diff --git a/index.html b/index.html index 780f488..68aae45 100644 --- a/index.html +++ b/index.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Cercalo Test Bench @@ -276,92 +276,93 @@ for the JavaScript code in this tag.

Table of Contents

-
-

1 Introduction

+
+

1 Introduction

-
-

1.1 Block Diagram

+
+

1.1 Block Diagram

-The block diagram of the setup to be controlled is shown in Fig. 1. +The block diagram of the setup to be controlled is shown in Fig. 1.

-
+

cercalo_diagram_simplify.png

Figure 1: Block Diagram of the Experimental Setup

@@ -391,10 +392,10 @@ The transfer functions in the system are:

-The block diagram with each transfer function is shown in Fig. 2. +The block diagram with each transfer function is shown in Fig. 2.

-
+

cercalo_diagram.png

Figure 2: Block Diagram of the Experimental Setup with detailed dynamics

@@ -402,14 +403,14 @@ The block diagram with each transfer function is shown in Fig. -

1.2 Cercalo

+
+

1.2 Cercalo

-From the Cercalo documentation, we have the parameters shown on table 1. +From the Cercalo documentation, we have the parameters shown on table 1.

- +
@@ -467,11 +468,11 @@ The Inductance and DC resistance of the two axis of the Cercalo have been measur

-Let's first consider the horizontal direction and we try to model the Cercalo by a spring/mass/damper system (Fig. 3). +Let's first consider the horizontal direction and we try to model the Cercalo by a spring/mass/damper system (Fig. 3).

-
+

mech_cercalo.png

Figure 3: 1 degree-of-freedom model of the Cercalo

@@ -510,7 +511,7 @@ The current \(I\) is also proportional to the voltage at the output of the buffe

Let's try to determine the equivalent mass and spring values. -From table 1, for the horizontal direction: +From table 1, for the horizontal direction: \[ \left| \frac{x}{I} \right|(0) = \left| \alpha \frac{x}{F} \right|(0) = 28.4\ \frac{mA}{deg} = 1.63\ \frac{A}{rad} \]

@@ -571,18 +572,18 @@ This will be done using the Newport.
-
-

1.3 Optical Setup

+
+

1.3 Optical Setup

-
-

1.4 Newport

+
+

1.4 Newport

-Parameters of the Newport are shown in Fig. 4. +Parameters of the Newport are shown in Fig. 4.

-It's dynamics for small angle excitation is shown in Fig. 5. +It's dynamics for small angle excitation is shown in Fig. 5.

@@ -594,14 +595,14 @@ And we have: \end{align*} -

+

newport_doc.png

Figure 4: Documentation of the Newport

-
+

newport_gain.png

Figure 5: Transfer function of the Newport

@@ -609,25 +610,25 @@ And we have:
-
-

1.5 4 quadrant Diode

+
+

1.5 4 quadrant Diode

-The front view of the 4 quadrant photo-diode is shown in Fig. 6. +The front view of the 4 quadrant photo-diode is shown in Fig. 6.

-
+

4qd_naming.png

Figure 6: Front view of the 4QD

-Each of the photo-diode is amplified using a 4-channel amplifier as shown in Fig. 7. +Each of the photo-diode is amplified using a 4-channel amplifier as shown in Fig. 7.

-
+

4qd_amplifier.png

Figure 7: Wiring of the amplifier. The amplifier is located on the bottom right of the board

@@ -635,8 +636,8 @@ Each of the photo-diode is amplified using a 4-channel amplifier as shown in Fig
-
-

1.6 ADC/DAC

+
+

1.6 ADC/DAC

Let's compute the theoretical noise of the ADC/DAC. @@ -656,14 +657,14 @@ with \(\Delta V\) the total range of the ADC, \(n\) its number of bits, \(q\) th

-
-

2 Identification of the system dynamics

+
+

2 Identification of the system dynamics

- +

-In this section, we seek to identify all the blocks as shown in Fig. 1. +In this section, we seek to identify all the blocks as shown in Fig. 1.

Table 1: Cercalo Parameters
@@ -760,8 +761,8 @@ All the files (data and Matlab scripts) are accessible -

2.1 Calibration of the 4 Quadrant Diode

+
+

2.1 Calibration of the 4 Quadrant Diode

Prior to any dynamic identification, we would like to be able to determine the meaning of the 4 quadrant diode measurement. @@ -776,8 +777,8 @@ We then should be able to obtain the "gain" of the 4QD in [V/rad].

-
-

2.1.1 Input / Output data

+
+

2.1.1 Input / Output data

The identification data is loaded @@ -811,7 +812,7 @@ uv.t = uv.t - uv.t +

calib_4qd_h.png

Figure 8: Identification signals when exciting the horizontal direction (png, pdf)

@@ -819,7 +820,7 @@ uv.t = uv.t - uv.t +

calib_4qd_v.png

Figure 9: Identification signals when exciting in the vertical direction (png, pdf)

@@ -827,8 +828,8 @@ uv.t = uv.t - uv.t -

2.1.2 Linear Regression to obtain the gain of the 4QD

+
+

2.1.2 Linear Regression to obtain the gain of the 4QD

We plot the angle of mirror @@ -858,7 +859,7 @@ where:

-The linear regression is shown in Fig. 10. +The linear regression is shown in Fig. 10.

@@ -868,17 +869,17 @@ bv = [ones +

4qd_linear_reg.png

Figure 10: Linear Regression (png, pdf)

-Thus, we obtain the "gain of the 4 quadrant photo-diode as shown on table 2. +Thus, we obtain the "gain of the 4 quadrant photo-diode as shown on table 2.

-
+
@@ -922,11 +923,11 @@ We obtain: -
-

2.2 Identification of the Cercalo Impedance, Current Amplifier and Voltage Amplifier dynamics

+
+

2.2 Identification of the Cercalo Impedance, Current Amplifier and Voltage Amplifier dynamics

-We wish here to determine \(G_i\) and \(G_a\) shown in Fig. 1. +We wish here to determine \(G_i\) and \(G_a\) shown in Fig. 1.

@@ -934,15 +935,15 @@ We ignore the electro-mechanical coupling.

-
-

2.2.1 Electrical Schematic

+
+

2.2.1 Electrical Schematic

-The schematic of the electrical circuit used to drive the Cercalo is shown in Fig. 11. +The schematic of the electrical circuit used to drive the Cercalo is shown in Fig. 11.

-
+

cercalo_amplifier.png

Figure 11: Current Amplifier Schematic

@@ -1029,8 +1030,8 @@ with
-
-

2.2.2 Theoretical Transfer Functions

+
+

2.2.2 Theoretical Transfer Functions

The values of the components in the current amplifier have been measured. @@ -1060,7 +1061,7 @@ Ga = blkdiag( +

current_amplifier_tf.png

Figure 12: Transfer function for the current amplifier (png, pdf)

@@ -1082,8 +1083,8 @@ Zc = tf(blkdiag -

2.2.3 Identified Transfer Functions

+
+

2.2.3 Identified Transfer Functions

Noise is generated using the DAC (\([U_{c,h}\ U_{c,v}]\)) and we measure the output of the voltage amplifier \([V_{c,h}, V_{c,v}]\). @@ -1110,7 +1111,7 @@ We remove the first seconds where the Cercalo is turned on.

-
+

current_amplifier_comp_theory_id.png

Figure 13: Identified and Theoretical Transfer Function \(G_a G_i\) (png, pdf)

@@ -1128,7 +1129,7 @@ Gi = tf(blkdiag +

current_amplifier_comp_theory_id_bis.png

Figure 14: Identified and Theoretical Transfer Function \(G_a G_i\) (png, pdf)

@@ -1206,11 +1207,11 @@ Continuous-time zero/pole/gain model.
-
-

2.3 Identification of the Cercalo Dynamics

+
+

2.3 Identification of the Cercalo Dynamics

-We now wish to identify the dynamics of the Cercalo identified by \(G_c\) on the block diagram in Fig. 1. +We now wish to identify the dynamics of the Cercalo identified by \(G_c\) on the block diagram in Fig. 1.

@@ -1222,8 +1223,8 @@ The transfer function obtained will be \(G_c G_i\), and because we have already

-
-

2.3.1 Input / Output data

+
+

2.3.1 Input / Output data

The identification data is loaded @@ -1258,7 +1259,7 @@ uv.t = uv.t - uv.t +

identification_uh.png

Figure 15: Identification signals when exciting the horizontal direction (png, pdf)

@@ -1266,7 +1267,7 @@ uv.t = uv.t - uv.t +

identification_uv.png

Figure 16: Identification signals when exciting in the vertical direction (png, pdf)

@@ -1274,8 +1275,8 @@ uv.t = uv.t - uv.t -

2.3.2 Coherence

+
+

2.3.2 Coherence

The window used for the spectral analysis is an hanning windows with temporal size equal to 1 second. @@ -1294,7 +1295,7 @@ The window used for the spectral analysis is an hanning windows wit

-
+

coh_cercalo.png

Figure 17: Coherence (png, pdf)

@@ -1302,8 +1303,8 @@ The window used for the spectral analysis is an hanning windows wit
-
-

2.3.3 Estimation of the Frequency Response Function Matrix

+
+

2.3.3 Estimation of the Frequency Response Function Matrix

We compute an estimate of the transfer functions. @@ -1317,14 +1318,14 @@ We compute an estimate of the transfer functions.

-
+

frf_cercalo_gain.png

Figure 18: Frequency Response Matrix (png, pdf)

-
+

frf_cercalo_phase.png

Figure 19: Frequency Response MatrixPhase (png, pdf)

@@ -1332,8 +1333,8 @@ We compute an estimate of the transfer functions.
-
-

2.3.4 Time Delay

+
+

2.3.4 Time Delay

Now, we would like to remove the time delay included in the FRF prior to the model extraction. @@ -1364,8 +1365,8 @@ tf_Ucv_Vpv = tf_Ucv_Vpv./G_delay_resp;

-
-

2.3.5 Extraction of a transfer function matrix

+
+

2.3.5 Extraction of a transfer function matrix

First we define the initial guess for the resonance frequencies and the weights associated. @@ -1415,11 +1416,11 @@ weight_Ucv_Vpv(f

-The weights are shown in Fig. 20. +The weights are shown in Fig. 20.

-
+

weights_cercalo.png

Figure 20: Weights amplitude (png, pdf)

@@ -1471,7 +1472,7 @@ An we run the vectfit3 algorithm.
-
+

identification_matrix_fit.png

Figure 21: Transfer Function Extraction of the FRF matrix (png, pdf)

@@ -1479,7 +1480,7 @@ An we run the vectfit3 algorithm. -
+

identification_matrix_fit_phase.png

Figure 22: Transfer Function Extraction of the FRF matrix (png, pdf)

@@ -1502,8 +1503,8 @@ Gc = [G_Uch_Vph, G_Ucv_Vph;
-
-

2.4 Identification of the Newport Dynamics

+
+

2.4 Identification of the Newport Dynamics

We here identify the transfer function from a reference sent to the Newport \([U_{n,h},\ U_{n,v}]\) to the measurement made by the 4QD \([V_{p,h},\ V_{p,v}]\). @@ -1514,8 +1515,8 @@ To do so, we inject noise to the Newport \([U_{n,h},\ U_{n,v}]\) and we record t

-
-

2.4.1 Input / Output data

+
+

2.4.1 Input / Output data

The identification data is loaded @@ -1550,14 +1551,14 @@ uv.t = uv.t - uv.t +

identification_unh.png

Figure 23: Identification signals when exciting the horizontal direction (png, pdf)

-
+

identification_unv.png

Figure 24: Identification signals when exciting in the vertical direction (png, pdf)

@@ -1565,8 +1566,8 @@ uv.t = uv.t - uv.t -

2.4.2 Coherence

+
+

2.4.2 Coherence

The window used for the spectral analysis is an hanning windows with temporal size equal to 1 second. @@ -1585,7 +1586,7 @@ The window used for the spectral analysis is an hanning windows wit

-
+

id_newport_coherence.png

Figure 25: Coherence (png, pdf)

@@ -1593,8 +1594,8 @@ The window used for the spectral analysis is an hanning windows wit
-
-

2.4.3 Estimation of the Frequency Response Function Matrix

+
+

2.4.3 Estimation of the Frequency Response Function Matrix

We compute an estimate of the transfer functions. @@ -1608,14 +1609,14 @@ We compute an estimate of the transfer functions.

-
+

frf_newport_gain.png

Figure 26: Frequency Response Matrix (png, pdf)

-
+

frf_newport_phase.png

Figure 27: Frequency Response Matrix Phase (png, pdf)

@@ -1623,8 +1624,8 @@ We compute an estimate of the transfer functions.
-
-

2.4.4 Time Delay

+
+

2.4.4 Time Delay

Now, we would like to remove the time delay included in the FRF prior to the model extraction. @@ -1646,7 +1647,7 @@ G_delay_resp = squeeze(freqr We then remove the time delay from the frequency response function.

-
+

time_delay_newport.png

Figure 28: Phase change due to time-delay in the Newport dynamics (png, pdf)

@@ -1654,11 +1655,11 @@ We then remove the time delay from the frequency response function.
-
-

2.4.5 Extraction of a transfer function matrix

+
+

2.4.5 Extraction of a transfer function matrix

-From Fig. 26, it seems reasonable to model the Newport dynamics as diagonal and constant. +From Fig. 26, it seems reasonable to model the Newport dynamics as diagonal and constant.

@@ -1669,8 +1670,8 @@ From Fig. 26, it seems reasonable to model the Newport
-
-

2.5 Full System

+
+

2.5 Full System

We now have identified: @@ -1732,12 +1733,12 @@ The file mat/plant.mat is accessible here

-
-

3 Active Damping

+
+

3 Active Damping

-
-

3.1 Load Plant

+
+

3.1 Load Plant

load('mat/plant.mat', 'sys', 'Gi', 'Zc', 'Ga', 'Gc', 'Gn', 'Gd');
@@ -1746,8 +1747,8 @@ The file mat/plant.mat is accessible here
-
-

3.2 Test

+
+

3.2 Test

bode(sys({'Vch', 'Vcv'}, {'Uch', 'Ucv'}));
@@ -1775,8 +1776,8 @@ sys_cl = connect(sys, Kppf,
-
-

4 TODO Huddle Test

+
+

4 TODO Huddle Test

We load the data taken during the Huddle Test. @@ -1861,8 +1862,8 @@ xlim( -

5 Plant Scaling

+
+

5 Plant Scaling

Table 2: Identified Gain of the 4 quadrant diode