.flex_bot.kRz = ones(6,1)*260; % Torsionnal stiffness [Nm/rad] -n_hexapod.flex_bot.kz = ones(6,1)*1e8; % Axial stiffness [N/m] - -n_hexapod.flex_bot.cRx = ones(6,1)*0.1; % [Nm/(rad/s)] -n_hexapod.flex_bot.cRy = ones(6,1)*0.1; % [Nm/(rad/s)] -n_hexapod.flex_bot.cRz = ones(6,1)*0.1; % [Nm/(rad/s)] -n_hexapod.flex_bot.cz = ones(6,1)*1e2; %[N/(m/s)] -#+end_src - -*** Flexible Joint - Top -#+begin_src matlab -n_hexapod.flex_top = struct(); - -n_hexapod.flex_top.type = 2; % 1: 2dof / 2: 3dof / 3: 4dof - -n_hexapod.flex_top.kRx = ones(6,1)*5; % X bending stiffness [Nm/rad] -n_hexapod.flex_top.kRy = ones(6,1)*5; % Y bending stiffness [Nm/rad] -n_hexapod.flex_top.kRz = ones(6,1)*260; % Torsionnal stiffness [Nm/rad] -n_hexapod.flex_top.kz = ones(6,1)*1e8; % Axial stiffness [N/m] - -n_hexapod.flex_top.cRx = ones(6,1)*0.1; % [Nm/(rad/s)] -n_hexapod.flex_top.cRy = ones(6,1)*0.1; % [Nm/(rad/s)] -n_hexapod.flex_top.cRz = ones(6,1)*0.1; % [Nm/(rad/s)] -n_hexapod.flex_top.cz = ones(6,1)*1e2; %[N/(m/s)] -#+end_src - -*** APA - 2 DoF -#+begin_src matlab -n_hexapod.actuator = struct(); - -n_hexapod.actuator.type = 1; - -n_hexapod.actuator.k = ones(6,1)*0.35e6; % [N/m] -n_hexapod.actuator.ke = ones(6,1)*1.5e6; % [N/m] -n_hexapod.actuator.ka = ones(6,1)*43e6; % [N/m] - -n_hexapod.actuator.c = ones(6,1)*3e1; % [N/(m/s)] -n_hexapod.actuator.ce = ones(6,1)*1e1; % [N/(m/s)] -n_hexapod.actuator.ca = ones(6,1)*1e1; % [N/(m/s)] - -n_hexapod.actuator.Leq = ones(6,1)*0.056; % [m] - -n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V] -n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m] -#+end_src - -*** APA - Flexible Frame -#+begin_src matlab -n_hexapod.actuator.type = 2; - -n_hexapod.actuator.K = readmatrix('APA300ML_b_mat_K.CSV'); % Stiffness Matrix -n_hexapod.actuator.M = readmatrix('APA300ML_b_mat_M.CSV'); % Mass Matrix -n_hexapod.actuator.xi = 0.01; % Damping ratio -n_hexapod.actuator.P = extractNodes('APA300ML_b_out_nodes_3D.txt'); % Node coordinates [m] - -n_hexapod.actuator.ks = 235e6; % Stiffness of one stack [N/m] -n_hexapod.actuator.cs = 1e1; % Stiffness of one stack [N/m] - -n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V] -n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m] -#+end_src - -*** APA - Fully Flexible -#+begin_src matlab -n_hexapod.actuator.type = 3; - -n_hexapod.actuator.K = readmatrix('APA300ML_full_mat_K.CSV'); % Stiffness Matrix -n_hexapod.actuator.M = readmatrix('APA300ML_full_mat_M.CSV'); % Mass Matrix -n_hexapod.actuator.xi = 0.01; % Damping ratio -n_hexapod.actuator.P = extractNodes('APA300ML_full_out_nodes_3D.txt'); % Node coordiantes [m] - -n_hexapod.actuator.Ga = ones(6,1)*1; % Actuator gain [N/V] -n_hexapod.actuator.Gs = ones(6,1)*1; % Sensor gain [V/m] -#+end_src - - -** Identification #+begin_src matlab %% Options for Linearized options = linearizeOptions; @@ -4515,13 +4700,29 @@ options.SampleTime = 0; %% Name of the Simulink File mdl = 'test_bench_struts'; +%% Open the Simulink File +open([mdl, '.slx']) +#+end_src + +** First Identification +The object containing all the data is created. +#+begin_src matlab +n_hexapod = struct(); +n_hexapod.flex_bot = initializeBotFlexibleJoint('type', '2dof'); +n_hexapod.flex_top = initializeTopFlexibleJoint('type', '2dof'); +n_hexapod.actuator = initializeAPA('type', '2dof'); +#+end_src + +#+begin_src matlab %% Input/Output definition clear io; io_i = 1; io(io_i) = linio([mdl, '/Va'], 1, 'openinput'); io_i = io_i + 1; % Actuator Voltage io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage io(io_i) = linio([mdl, '/dL'], 1, 'openoutput'); io_i = io_i + 1; % Relative Motion Outputs io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1; % Vertical Motion +#+end_src +#+begin_src matlab %% Run the linearization Gs = linearize(mdl, io, 0.0, options); Gs.InputName = {'Va'}; @@ -4535,26 +4736,32 @@ figure; tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); ax1 = nexttile([2,1]); -hold on; -plot(freqs, abs(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz'))), 'DisplayName', '') -hold off; +plot(freqs, abs(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz'))), 'k-') set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]); hold off; -legend('location', 'southwest'); ax2 = nexttile; hold on; -plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz')))) +plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz'))), 'k-') set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); hold off; yticks(-360:45:360); -ylim([-180, 180]) +ylim([0, 180]) linkaxes([ax1,ax2],'x'); #+end_src +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/strut_bench_model_iff_bode.pdf', 'width', 'wide', 'height', 'normal'); +#+end_src + +#+name: fig:strut_bench_model_iff_bode +#+caption: Identified transfer function from $V_a$ to $V_s$ +#+RESULTS: +[[file:figs/strut_bench_model_iff_bode.png]] + #+begin_src matlab :exports none freqs = logspace(1, 4, 1000); @@ -4584,56 +4791,58 @@ ylim([-180, 180]) linkaxes([ax1,ax2],'x'); #+end_src -** Compare flexible joints -*** Perfect -#+begin_src matlab -n_hexapod.flex_bot.type = 1; % 1: 2dof / 2: 3dof / 3: 4dof -n_hexapod.flex_top.type = 2; % 1: 2dof / 2: 3dof / 3: 4dof +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/strut_bench_model_dvf_bode.pdf', 'width', 'wide', 'height', 'tall'); #+end_src +#+name: fig:strut_bench_model_dvf_bode +#+caption: Identified transfer function from $V_a$ to $d_L$ +#+RESULTS: +[[file:figs/strut_bench_model_dvf_bode.png]] + +** Effect of flexible joints +Perfect #+begin_src matlab +n_hexapod.flex_bot = initializeBotFlexibleJoint('type', '2dof'); +n_hexapod.flex_top = initializeTopFlexibleJoint('type', '3dof'); + Gp = linearize(mdl, io, 0.0, options); Gp.InputName = {'Va'}; Gp.OutputName = {'Vs', 'dL', 'z'}; #+end_src -*** Top Flexible +Top Flexible #+begin_src matlab -n_hexapod.flex_bot.type = 1; % 1: 2dof / 2: 3dof / 3: 4dof -n_hexapod.flex_top.type = 3; % 1: 2dof / 2: 3dof / 3: 4dof -#+end_src +n_hexapod.flex_bot = initializeBotFlexibleJoint('type', '2dof'); +n_hexapod.flex_top = initializeTopFlexibleJoint('type', '4dof'); -#+begin_src matlab Gt = linearize(mdl, io, 0.0, options); Gt.InputName = {'Va'}; Gt.OutputName = {'Vs', 'dL', 'z'}; #+end_src -*** Bottom Flexible +Bottom Flexible #+begin_src matlab -n_hexapod.flex_bot.type = 3; % 1: 2dof / 2: 3dof / 3: 4dof -n_hexapod.flex_top.type = 2; % 1: 2dof / 2: 3dof / 3: 4dof -#+end_src +n_hexapod.flex_bot = initializeBotFlexibleJoint('type', '4dof'); +n_hexapod.flex_top = initializeTopFlexibleJoint('type', '3dof'); -#+begin_src matlab Gb = linearize(mdl, io, 0.0, options); Gb.InputName = {'Va'}; Gb.OutputName = {'Vs', 'dL', 'z'}; #+end_src -*** Both Flexible +Both Flexible #+begin_src matlab -n_hexapod.flex_bot.type = 3; % 1: 2dof / 2: 3dof / 3: 4dof -n_hexapod.flex_top.type = 3; % 1: 2dof / 2: 3dof / 3: 4dof -#+end_src +n_hexapod.flex_bot = initializeBotFlexibleJoint('type', '4dof'); +n_hexapod.flex_top = initializeTopFlexibleJoint('type', '4dof'); -#+begin_src matlab Gf = linearize(mdl, io, 0.0, options); Gf.InputName = {'Va'}; Gf.OutputName = {'Vs', 'dL', 'z'}; #+end_src -*** Comparison +Comparison in Figures [[fig:strut_effect_joint_comp_vs]], [[fig:strut_effect_joint_comp_dl]] and [[fig:strut_effect_joint_comp_z]]. + #+begin_src matlab :exports none freqs = logspace(1, 4, 1000); @@ -4650,7 +4859,7 @@ hold off; set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]); hold off; -legend('location', 'southwest'); +legend('location', 'southeast'); ax2 = nexttile; hold on; @@ -4667,6 +4876,15 @@ ylim([-180, 180]) linkaxes([ax1,ax2],'x'); #+end_src +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/strut_effect_joint_comp_vs.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:strut_effect_joint_comp_vs +#+caption: Effect of the joint's flexibility on the transfer function from $V_a$ to $V_s$ +#+RESULTS: +[[file:figs/strut_effect_joint_comp_vs.png]] + #+begin_src matlab :exports none freqs = logspace(1, 4, 1000); @@ -4700,6 +4918,15 @@ ylim([-180, 180]) linkaxes([ax1,ax2],'x'); #+end_src +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/strut_effect_joint_comp_dl.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:strut_effect_joint_comp_dl +#+caption: Effect of the joint's flexibility on the transfer function from $V_a$ to $d_L$ (encoder) +#+RESULTS: +[[file:figs/strut_effect_joint_comp_dl.png]] + #+begin_src matlab :exports none freqs = logspace(1, 4, 1000); @@ -4733,7 +4960,414 @@ ylim([-180, 180]) linkaxes([ax1,ax2],'x'); #+end_src +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/strut_effect_joint_comp_z.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:strut_effect_joint_comp_z +#+caption: Effect of the joint's flexibility on the transfer function from $V_a$ to $z$ (interferometer) +#+RESULTS: +[[file:figs/strut_effect_joint_comp_z.png]] + +#+begin_important +Imperfection of the flexible joints has the largest impact on the transfer function from $V_a$ to $d_L$. +However, it has relatively small impact on the transfer functions from $V_a$ to $V_s$ and to $z$. +#+end_important + +** Integral Force Feedback +*** Initialize the system +#+begin_src matlab +n_hexapod = struct(); +n_hexapod.flex_bot = initializeBotFlexibleJoint('type', '2dof'); +n_hexapod.flex_top = initializeTopFlexibleJoint('type', '3dof'); +n_hexapod.actuator = initializeAPA('type', '2dof'); +#+end_src + +*** Plant Identification +#+begin_src matlab +G = linearize(mdl, io, 0.0, options); +G.InputName = {'Va'}; +G.OutputName = {'Vs', 'dL', 'z'}; +#+end_src + +#+begin_src matlab +Giff = G('Vs', 'Va'); +#+end_src + +*** Root Locus +\begin{equation} +K_{\text{IFF}} = \frac{g}{s + \omega_c} +\end{equation} + +#+begin_src matlab +wc = 2*pi*20; +#+end_src + +#+begin_src matlab :exports none +gains = logspace(1, 5, 300); + +figure; + +hold on; +% Pure Integrator +set(gca,'ColorOrderIndex',1); +plot(real(pole(Giff)), imag(pole(Giff)), 'x', 'DisplayName', '$g = 0$'); +set(gca,'ColorOrderIndex',1); +plot(real(tzero(Giff)), imag(tzero(Giff)), 'o', 'HandleVisibility', 'off'); +for g = gains + clpoles = pole(feedback(Giff, (g/(s + wc)))); + set(gca,'ColorOrderIndex',1); + plot(real(clpoles), imag(clpoles), '.', 'HandleVisibility', 'off'); +end + +g = 8e2; +clpoles = pole(feedback(Giff, (g/(s + wc)))); +set(gca,'ColorOrderIndex',1); +plot(real(clpoles), imag(clpoles), 'rx', 'DisplayName', '$g = 1.5 \cdot 10^4$'); +axis square; +xlim([-600, 5]); ylim([-5, 600]); +xlabel('Real Part'); ylabel('Imaginary Part'); +legend('location', 'northwest'); +#+end_src + * Function +** =initializeBotFlexibleJoint= - Initialize Flexible Joint +:PROPERTIES: +:header-args:matlab+: :tangle matlab/src/initializeBotFlexibleJoint.m +:header-args:matlab+: :comments none :mkdirp yes :eval no +:END: +<> + +*** Function description +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +function [flex_bot] = initializeBotFlexibleJoint(args) +% initializeBotFlexibleJoint - +% +% Syntax: [flex_bot] = initializeBotFlexibleJoint(args) +% +% Inputs: +% - args - +% +% Outputs: +% - flex_bot - +#+end_src + +*** Optional Parameters +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +arguments + args.type char {mustBeMember(args.type,{'2dof', '3dof', '4dof'})} = '2dof' + + args.kRx (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*5 + args.kRy (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*5 + args.kRz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*260 + args.kz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*1e8 + + args.cRx (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.1 + args.cRy (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.1 + args.cRz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.1 + args.cz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*1e2 +end +#+end_src + +*** Initialize the structure +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +flex_bot = struct(); +#+end_src + +*** Set the Joint's type +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +switch args.type + case '2dof' + flex_bot.type = 1; + case '3dof' + flex_bot.type = 2; + case '4dof' + flex_bot.type = 3; +end +#+end_src + +*** Set parameters +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +flex_bot.kRx = args.kRx; +flex_bot.kRy = args.kRy; +flex_bot.kRz = args.kRz; +flex_bot.kz = args.kz; +#+end_src + +#+begin_src matlab +flex_bot.cRx = args.cRx; +flex_bot.cRy = args.cRy; +flex_bot.cRz = args.cRz; +flex_bot.cz = args.cz; +#+end_src + +** =initializeTopFlexibleJoint= - Initialize Flexible Joint +:PROPERTIES: +:header-args:matlab+: :tangle matlab/src/initializeTopFlexibleJoint.m +:header-args:matlab+: :comments none :mkdirp yes :eval no +:END: +<> + +*** Function description +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +function [flex_top] = initializeTopFlexibleJoint(args) +% initializeTopFlexibleJoint - +% +% Syntax: [flex_top] = initializeTopFlexibleJoint(args) +% +% Inputs: +% - args - +% +% Outputs: +% - flex_top - +#+end_src + +*** Optional Parameters +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +arguments + args.type char {mustBeMember(args.type,{'2dof', '3dof', '4dof'})} = '2dof' + + args.kRx (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*5 + args.kRy (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*5 + args.kRz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*260 + args.kz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*1e8 + + args.cRx (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.1 + args.cRy (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.1 + args.cRz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.1 + args.cz (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*1e2 +end +#+end_src + +*** Initialize the structure +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +flex_top = struct(); +#+end_src + +*** Set the Joint's type +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +switch args.type + case '2dof' + flex_top.type = 1; + case '3dof' + flex_top.type = 2; + case '4dof' + flex_top.type = 3; +end +#+end_src + +*** Set parameters +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +flex_top.kRx = args.kRx; +flex_top.kRy = args.kRy; +flex_top.kRz = args.kRz; +flex_top.kz = args.kz; +#+end_src + +#+begin_src matlab +flex_top.cRx = args.cRx; +flex_top.cRy = args.cRy; +flex_top.cRz = args.cRz; +flex_top.cz = args.cz; +#+end_src + +** =initializeAPA= - Initialize APA +:PROPERTIES: +:header-args:matlab+: :tangle matlab/src/initializeAPA.m +:header-args:matlab+: :comments none :mkdirp yes :eval no +:END: +<> + +*** Function description +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +function [actuator] = initializeAPA(args) +% initializeAPA - +% +% Syntax: [actuator] = initializeAPA(args) +% +% Inputs: +% - args - +% +% Outputs: +% - actuator - +#+end_src + +*** Optional Parameters +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +arguments + args.type char {mustBeMember(args.type,{'2dof', 'flexible frame', 'flexible'})} = '2dof' + + args.Ga (1,1) double {mustBeNumeric} = 0 + args.Gs (1,1) double {mustBeNumeric} = 0 + + % For 2DoF + args.k (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*0.35e6 + args.ke (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*1.5e6 + args.ka (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*43e6 + + args.c (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*3e1 + args.ce (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*2e1 + args.ca (6,1) double {mustBeNumeric, mustBePositive} = ones(6,1)*2e1 + + args.Leq (6,1) double {mustBeNumeric} = ones(6,1)*0.056 + + % Force Flexible APA + args.xi (1,1) double {mustBeNumeric, mustBePositive} = 0.5 + + % For Flexible Frame + args.ks (1,1) double {mustBeNumeric, mustBePositive} = 235e6 + args.cs (1,1) double {mustBeNumeric, mustBePositive} = 1e1 +end +#+end_src + +*** Initialize Structure +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +actuator = struct(); +#+end_src + +*** Type +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +switch args.type + case '2dof' + actuator.type = 1; + case 'flexible frame' + actuator.type = 2; + case 'flexible' + actuator.type = 3; +end +#+end_src + +*** Actuator/Sensor Constants +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +if args.Ga == 0 + switch args.type + case '2dof' + actuator.Ga = -46.4; + case 'flexible frame' + actuator.Ga = 1; % TODO + case 'flexible' + actuator.Ga = 23.4; + end +else + actuator.Ga = args.Ga; % Actuator gain [N/V] +end +#+end_src + +#+begin_src matlab +if args.Gs == 0 + switch args.type + case '2dof' + actuator.Gs = 0.098; + case 'flexible frame' + actuator.Gs = 1; % TODO + case 'flexible' + actuator.Gs = -4674824; + end +else + actuator.Gs = args.Gs; % Sensor gain [V/m] +end +#+end_src + +*** 2DoF parameters +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +actuator.k = args.k; % [N/m] +actuator.ke = args.ke; % [N/m] +actuator.ka = args.ka; % [N/m] + +actuator.c = args.c; % [N/(m/s)] +actuator.ce = args.ce; % [N/(m/s)] +actuator.ca = args.ca; % [N/(m/s)] + +actuator.Leq = args.Leq; % [m] +#+end_src + +*** Flexible frame and fully flexible +:PROPERTIES: +:UNNUMBERED: t +:END: + +#+begin_src matlab +switch args.type + case 'flexible frame' + actuator.K = readmatrix('APA300ML_b_mat_K.CSV'); % Stiffness Matrix + actuator.M = readmatrix('APA300ML_b_mat_M.CSV'); % Mass Matrix + actuator.P = extractNodes('APA300ML_b_out_nodes_3D.txt'); % Node coordinates [m] + case 'flexible' + actuator.K = readmatrix('full_APA300ML_K.CSV'); % Stiffness Matrix + actuator.M = readmatrix('full_APA300ML_M.CSV'); % Mass Matrix + actuator.P = extractNodes('full_APA300ML_out_nodes_3D.txt'); % Node coordiantes [m] +end + +actuator.xi = args.xi; % Damping ratio + +actuator.ks = args.ks; % Stiffness of one stack [N/m] +actuator.cs = args.cs; % Damping of one stack [N/m] +#+end_src + ** =generateSweepExc=: Generate sweep sinus excitation :PROPERTIES: :header-args:matlab+: :tangle ./matlab/src/generateSweepExc.m