diff --git a/content/zettels/analog_to_digital_converters.md b/content/zettels/analog_to_digital_converters.md index fc7eac4..9b9c69e 100644 --- a/content/zettels/analog_to_digital_converters.md +++ b/content/zettels/analog_to_digital_converters.md @@ -1,20 +1,20 @@ +++ title = "Analog to Digital Converters" -author = ["Thomas Dehaeze"] +author = ["Dehaeze Thomas"] keywords = ["electronics"] draft = false category = "equipment" +++ Tags -: [Electronics]({{}}) +: [Electronics]({{< relref "electronics.md" >}}) ## Types of Analog to Digital Converters {#types-of-analog-to-digital-converters} -- Delta Sigma ([Baker 2011](#orgbdb61af)) +- Delta Sigma - Successive Approximation @@ -33,11 +33,11 @@ Let's suppose that the ADC is ideal and the only noise comes from the quantizati Interestingly, the noise amplitude is uniformly distributed. The quantization noise can take a value between \\(\pm q/2\\), and the probability density function is constant in this range (i.e., it’s a uniform distribution). -Since the integral of the probability density function is equal to one, its value will be \\(1/q\\) for \\(-q/2 < e < q/2\\) (Fig. [1](#org4bd731c)). +Since the integral of the probability density function is equal to one, its value will be \\(1/q\\) for \\(-q/2 < e < q/2\\) (Fig. [1](#figure--fig:probability-density-function-adc)). - + -{{< figure src="/ox-hugo/probability_density_function_adc.png" caption="Figure 1: Probability density function \\(p(e)\\) of the ADC error \\(e\\)" >}} +{{< figure src="/ox-hugo/probability_density_function_adc.png" caption="Figure 1: Probability density function \\(p(e)\\) of the ADC error \\(e\\)" >}} Now, we can calculate the time average power of the quantization noise as @@ -59,13 +59,12 @@ Thus, the two-sided PSD (from \\(\frac{-f\_s}{2}\\) to \\(\frac{f\_s}{2}\\)), we \end{equation}
-
Finally, the Power Spectral Density of the quantization noise of an ADC is equal to: \begin{equation} \begin{aligned} - \Gamma &= \frac{q^2}{12 f\_s} \\\\\\ + \Gamma &= \frac{q^2}{12 f\_s} \\\\ &= \frac{\left(\frac{\Delta V}{2^n}\right)^2}{12 f\_s} \text{ in } \left[ \frac{V^2}{Hz} \right] \end{aligned} \end{equation} @@ -73,7 +72,6 @@ Finally, the Power Spectral Density of the quantization noise of an ADC is equal
-
Let's take a 18bits ADC with a range of +/-10V and a sample frequency of 10kHz. @@ -87,7 +85,4 @@ The quantization is: {{< youtube b9lxtOJj3yU >}} - -## Bibliography {#bibliography} - -Baker, Bonnie. 2011. “How Delta-Sigma Adcs Work, Part.” _Analog Applications_ 7. +## Oversampling {#oversampling} diff --git a/content/zettels/decimation.md b/content/zettels/decimation.md index e8daba5..9ccf8f4 100644 --- a/content/zettels/decimation.md +++ b/content/zettels/decimation.md @@ -108,6 +108,24 @@ Which is much more efficient that the single stage decimation.
+There are two **practical issues** to consider for two-stage decimation: + +- First, if the dual-filter system is required to have a pass-band peak-peak ripple of \\(R\\) dB, then both filters must be designed to have a pass-band peak-peak ripple of no greater than \\(R/2\\) dB. +- Second, the number of multiplications needed to compute each \\(x\_{\text{new}}(m)\\) output sample is much larger than \\(N\_\text{total}\\) because we must compute so many \\(\text{LPF}\_1\\) and \\(\text{LPF}\_2\\) output samples destined to be discarded. + +In order to cope with the second issue, an efficient decimation filter implementation scheme called _polyphase decomposition_ can be used. + +The advantages of two stage decimation, over single-stage decimation are: + +
    +
  • an overall reduction in computation workload
    • +
  • reduced signal and filter coefficient data storage
    • +
  • simpler filter designs
    • +
  • a decrease in the ill effects of finite binary-work-length filter coefficients
    • +
+ +These advantages become more pronounced as the overall desired decimation factor \(M\) becomes larger. + ## References: {#references} diff --git a/content/zettels/integral_force_feedback.md b/content/zettels/integral_force_feedback.md index 1fc6452..bd74a06 100644 --- a/content/zettels/integral_force_feedback.md +++ b/content/zettels/integral_force_feedback.md @@ -1,8 +1,13 @@ +++ title = "Integral Force Feedback" -author = ["Thomas Dehaeze"] +author = ["Dehaeze Thomas"] draft = false +++ Tags -: [Active Damping]({{< relref "active_damping" >}}) +: [Active Damping]({{< relref "active_damping.md" >}}), [Piezoelectric Actuators]({{< relref "piezoelectric_actuators.md" >}}), [Force Sensors]({{< relref "force_sensors.md" >}}) + + +## Self-Sensing for perfect collocation {#self-sensing-for-perfect-collocation} + +This can be done with a [Voice Coil Actuator]({{< relref "voice_coil_actuators.md" >}}) (see ) or with a [Piezoelectric Actuator]({{< relref "piezoelectric_actuators.md" >}}) (see ). diff --git a/content/zettels/piezoelectric_actuators.md b/content/zettels/piezoelectric_actuators.md index 480f486..7321f32 100644 --- a/content/zettels/piezoelectric_actuators.md +++ b/content/zettels/piezoelectric_actuators.md @@ -1,12 +1,12 @@ +++ title = "Piezoelectric Actuators" -author = ["Thomas Dehaeze"] +author = ["Dehaeze Thomas"] draft = false category = "equipment" +++ Tags -: [Actuators]({{}}), [Voltage Amplifier]({{}}) +: [Actuators]({{< relref "actuators.md" >}}), [Voltage Amplifier]({{< relref "voltage_amplifier.md" >}}) ## Piezoelectric Stack Actuators {#piezoelectric-stack-actuators} @@ -18,9 +18,9 @@ Tags |----------------------------------------------------------------------------------------------------------------------|-----------| | [Cedrat](http://www.cedrat-technologies.com/) | France | | [PI](https://www.physikinstrumente.com/en/) | USA | -| [Piezo System](https://www.piezosystem.com/products/piezo%5Factuators/stacktypeactuators/) | Germany | +| [Piezo System](https://www.piezosystem.com/products/piezo_actuators/stacktypeactuators/) | Germany | | [Noliac](http://www.noliac.com/products/actuators/plate-stacks/) | Denmark | -| [Thorlabs](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) | USA | +| [Thorlabs](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=8700) | USA | | [PiezoDrive](https://www.piezodrive.com/actuators/) | Australia | | [Mechano Transformer](http://www.mechano-transformer.com/en/products/10.html) | Japan | | [CoreMorrow](http://www.coremorrow.com/en/pro-9-1.html) | China | @@ -33,7 +33,7 @@ Tags ### Model {#model} -A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#orgd563065)) ([Notes]({{}})). +A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb.md" >}})). Basically, it can be represented by a spring \\(k\_a\\) with the force source \\(F\_a\\) in parallel. @@ -57,25 +57,25 @@ Some manufacturers propose "raw" plate actuators that can be used as actuator / ## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators} -The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#orgb463c4c)): +The Amplified Piezo Actuators principle is presented in : > The displacement amplification effect is related in a first approximation to the ratio of the shell long axis length to the short axis height. > The flatter is the actuator, the higher is the amplification. -A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#org2bf81f0)). +A model of an amplified piezoelectric actuator is described in . - + -{{< figure src="/ox-hugo/ling16_topology_piezo_mechanism_types.png" caption="Figure 1: Topology of several types of compliant mechanisms ling16_enhan_mathem_model_displ_amplif" >}} +{{< figure src="/ox-hugo/ling16_topology_piezo_mechanism_types.png" caption="Figure 1: Topology of several types of compliant mechanisms " >}} | Manufacturers | Country | |----------------------------------------------------------------------------------------------------|-----------| | [Cedrat](https://www.cedrat-technologies.com/en/products/actuators/amplified-piezo-actuators.html) | France | | [PiezoDrive](https://www.piezodrive.com/actuators/ap-series-amplified-piezoelectric-actuators/) | Australia | | [Dynamic-Structures](https://www.dynamic-structures.com/category/piezo-actuators-stages) | USA | -| [Thorlabs](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) | USA | +| [Thorlabs](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=8700) | USA | | [Noliac](http://www.noliac.com/products/actuators/amplified-actuators/) | Denmark | -| [Mechano Transformer](http://www.mechano-transformer.com/en/products/01a%5Factuator%5F5.html) | Japan | +| [Mechano Transformer](http://www.mechano-transformer.com/en/products/01a_actuator_5.html) | Japan | | [CoreMorrow](http://www.coremorrow.com/en/pro-13-1.html) | China | | [PiezoData](https://www.piezodata.com/piezoelectric-actuator-amplifier/) | China | @@ -99,7 +99,7 @@ Typical specifications of piezoelectric stack actuators are usually in terms of: The maximum displacement specified is the displacement of the actuator when the maximum voltage is applied without any load. -Typical maximum strain of Piezoelectric Stack Actuators is \\(0.1\%\\). +Typical maximum strain of Piezoelectric Stack Actuators is \\(0.1\\%\\). The free displacement \\(\Delta L\_{f}\\) is then related to the length \\(L\\) of piezoelectric stack by: \begin{equation} @@ -142,72 +142,62 @@ with: ### Resolution {#resolution} -The resolution is limited by the noise in the [Voltage Amplifier]({{}}). +The resolution is limited by the noise in the [Voltage Amplifier]({{< relref "voltage_amplifier.md" >}}). -Typical [Signal to Noise Ratio]({{}}) of voltage amplifiers is \\(100dB = 10^{5}\\). +Typical [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio.md" >}}) of voltage amplifiers is \\(100dB = 10^{5}\\). Thus, for a piezoelectric stack with a displacement \\(L\\), the resolution will be \begin{equation} r \approx \frac{L}{10^5} \end{equation} -For a piezoelectric stack with a displacement of \\(100\,[\mu m]\\), the resolution will be \\(\approx 1\,[nm]\\). +For a piezoelectric stack with a displacement of \\(100\\,[\mu m]\\), the resolution will be \\(\approx 1\\,[nm]\\). ### Electrical Capacitance {#electrical-capacitance} -The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#orgca6870e)). +The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#figure--fig:piezoelectric-capacitance-voltage-max)). This is due to the fact that voltage amplifier has a limitation on the deliverable current. -[Voltage Amplifier]({{}}) with high maximum output current should be used if either high bandwidth is wanted or piezoelectric stacks with high capacitance are to be used. +[Voltage Amplifier]({{< relref "voltage_amplifier.md" >}}) with high maximum output current should be used if either high bandwidth is wanted or piezoelectric stacks with high capacitance are to be used. - + -{{< figure src="/ox-hugo/piezoelectric_capacitance_voltage_max.png" caption="Figure 2: Maximum sin-wave amplitude as a function of frequency for several piezoelectric capacitance" >}} +{{< figure src="/ox-hugo/piezoelectric_capacitance_voltage_max.png" caption="Figure 2: Maximum sin-wave amplitude as a function of frequency for several piezoelectric capacitance" >}} ## Piezoelectric actuator experiencing a mass load {#piezoelectric-actuator-experiencing-a-mass-load} -When the piezoelectric actuator is supporting a payload, it will experience a static deflection due to its finite stiffness \\(\Delta l\_n = \frac{mg}{k\_p}\\), but its stroke will remain unchanged (Figure [3](#orge05f5e6)). +When the piezoelectric actuator is supporting a payload, it will experience a static deflection due to its finite stiffness \\(\Delta l\_n = \frac{mg}{k\_p}\\), but its stroke will remain unchanged (Figure [3](#figure--fig:piezoelectric-mass-load)). - + -{{< figure src="/ox-hugo/piezoelectric_mass_load.png" caption="Figure 3: Motion of a piezoelectric stack actuator under external constant force" >}} +{{< figure src="/ox-hugo/piezoelectric_mass_load.png" caption="Figure 3: Motion of a piezoelectric stack actuator under external constant force" >}} ## Piezoelectric actuator in contact with a spring load {#piezoelectric-actuator-in-contact-with-a-spring-load} -Then the piezoelectric actuator is in contact with a spring load \\(k\_e\\), its maximum stroke \\(\Delta L\\) is less than its free stroke \\(\Delta L\_f\\) (Figure [4](#orgfcd374f)): +Then the piezoelectric actuator is in contact with a spring load \\(k\_e\\), its maximum stroke \\(\Delta L\\) is less than its free stroke \\(\Delta L\_f\\) (Figure [4](#figure--fig:piezoelectric-spring-load)): \begin{equation} \Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e} \end{equation} - + -{{< figure src="/ox-hugo/piezoelectric_spring_load.png" caption="Figure 4: Motion of a piezoelectric stack actuator in contact with a stiff environment" >}} +{{< figure src="/ox-hugo/piezoelectric_spring_load.png" caption="Figure 4: Motion of a piezoelectric stack actuator in contact with a stiff environment" >}} -For piezo actuators, force and displacement are inversely related (Figure [5](#orgada6c4c)). +For piezo actuators, force and displacement are inversely related (Figure [5](#figure--fig:piezoelectric-force-displ-relation)). Maximum, or blocked, force (\\(F\_b\\)) occurs when there is no displacement. Likewise, at maximum displacement, or free stroke, (\\(\Delta L\_f\\)) no force is generated. When an external load is applied, the stiffness of the load (\\(k\_e\\)) determines the displacement (\\(\Delta L\_A\\)) and force (\\(\Delta F\_A\\)) that can be produced. - + -{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}} +{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}} ## Driving Electronics {#driving-electronics} -Piezoelectric actuators can be driven either using a voltage to charge converter or a [Voltage Amplifier]({{}}). -Limitations of the electronics is discussed in [Design, modeling and control of nanopositioning systems]({{}}). - - - -## Bibliography {#bibliography} - -Claeyssen, Frank, R. Le Letty, F. Barillot, and O. Sosnicki. 2007. “Amplified Piezoelectric Actuators: Static & Dynamic Applications.” _Ferroelectrics_ 351 (1):3–14. . - -Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” _IEEE/ASME Transactions on Mechatronics_ 15 (3):433–47. . - -Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.” +Piezoelectric actuators can be driven either using a voltage to charge converter or a [Voltage Amplifier]({{< relref "voltage_amplifier.md" >}}). +Limitations of the electronics is discussed in [Design, modeling and control of nanopositioning systems]({{< relref "fleming14_desig_model_contr_nanop_system.md" >}}). diff --git a/content/zettels/stepper_motor.md b/content/zettels/stepper_motor.md index d1e5d93..f3b67a3 100644 --- a/content/zettels/stepper_motor.md +++ b/content/zettels/stepper_motor.md @@ -17,3 +17,11 @@ Tags For a two phase stepper motor, there are (typically) 200 steps per revolution. Errors with a period of 200 period/revolution can be expected. + + +## Manufacturers {#manufacturers} + +| Manufacturers | Country | +|--------------------------------------------------------------------------|----------------| +| [AML](https://arunmicro.com/) | United Kingdom | +| [Sanyo](https://www.sanyodenki.com/catalogs/servo/stepping_systems.html) | | diff --git a/static/ltximg/org-ltximg_00469a3526baf2d7fc2146a5de72bb4d44072225.svg b/static/ltximg/org-ltximg_00469a3526baf2d7fc2146a5de72bb4d44072225.svg new file mode 100644 index 0000000..7f2e871 --- /dev/null +++ b/static/ltximg/org-ltximg_00469a3526baf2d7fc2146a5de72bb4d44072225.svg @@ -0,0 +1,58 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/static/ltximg/org-ltximg_0c79851aafb283167985422b093b95a6061fd771.svg b/static/ltximg/org-ltximg_0c79851aafb283167985422b093b95a6061fd771.svg new file mode 100644 index 0000000..7975bd6 --- /dev/null +++ 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