-
-
- 1. Encoder Model -
- 2. Noise Measurement +
- 1. Expected Performances +
- 2. Encoder Model +
- 3. Noise Measurement -
- 3. Linearity Measurement +
- 4. Linearity Measurement - -
- 4. Dynamical Measurement -
This report is also available as a pdf.
-
-You can find below the document of: +You can find below the documentation of:
- Vionic Encoder @@ -77,70 +76,81 @@ You can find below the document of:
-We would like to characterize the encoder measurement system. -
- -+In this document, we wish to characterize the performances of the encoder measurement system. In particular, we would like to measure:
-
-
- Power Spectral Density of the measurement noise -
- Bandwidth of the sensor -
- Linearity of the sensor +
- the measurement noise +
- the linearity of the sensor +
- the bandwidth of the sensor
+This document is structured as follow: +
+-
+
- Section 1: the expected performance of the Vionic encoder system are described +
- Section 2: a simple model of the encoder is developed +
- Section 3: the noise of the encoder is measured and a model of the noise is identified +
- Section 4: the linearity of the sensor is estimated +
1 Expected Performances
++The Vionic encoder is shown in Figure 1. +
+ + +
Figure 1: Picture of the Vionic Encoder
-
-
- 1: 2YA275 -
- 2: 2YA274 -
- 3: 2YA273 -
- 4: 2YA270 -
- 5: 2YA272 -
- 6: 2YA271 -
- 7: 2YJ313 -
1 Encoder Model
--The Encoder is characterized by its dynamics \(G_m(s)\) from the “true” displacement \(y\) to measured displacement \(y_m\). -Ideally, this dynamics is constant over a wide frequency band with very small phase drop. +From the Renishaw website: +
+++ ++The VIONiC encoder features the third generation of Renishaw’s unique filtering optics that average the contributions from many scale periods and effectively filter out non-periodic features such as dirt. +The nominally square-wave scale pattern is also filtered to leave a pure sinusoidal fringe field at the detector. +Here, a multiple finger structure is employed, fine enough to produce photocurrents in the form of four symmetrically phased signals. +These are combined to remove DC components and produce sine and cosine signal outputs with high spectral purity and low offset while maintaining bandwidth to beyond 500 kHz.
-It is also characterized by its measurement noise \(n\) that can be described by its Power Spectral Density (PSD). +Fully integrated advanced dynamic signal conditioning, Auto Gain , Auto Balance and Auto Offset Controls combine to ensure ultra-low Sub-Divisional Error (SDE) of typically \(<\pm 15\, nm\).
-The model of the encoder is shown in Figure 2. +This evolution of filtering optics, combined with carefully-selected electronics, provide incremental signals with wide bandwidth achieving a maximum speed of 12 m/s with the lowest positional jitter (noise) of any encoder in its class. +Interpolation is within the readhead, with fine resolution versions being further augmented by additional noise-reducing electronics to achieve jitter of just 1.6 nm RMS. +
+
+The expected interpolation errors (non-linearity) is shown in Figure 2.
-
+
Figure 2: Model of the Encoder
+Figure 2: Expected interpolation errors for the Vionic Encoder
-We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) with unity ASD as shown in Figure 4. +The characteristics as advertise in the manual as well as our specifications are shown in Table 1.
- -
-
| Characteristics | Manual | -Specifications | +Specification | |
|---|---|---|---|---|
| Range | -Ruler length | -> 200 [um] | -||
| Resolution | -2.5 [nm] | -< 50 [nm rms] | -||
| Sub-Divisional Error | -\(< \pm 15\,nm\) | +Time Delay | + | < 0.5 ms |
| Bandwidth | -To be checked | -> 5 [kHz] | +> 500 kHz | +> 5 kHz | +
| Noise | +< 1.6 nm rms | +< 50 nm rms | +||
| Linearity | +< +/- 15 nm | ++ | ||
| Range | +Ruler length | +> 200 um |
-
Figure 4: Expected interpolation errors for the Vionic Encoder
-2 Noise Measurement
+2 Encoder Model
+The Encoder is characterized by its dynamics \(G_m(s)\) from the “true” displacement \(y\) to measured displacement \(y_m\). +Ideally, this dynamics is constant over a wide frequency band with very small phase drop. +
+ ++It is also characterized by its measurement noise \(n\) that can be described by its Power Spectral Density (PSD) \(\Gamma_n(\omega)\). +
+ ++The model of the encoder is shown in Figure 3. +
+ + +
+
Figure 3: Model of the Encoder
++We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) with unity ASD as shown in Figure 2. +
+ + +
2.1 Test Bench
-3 Noise Measurement
+ +3.1 Test Bench
+To measure the noise \(n\) of the encoder, one can rigidly fix the head and the ruler together such that no motion should be measured. Then, the measured signal \(y_m\) corresponds to the noise \(n\). @@ -210,53 +257,62 @@ Then, the measured signal \(y_m\) corresponds to the noise \(n\).
2.2 Results
--First we load the data. -
-%% Load Data -enc1 = load('noise_meas_100s_20kHz_1.mat', 't', 'x'); -enc2 = load('noise_meas_100s_20kHz_2.mat', 't', 'x'); -enc3 = load('noise_meas_100s_20kHz_3.mat', 't', 'x'); -enc4 = load('noise_meas_100s_20kHz_4.mat', 't', 'x'); -enc6 = load('noise_meas_100s_20kHz_6.mat', 't', 'x'); -enc7 = load('noise_meas_100s_20kHz_7.mat', 't', 'x'); -+
3.2 Thermal drifts
+-
+
[ ]picture of the setup
+[ ]long thermal drifts
+[ ]once stabilize, look at the noise
+[ ]compute low frequency ASD (may still be thermal drifts of the mechanics and not noise)
+
3.3 Time Domain signals
+-The raw measured data as well as the low pass filtered data (using a first order low pass filter with a cut-off at 10Hz) are shown in Figure 5. +First we load the data. +The raw measured data as well as the low pass filtered data (using a first order low pass filter with a cut-off at 10Hz) are shown in Figure 5.
-
Figure 5: Time domain measurement (raw data and low pass filtered data with first order 10Hz LPF)
-The time domain data for all the encoders are compared in Figure 6. +The time domain data for all the encoders are compared in Figure 6.
-
Figure 6: Comparison of the time domain measurement
3.4 Noise Spectral Density
+-The amplitude spectral density is computed and shown in Figure 7. +The amplitude spectral density is computed and shown in Figure 7.
-
Figure 7: Amplitude Spectral Density of the measured signal
3.5 Noise Model
+Let’s create a transfer function that approximate the measured noise of the encoder.
@@ -266,29 +322,49 @@ Let’s create a transfer function that approximate the measured noise of th-The amplitude of the transfer function and the measured ASD are shown in Figure 8. +The amplitude of the transfer function and the measured ASD are shown in Figure 8.
-
Figure 8: Measured ASD of the noise and modelled one
+Figure 8: Measured ASD of the noise and modeled one
+3.6 Validity of the noise model
++The cumulative amplitude spectrum is now computed and shown in Figure 9. +
+ ++We can see that the Root Mean Square value of the measurement noise is \(\approx 1.6 \, nm\) as advertise in the datasheet. +
+ + +
+
Figure 9: Meassured CAS of the noise and modeled one
3 Linearity Measurement
-4 Linearity Measurement
+ -3.1 Test Bench
-4.1 Test Bench
+In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity. An interferometer or capacitive sensor should work fine. @@ -296,7 +372,7 @@ An actuator should also be there so impose a displacement.
-One idea is to use the test-bench shown in Figure 9. +One idea is to use the test-bench shown in Figure 10.
@@ -309,38 +385,22 @@ As the interferometer has a very large bandwidth, we should be able to estimate
-
Figure 9: Schematic of the test bench
+Figure 10: Schematic of the test bench
3.2 Results
-Created: 2021-02-03 mer. 11:20
+Created: 2021-02-10 mer. 15:14