diff --git a/figs/exp_setup_schematic.svg b/figs/exp_setup_schematic.svg index 2918c30..946f985 100644 --- a/figs/exp_setup_schematic.svg +++ b/figs/exp_setup_schematic.svg @@ -15,7 +15,7 @@ viewBox="0 0 406.60148 227.37745" sodipodi:docname="exp_setup_schematic.svg" inkscape:version="1.0.1 (3bc2e813f5, 2020-09-07)" - inkscape:export-filename="/home/thomas/Cloud/thesis/matlab/encoder-test-bench/figs/exp_setup_schematic.png" + inkscape:export-filename="/home/thomas/Cloud/thesis/matlab/test-bench-force-sensor/figs/exp_setup_schematic.png" inkscape:export-xdpi="252" inkscape:export-ydpi="252"> - + Piezoelectric Force Sensor - Test Bench @@ -34,29 +34,29 @@

Table of Contents

@@ -71,19 +71,19 @@ In this document is studied how a piezoelectric stack can be used to measured th It is divided in the following sections:

-
-

1 Change of Stiffness due to Sensors stack being open/closed circuit

+
+

1 Change of Stiffness due to Sensors stack being open/closed circuit

- +

-The experimental Setup is schematically represented in Figure 1. +The experimental Setup is schematically represented in Figure 1.

@@ -91,7 +91,7 @@ The dynamics from the voltage \(u\) used to drive the actuator stacks to the enc

-
+

exp_setup_schematic.png

Figure 1: Schematic of the Experiment

@@ -106,7 +106,7 @@ When the switch is closed, this correspond of having a measurement electronics w We wish here to see how the system dynamics is changing in the two extreme cases.

-
+

The equipment used in the test bench are:

@@ -120,8 +120,8 @@ The equipment used in the test bench are:
-
-

1.1 Load Data

+
+

1.1 Load Data

oc = load('identification_open_circuit.mat', 't', 'encoder', 'u');
@@ -131,8 +131,8 @@ sc = load('identification_short_circuit.mat',
-
-

1.2 Transfer Functions

+
+

1.2 Transfer Functions

Ts = 1e-4; % Sampling Time [s]
@@ -150,26 +150,25 @@ win = hann(ceil(10/Ts));
-
+

stiffness_force_sensor_coherence.png

- -
+

stiffness_force_sensor_bode.png

-
+

stiffness_force_sensor_bode_zoom.png

Figure 4: Zoom on the change of resonance

-
+

The change of resonance frequency / stiffness is very small and is not important here.

@@ -179,25 +178,25 @@ The change of resonance frequency / stiffness is very small and is not important
-
-

2 Effect of a Resistor in Parallel with the Stack Sensor

+
+

2 Effect of a Resistor in Parallel with the Stack Sensor

- +

-The setup is shown in Figure 5 where two stacks are used as actuator (in parallel) and one stack is used as sensor. +The setup is shown in Figure 5 where two stacks are used as actuator (in parallel) and one stack is used as sensor. The voltage amplifier used has a gain of 20 [V/V] (Cedrat LA75B).

-
+

force_sensor_setup.png

Figure 5: Schematic of the setup

-
+

The equipment used in the test bench are:

@@ -211,8 +210,8 @@ The equipment used in the test bench are:
-
-

2.1 Excitation steps and measured generated voltage

+
+

2.1 Excitation steps and measured generated voltage

The measured data is loaded. @@ -223,10 +222,10 @@ The measured data is loaded.

-The excitation signal (steps) and measured voltage across the sensor stack are shown in Figure 6. +The excitation signal (steps) and measured voltage across the sensor stack are shown in Figure 6.

-
+

force_sen_steps_time_domain.png

Figure 6: Time domain signal during the 3 actuator voltage steps

@@ -234,8 +233,8 @@ The excitation signal (steps) and measured voltage across the sensor stack are s
-
-

2.2 Estimation of the voltage offset and discharge time constant

+
+

2.2 Estimation of the voltage offset and discharge time constant

The measured voltage shows an exponential decay which indicates that the charge across the capacitor formed by the stack is discharging into a resistor. @@ -324,8 +323,8 @@ The obtained values are shown below.

-
-

2.3 Estimation of the ADC input impedance

+
+

2.3 Estimation of the ADC input impedance

With the capacitance being \(C = 4.4 \mu F\), the internal impedance of the Speedgoat ADC can be computed as follows: @@ -347,15 +346,15 @@ The input impedance of the Speedgoat’s ADC should then be close to \(1.5\,

-
-

2.4 Explanation of the Voltage offset

+
+

2.4 Explanation of the Voltage offset

-As shown in Figure 6, the voltage across the Piezoelectric sensor stack shows a constant voltage offset. +As shown in Figure 6, the voltage across the Piezoelectric sensor stack shows a constant voltage offset.

-We can explain this offset by looking at the electrical model shown in Figure 7 (taken from (Reza and Andrew 2006)). +We can explain this offset by looking at the electrical model shown in Figure 7 (taken from (Reza and Andrew 2006)).

@@ -364,7 +363,7 @@ Note that the impedance of the piezoelectric stack is much larger that that at D

-
+

force_sensor_model_electronics_without_R.png

Figure 7: Model of a piezoelectric transducer (left) and instrumentation amplifier (right)

@@ -384,11 +383,11 @@ The estimated input bias current is then:
-
-

2.5 Effect of an additional Parallel Resistor

+
+

2.5 Effect of an additional Parallel Resistor

-Be looking at Figure 7, we can see that an additional resistor in parallel with \(R_{in}\) would have two effects: +Be looking at Figure 7, we can see that an additional resistor in parallel with \(R_{in}\) would have two effects:

  • reduce the input voltage offset @@ -431,11 +430,11 @@ Which is much more acceptable.

    -A resistor \(R_p \approx 100\,k\Omega\) is then added in parallel with the force sensor as shown in Figure 8. +A resistor \(R_p \approx 100\,k\Omega\) is then added in parallel with the force sensor as shown in Figure 8.

    -
    +

    force_sensor_model_electronics.png

    Figure 8: Model of a piezoelectric transducer (left) and instrumentation amplifier (right) with the additional resistor \(R_p\)

    @@ -443,8 +442,8 @@ A resistor \(R_p \approx 100\,k\Omega\) is then added in parallel with the force
    -
    -

    2.6 Obtained voltage offset and time constant with the added resistor

    +
    +

    2.6 Obtained voltage offset and time constant with the added resistor

    After the resistor is added, the same steps response is performed. @@ -456,11 +455,11 @@ After the resistor is added, the same steps response is performed.

    -The results are shown in Figure 9. +The results are shown in Figure 9.

    -
    +

    force_sen_steps_time_domain_par_R.png

    Figure 9: Time domain signal during the actuator voltage steps

    @@ -572,19 +571,19 @@ This validates the model of the ADC and the effectiveness of the added resistor.
    -
    -

    3 Generated Number of Charge / Voltage

    +
    +

    3 Generated Number of Charge / Voltage

    - +

    In this section, we wish to estimate the relation between the displacement performed by the stack actuator and the generated voltage/charge on the sensor stack.

    -
    -

    3.1 Data Loading

    +
    +

    3.1 Data Loading

    The measured data is loaded and the first 25 seconds of data corresponding to transient data are removed. @@ -602,22 +601,22 @@ t = t(t>25);

    -
    -

    3.2 Excitation signal and corresponding displacement

    +
    +

    3.2 Excitation signal and corresponding displacement

    -The driving voltage is a sinus at 0.5Hz centered on 3V and with an amplitude of 3V (Figure 10). +The driving voltage is a sinus at 0.5Hz centered on 3V and with an amplitude of 3V (Figure 10).

    -
    +

    force_sensor_sin_u.png

    Figure 10: Driving Voltage

    -The corresponding displacement as measured by the encoder is shown in Figure 11. +The corresponding displacement as measured by the encoder is shown in Figure 11.

    @@ -634,7 +633,7 @@ The full stroke is: -

    +

    force_sensor_sin_encoder.png

    Figure 11: Encoder measurement

    @@ -642,15 +641,15 @@ The full stroke is:
    -
    -

    3.3 Generated Voltage

    +
    +

    3.3 Generated Voltage

    -The generated voltage by the stack is shown in Figure 12. +The generated voltage by the stack is shown in Figure 12.

    -
    +

    force_sensor_sin_stack.png

    Figure 12: Voltage measured on the stack used as a sensor

    @@ -658,8 +657,8 @@ The generated voltage by the stack is shown in Figure 12
    -
    -

    3.4 Generated Charge

    +
    +

    3.4 Generated Charge

    The capacitance of the stack is @@ -681,11 +680,11 @@ where \(U_C\) is the voltage in Volts, \(Q\) the charge in Coulombs and \(C\) th

    -The corresponding generated charge is then shown in Figure 13. +The corresponding generated charge is then shown in Figure 13.

    -
    +

    force_sensor_sin_charge.png

    Figure 13: Generated Charge

    @@ -693,11 +692,11 @@ The corresponding generated charge is then shown in Figure
    -
    -

    3.5 Generated Voltage/Charge as a function of the displacement

    +
    +

    3.5 Generated Voltage/Charge as a function of the displacement

    -The relation between the generated voltage and the measured displacement is almost linear as shown in Figure 14. +The relation between the generated voltage and the measured displacement is almost linear as shown in Figure 14.

    @@ -706,7 +705,7 @@ The relation between the generated voltage and the measured displacement is almo
    -
    +

    force_sensor_linear_relation.png

    Figure 14: Almost linear relation between the relative displacement and the generated voltage

    @@ -735,7 +734,7 @@ With a 16bits ADC, the resolution will then be equals to (in [nm]):

    Author: Dehaeze Thomas

    -

    Created: 2020-11-10 mar. 13:41

    +

    Created: 2020-11-10 mar. 13:46

    diff --git a/index.org b/index.org index 4a094de..2f9e370 100644 --- a/index.org +++ b/index.org @@ -128,12 +128,11 @@ The equipment used in the test bench are: #+RESULTS: [[file:figs/stiffness_force_sensor_coherence.png]] - #+begin_src matlab :exports none figure; - tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None'); + tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None'); - ax1 = nexttile; + ax1 = nexttile([2,1]); hold on; plot(f, abs(tf_oc_est), '-', 'DisplayName', 'Open-Circuit') plot(f, abs(tf_sc_est), '-', 'DisplayName', 'Short-Circuit') @@ -166,9 +165,33 @@ The equipment used in the test bench are: #+RESULTS: [[file:figs/stiffness_force_sensor_bode.png]] +#+begin_src matlab :exports none + figure; + tiledlayout(1, 2, 'TileSpacing', 'None', 'Padding', 'None'); + + ax1 = nexttile; + hold on; + plot(f, abs(tf_oc_est), '-', 'DisplayName', 'Open-Circuit') + plot(f, abs(tf_sc_est), '-', 'DisplayName', 'Short-Circuit') + set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log'); + ylabel('Amplitude'); xlabel('Frequency [Hz]'); + hold off; + xlim([200, 280]); + legend('location', 'southwest'); + + ax3 = nexttile; + hold on; + plot(f, abs(tf_oc_est), '-', 'DisplayName', 'Open-Circuit') + plot(f, abs(tf_sc_est), '-', 'DisplayName', 'Short-Circuit') + set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log'); + ylabel('Amplitude'); xlabel('Frequency [Hz]'); + hold off; + xlim([800, 950]); + legend('location', 'southwest'); +#+end_src + #+begin_src matlab :tangle no :exports results :results file replace - xlim([180, 280]); - exportFig('figs/stiffness_force_sensor_bode_zoom.pdf', 'width', 'small', 'height', 'tall'); + exportFig('figs/stiffness_force_sensor_bode_zoom.pdf', 'width', 'wide', 'height', 'normal'); #+end_src #+name: fig:stiffness_force_sensor_bode_zoom