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Thomas Dehaeze 2025-04-08 23:29:15 +02:00
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@ -893,9 +893,9 @@ Several considerations:
** Introduction :ignore: ** Introduction :ignore:
As was shown during the literature review of Stewart platforms, there is a large diversity of designs and included sensors and actuators. The literature review of Stewart platforms revealed a wide diversity of designs with various sensor and actuator configurations.
Depending on the control objectives, which may include active damping, vibration isolation, or precise positioning, different sensor configurations are implemented. Control objectives (such as active damping, vibration isolation, or precise positioning) dictate specific sensor configurations.
The specific selection of the sensors, whether inertial sensors, force sensors, or relative position sensors, is heavily influenced by the control requirements of the system. The selection between inertial sensors, force sensors, or relative position sensors is primarily determined by the system's control requirements.
In cases where multiple control objectives must be achieved simultaneously, as is the case for the Nano Active Stabilization System (NASS) where the Stewart platform must both position the sample and provide isolation from micro-station vibrations, combining multiple sensors within the control architecture has been demonstrated to yield significant performance benefits. In cases where multiple control objectives must be achieved simultaneously, as is the case for the Nano Active Stabilization System (NASS) where the Stewart platform must both position the sample and provide isolation from micro-station vibrations, combining multiple sensors within the control architecture has been demonstrated to yield significant performance benefits.
From the literature, three principal approaches for combining sensors have been identified: High Authority Control-Low Authority Control (HAC-LAC), sensor fusion, and two-sensor control architectures. From the literature, three principal approaches for combining sensors have been identified: High Authority Control-Low Authority Control (HAC-LAC), sensor fusion, and two-sensor control architectures.
@ -1022,13 +1022,13 @@ From the literature, three principal approaches for combining sensors have been
#+end_subfigure #+end_subfigure
#+end_figure #+end_figure
The HAC-LAC approach, used during the conceptual phase, represents a dual-loop control strategy where two control loops utilize different sensors for different purposes (Figure ref:fig:detail_control_sensor_arch_hac_lac). The HAC-LAC approach, implemented during the conceptual phase, employs a dual-loop control strategy in which two control loops utilize different sensors for distinct purposes (Figure ref:fig:detail_control_sensor_arch_hac_lac).
In [[cite:&li01_simul_vibrat_isolat_point_contr]], vibration isolation is provided by accelerometers collocated with the voice coil actuators, while external rotational sensors are utilized to achieve pointing control. In [[cite:&li01_simul_vibrat_isolat_point_contr]], vibration isolation is provided by accelerometers collocated with the voice coil actuators, while external rotational sensors are utilized to achieve pointing control.
In [[cite:&geng95_intel_contr_system_multip_degree]], force sensors collocated with the magnetostrictive actuators are used for active damping using decentralized IFF, and subsequently accelerometers are employed for adaptive vibration isolation. In [[cite:&geng95_intel_contr_system_multip_degree]], force sensors collocated with the magnetostrictive actuators are used for active damping using decentralized IFF, and subsequently accelerometers are employed for adaptive vibration isolation.
Similarly, in [[cite:&wang16_inves_activ_vibrat_isolat_stewar]], piezoelectric actuators with collocated force sensors are used in a decentralized manner to provide active damping while accelerometers are implemented in an adaptive feedback loop to suppress periodic vibrations. Similarly, in [[cite:&wang16_inves_activ_vibrat_isolat_stewar]], piezoelectric actuators with collocated force sensors are used in a decentralized manner to provide active damping while accelerometers are implemented in an adaptive feedback loop to suppress periodic vibrations.
In [[cite:&xie17_model_contr_hybrid_passiv_activ]], force sensors are integrated in the struts for decentralized force feedback while accelerometers fixed to the top platform are employed for centralized control. In [[cite:&xie17_model_contr_hybrid_passiv_activ]], force sensors are integrated in the struts for decentralized force feedback while accelerometers fixed to the top platform are employed for centralized control.
Sensor fusion, the second approach (illustrated in Figure ref:fig:detail_control_sensor_arch_sensor_fusion), involves filtering signals from two sensors using complementary filters[fn:detail_control_1] that are subsequently summed to obtain an improved sensor signal. The second approach, sensor fusion (illustrated in Figure ref:fig:detail_control_sensor_arch_sensor_fusion), involves filtering signals from two sensors using complementary filters[fn:detail_control_1] and summing them to create an improved sensor signal.
In [[cite:&hauge04_sensor_contr_space_based_six]], geophones (used at low frequency) are merged with force sensors (used at high frequency). In [[cite:&hauge04_sensor_contr_space_based_six]], geophones (used at low frequency) are merged with force sensors (used at high frequency).
It is demonstrated that combining both sensors using sensor fusion can improve performance compared to using the individual sensors independently. It is demonstrated that combining both sensors using sensor fusion can improve performance compared to using the individual sensors independently.
In [[cite:&tjepkema12_sensor_fusion_activ_vibrat_isolat_precis_equip]], sensor fusion architecture is implemented with an accelerometer and a force sensor. In [[cite:&tjepkema12_sensor_fusion_activ_vibrat_isolat_precis_equip]], sensor fusion architecture is implemented with an accelerometer and a force sensor.
@ -1058,6 +1058,11 @@ The investigation is then extended beyond the conventional two-sensor scenario,
** Review of Sensor Fusion ** Review of Sensor Fusion
<<ssec:detail_control_sensor_review>> <<ssec:detail_control_sensor_review>>
Sensors used to measure physical quantities have two primary limitations: measurement accuracy which is compromised by various noise sources (including electrical noise from conditioning electronics), and limited measurement bandwidth.
Sensor fusion offers a solution to these limitations by combining multiple sensors [[cite:&bendat57_optim_filter_indep_measur_two]].
By strategically selecting sensors with complementary characteristics, a "super sensor" can be created that combines the advantages of each individual sensor.
Measuring a physical quantity using sensors is always subject to several limitations. Measuring a physical quantity using sensors is always subject to several limitations.
First, the accuracy of the measurement is affected by various noise sources, such as electrical noise from the conditioning electronics. First, the accuracy of the measurement is affected by various noise sources, such as electrical noise from the conditioning electronics.
Second, the frequency range in which the measurement is relevant is bounded by the bandwidth of the sensor. Second, the frequency range in which the measurement is relevant is bounded by the bandwidth of the sensor.
@ -1577,17 +1582,16 @@ As it is generally desired to limit the dynamical uncertainty of the super senso
<<ssec:detail_control_sensor_hinf_method>> <<ssec:detail_control_sensor_hinf_method>>
**** Introduction :ignore: **** Introduction :ignore:
As demonstrated in Section ref:ssec:detail_control_sensor_fusion_requirements, both the noise characteristics and robustness of the super sensor are functions of the complementary filters' norm. As established in Section ref:ssec:detail_control_sensor_fusion_requirements, the super sensor's noise characteristics and robustness are directly dependent on the complementary filters' norm.
Consequently, a synthesis method that enables precise shaping of complementary filter norms would provide significant practical benefits. A synthesis method enabling precise shaping of these norms would therefore offer substantial practical benefits.
In this section, such a synthesis approach is developed by formulating the design objective as a standard $\mathcal{H}_\infty$ optimization problem. This section develops such an approach by formulating the design objective as a standard $\mathcal{H}_\infty$ optimization problem.
The proper design of weighting functions, which are used to specify the desired complementary filter shapes during synthesis, is discussed in detail. The methodology for designing appropriate weighting functions (which specify desired complementary filter shapes during synthesis) is examined in detail, and the efficacy of the proposed method is validated with a simple example.
Finally, the efficacy of the proposed synthesis method is validated through a simple example.
**** Synthesis Objective **** Synthesis Objective
The primary objective is to shape the norms of two filters $H_1(s)$ and $H_2(s)$ while ensuring they maintain their complementary property as defined in eqref:eq:detail_control_sensor_comp_filter. The primary objective is to shape the norms of two filters $H_1(s)$ and $H_2(s)$ while ensuring they maintain their complementary property as defined in eqref:eq:detail_control_sensor_comp_filter.
This is equivalent to finding proper and stable transfer functions $H_1(s)$ and $H_2(s)$ that satisfy conditions eqref:eq:detail_control_sensor_hinf_cond_complementarity, eqref:eq:detail_control_sensor_hinf_cond_h1, and eqref:eq:detail_control_sensor_hinf_cond_h2. This is equivalent to finding proper and stable transfer functions $H_1(s)$ and $H_2(s)$ that satisfy conditions eqref:eq:detail_control_sensor_hinf_cond_complementarity, eqref:eq:detail_control_sensor_hinf_cond_h1, and eqref:eq:detail_control_sensor_hinf_cond_h2.
The functions $W_1(s)$ and $W_2(s)$ represent weighting transfer functions that are carefully selected to specify the maximum desired norm of the complementary filters during synthesis. Weighting transfer functions $W_1(s)$ and $W_2(s)$ are strategically selected to define the maximum desired norm of the complementary filters during the synthesis process.
\begin{subequations}\label{eq:detail_control_sensor_comp_filter_problem_form} \begin{subequations}\label{eq:detail_control_sensor_comp_filter_problem_form}
\begin{align} \begin{align}
@ -1872,15 +1876,15 @@ This straightforward example demonstrates that the proposed methodology for shap
** Synthesis of a set of three complementary filters ** Synthesis of a set of three complementary filters
<<ssec:detail_control_sensor_hinf_three_comp_filters>> <<ssec:detail_control_sensor_hinf_three_comp_filters>>
Some applications require merging more than two sensors [[cite:&stoten01_fusion_kinet_data_using_compos_filter;&fonseca15_compl]]. Certain applications necessitate the fusion of more than two sensors [[cite:&stoten01_fusion_kinet_data_using_compos_filter;&fonseca15_compl]].
For instance, at LIGO, three sensors (an LVDT, a seismometer, and a geophone) are merged to form a super sensor [[cite:&matichard15_seism_isolat_advan_ligo]]. At LIGO, for example, a super sensor is formed by merging three distinct sensors: an LVDT, a seismometer, and a geophone [[cite:&matichard15_seism_isolat_advan_ligo]].
When merging $n>2$ sensors using complementary filters, two architectures can be employed as shown in Figure ref:fig:detail_control_sensor_fusion_three. For merging $n>2$ sensors with complementary filters, two architectural approaches are possible, as illustrated in Figure ref:fig:detail_control_sensor_fusion_three.
The fusion can be performed either in a "sequential" manner where $n-1$ sets of two complementary filters are used (Figure ref:fig:detail_control_sensor_fusion_three_sequential), or in a "parallel" manner where one set of $n$ complementary filters is used (Figure ref:fig:detail_control_sensor_fusion_three_parallel). Fusion can be implemented either "sequentially," utilizing $n-1$ sets of two complementary filters (Figure ref:fig:detail_control_sensor_fusion_three_sequential), or "in parallel," employing a single set of $n$ complementary filters (Figure ref:fig:detail_control_sensor_fusion_three_parallel).
In the sequential approach, typical sensor fusion synthesis techniques can be applied. While conventional sensor fusion synthesis techniques can be applied to the sequential approach, parallel architecture implementation requires a novel synthesis method for multiple complementary filters.
However, when a parallel architecture is implemented, a new synthesis method for a set of more than two complementary filters is required, as only simple analytical formulas have been proposed in the literature [[cite:&stoten01_fusion_kinet_data_using_compos_filter;&fonseca15_compl]]. Previous literature has offered only simple analytical formulas for this purpose [[cite:&stoten01_fusion_kinet_data_using_compos_filter;&fonseca15_compl]].
A generalization of the proposed complementary filter synthesis method is presented in this section. This section presents a generalization of the proposed complementary filter synthesis method to address this gap.
#+begin_src latex :file detail_control_sensor_fusion_three_sequential.pdf #+begin_src latex :file detail_control_sensor_fusion_three_sequential.pdf
\tikzset{block/.default={0.8cm}{0.8cm}} \tikzset{block/.default={0.8cm}{0.8cm}}