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@ -312,7 +312,7 @@ The research presented in this manuscript has been possible thanks to the Fonds
Synchrotron radiation facilities, are particle accelerators where electrons are accelerated to near the speed of light. Synchrotron radiation facilities, are particle accelerators where electrons are accelerated to near the speed of light.
As these electrons traverse magnetic fields, typically generated by insertion devices or bending magnets, they produce exceptionally bright light known as synchrotron light. As these electrons traverse magnetic fields, typically generated by insertion devices or bending magnets, they produce exceptionally bright light known as synchrotron light.
This intense electromagnetic radiation, particularly in the X-ray spectrum, is subsequently utilized for the detailed study of matter. This intense electromagnetic radiation, particularly in the X-ray spectrum, is subsequently used for the detailed study of matter.
Approximately 70 synchrotron light sources are operational worldwide, some of which are indicated in Figure\nbsp{}ref:fig:introduction_synchrotrons. Approximately 70 synchrotron light sources are operational worldwide, some of which are indicated in Figure\nbsp{}ref:fig:introduction_synchrotrons.
This global distribution of such facilities underscores the significant utility of synchrotron light for the scientific community. This global distribution of such facilities underscores the significant utility of synchrotron light for the scientific community.
@ -429,7 +429,7 @@ Tomography experiments, schematically represented in Figure\nbsp{}ref:fig:introd
Detector images are captured at numerous rotation angles, allowing the reconstruction of three-dimensional sample structure (Figure\nbsp{}ref:fig:introduction_tomography_results)\nbsp{}[[cite:&schoeppler17_shapin_highl_regul_glass_archit]]. Detector images are captured at numerous rotation angles, allowing the reconstruction of three-dimensional sample structure (Figure\nbsp{}ref:fig:introduction_tomography_results)\nbsp{}[[cite:&schoeppler17_shapin_highl_regul_glass_archit]].
This reconstruction depends critically on maintaining the sample's point of interest within the beam throughout the rotation process. This reconstruction depends critically on maintaining the sample's point of interest within the beam throughout the rotation process.
Mapping or scanning experiments, depicted in Figure\nbsp{}ref:fig:introduction_scanning_schematic, typically utilize focusing optics to have a small beam size at the sample's location. Mapping or scanning experiments, depicted in Figure\nbsp{}ref:fig:introduction_scanning_schematic, typically use focusing optics to have a small beam size at the sample's location.
The sample is then translated perpendicular to the beam (along Y and Z axes), while data is collected at each position. The sample is then translated perpendicular to the beam (along Y and Z axes), while data is collected at each position.
An example\nbsp{}[[cite:&sanchez-cano17_synch_x_ray_fluor_nanop]] of a resulting two-dimensional map, acquired with 20nm step increments, is shown in Figure\nbsp{}ref:fig:introduction_scanning_results. An example\nbsp{}[[cite:&sanchez-cano17_synch_x_ray_fluor_nanop]] of a resulting two-dimensional map, acquired with 20nm step increments, is shown in Figure\nbsp{}ref:fig:introduction_scanning_results.
The fidelity and resolution of such images are intrinsically linked to the focused beam size and the positioning precision of the sample relative to the focused beam. The fidelity and resolution of such images are intrinsically linked to the focused beam size and the positioning precision of the sample relative to the focused beam.
@ -535,7 +535,7 @@ While effective for mitigating radiation damage, this sequential process can be
An alternative, more efficient approach is the "fly-scan" or "continuous-scan" methodology\nbsp{}[[cite:&xu23_high_nsls_ii]], depicted in Figure\nbsp{}ref:fig:introduction_scan_fly. An alternative, more efficient approach is the "fly-scan" or "continuous-scan" methodology\nbsp{}[[cite:&xu23_high_nsls_ii]], depicted in Figure\nbsp{}ref:fig:introduction_scan_fly.
Here, the sample is moved continuously while the detector is triggered to acquire data "on the fly" at predefined positions or time intervals. Here, the sample is moved continuously while the detector is triggered to acquire data "on the fly" at predefined positions or time intervals.
This technique significantly accelerates data acquisition, enabling better utilization of valuable beamtime while potentially enabling finer spatial resolution\nbsp{}[[cite:&huang15_fly_scan_ptych]]. This technique significantly accelerates data acquisition, enabling better use of valuable beamtime while potentially enabling finer spatial resolution\nbsp{}[[cite:&huang15_fly_scan_ptych]].
Recent developments in detector technology have yielded sensors with improved spatial resolution, lower noise characteristics, and substantially higher frame rates\nbsp{}[[cite:&hatsui15_x_ray_imagin_detec_synch_xfel_sourc]]. Recent developments in detector technology have yielded sensors with improved spatial resolution, lower noise characteristics, and substantially higher frame rates\nbsp{}[[cite:&hatsui15_x_ray_imagin_detec_synch_xfel_sourc]].
Historically, detector integration times for scanning and tomography experiments were in the range of 0.1 to 1 second. Historically, detector integration times for scanning and tomography experiments were in the range of 0.1 to 1 second.
@ -556,7 +556,7 @@ To contextualize the system developed within this thesis, a brief overview of ex
The aim is to identify the specific characteristics that distinguish the proposed system from current state-of-the-art implementations. The aim is to identify the specific characteristics that distinguish the proposed system from current state-of-the-art implementations.
Positioning systems can be broadly categorized based on their kinematic architecture, typically serial or parallel, as exemplified by the 3-Degree-of-Freedom (DoF) platforms in Figure\nbsp{}ref:fig:introduction_kinematics. Positioning systems can be broadly categorized based on their kinematic architecture, typically serial or parallel, as exemplified by the 3-Degree-of-Freedom (DoF) platforms in Figure\nbsp{}ref:fig:introduction_kinematics.
Serial kinematics (Figure\nbsp{}ref:fig:introduction_serial_kinematics) utilizes stacked stages where each degree of freedom is controlled by a dedicated actuator. Serial kinematics (Figure\nbsp{}ref:fig:introduction_serial_kinematics) is composed of stacked stages where each degree of freedom is controlled by a dedicated actuator.
This configuration offers great mobility, but positioning errors (e.g., guiding inaccuracies, thermal expansion) accumulate through the stack, compromising overall accuracy. This configuration offers great mobility, but positioning errors (e.g., guiding inaccuracies, thermal expansion) accumulate through the stack, compromising overall accuracy.
Similarly, the overall dynamic performance (stiffness, resonant frequencies) is limited by the softest component in the stack, often resulting in poor dynamic behavior when many stages are combined. Similarly, the overall dynamic performance (stiffness, resonant frequencies) is limited by the softest component in the stack, often resulting in poor dynamic behavior when many stages are combined.
@ -816,7 +816,7 @@ While the resulting system is highly specific, the documented effectiveness of t
***** Experimental validation of multi-body simulations with reduced order flexible bodies obtained by FEA ***** Experimental validation of multi-body simulations with reduced order flexible bodies obtained by FEA
A key tool employed extensively in this work was a combined multi-body simulation and Finite Element Analysis technique, specifically utilizing Component Mode Synthesis to represent flexible bodies within the multi-body framework\nbsp{}[[cite:&brumund21_multib_simul_reduc_order_flexib_bodies_fea]]. A key tool employed extensively in this work was a combined multi-body simulation and Finite Element Analysis technique, specifically using Component Mode Synthesis to represent flexible bodies within the multi-body framework\nbsp{}[[cite:&brumund21_multib_simul_reduc_order_flexib_bodies_fea]].
This hybrid approach, while established, was experimentally validated in this work for components critical to the NASS, namely amplified piezoelectric actuators and flexible joints. This hybrid approach, while established, was experimentally validated in this work for components critical to the NASS, namely amplified piezoelectric actuators and flexible joints.
It proved invaluable for designing and optimizing components intended for integration into a larger, complex dynamic system. It proved invaluable for designing and optimizing components intended for integration into a larger, complex dynamic system.
This methodology, detailed in Section\nbsp{}ref:sec:detail_fem, is presented as a potentially useful tool for future mechatronic instrument development. This methodology, detailed in Section\nbsp{}ref:sec:detail_fem, is presented as a potentially useful tool for future mechatronic instrument development.
@ -827,7 +827,7 @@ The requirement for robust operation across diverse conditions—including paylo
This challenge was met by embedding robustness directly into the active platform's design, rather than depending solely on complex post-design control synthesis techniques such as $\mathcal{H}_\infty\text{-synthesis}$ and $\mu\text{-synthesis}$. This challenge was met by embedding robustness directly into the active platform's design, rather than depending solely on complex post-design control synthesis techniques such as $\mathcal{H}_\infty\text{-synthesis}$ and $\mu\text{-synthesis}$.
Key elements of this strategy included the model-based evaluation of active stage designs to identify architectures inherently easier to control, the incorporation of collocated actuator/sensor pairs to leverage passivity-based guaranteed stability, and the comparison of architecture to combine several sensors such as sensor fusion and High Authority Control / Low Authority Control (HAC-LAC). Key elements of this strategy included the model-based evaluation of active stage designs to identify architectures inherently easier to control, the incorporation of collocated actuator/sensor pairs to leverage passivity-based guaranteed stability, and the comparison of architecture to combine several sensors such as sensor fusion and High Authority Control / Low Authority Control (HAC-LAC).
Furthermore, decoupling strategies for parallel manipulators were compared (Section\nbsp{}ref:sec:detail_control_decoupling), addressing a topic identified as having limited treatment in the literature. Furthermore, decoupling strategies for parallel manipulators were compared (Section\nbsp{}ref:sec:detail_control_decoupling), addressing a topic identified as having limited treatment in the literature.
Consequently, the specified performance targets were met utilizing controllers which, facilitated by this design approach, proved to be robust, readily tunable, and easily maintained. Consequently, the specified performance targets were met using controllers which, facilitated by this design approach, proved to be robust, readily tunable, and easily maintained.
***** Active Damping of rotating mechanical systems using Integral Force Feedback ***** Active Damping of rotating mechanical systems using Integral Force Feedback
@ -850,7 +850,7 @@ The integration of such filters into feedback control architectures can also lea
The conclusion of this work involved the experimental implementation and validation of the complete NASS on the ID31 beamline. The conclusion of this work involved the experimental implementation and validation of the complete NASS on the ID31 beamline.
Experimental results, presented in Section\nbsp{}ref:sec:test_id31, demonstrate that the system successfully improves the effective positioning accuracy of the micro-station from its native $\approx 10\,\mu m$ level down to the target $\approx 100\,nm$ range during representative scientific experiments. Experimental results, presented in Section\nbsp{}ref:sec:test_id31, demonstrate that the system successfully improves the effective positioning accuracy of the micro-station from its native $\approx 10\,\mu m$ level down to the target $\approx 100\,nm$ range during representative scientific experiments.
Crucially, robustness to variations in sample mass and diverse experimental conditions was verified. Crucially, robustness to variations in sample mass and diverse experimental conditions was verified.
The NASS thus provides a versatile end-station solution, uniquely combining high payload capacity with nanometer-level accuracy, enabling optimal utilization of the advanced capabilities of the ESRF-EBS beam and associated detectors. The NASS thus provides a versatile end-station solution, uniquely combining high payload capacity with nanometer-level accuracy, enabling optimal use of the advanced capabilities of the ESRF-EBS beam and associated detectors.
To the author's knowledge, this represents the first demonstration of such a 5-DoF active stabilization platform being used to enhance the accuracy of a complex positioning system to this level. To the author's knowledge, this represents the first demonstration of such a 5-DoF active stabilization platform being used to enhance the accuracy of a complex positioning system to this level.
** Outline ** Outline
@ -4632,7 +4632,7 @@ To overcome this limitation, external metrology systems have been implemented to
A review of existing sample stages with active vibration control reveals various approaches to implementing such feedback systems. A review of existing sample stages with active vibration control reveals various approaches to implementing such feedback systems.
In many cases, sample position control is limited to translational degrees of freedom. In many cases, sample position control is limited to translational degrees of freedom.
At NSLS-II, for instance, a system capable of $100\,\mu m$ stroke has been developed for payloads up to 500g, utilizing interferometric measurements for position feedback (Figure\nbsp{}ref:fig:nhexa_stages_nazaretski). At NSLS-II, for instance, a system capable of $100\,\mu m$ stroke has been developed for payloads up to 500g, using interferometric measurements for position feedback (Figure\nbsp{}ref:fig:nhexa_stages_nazaretski).
Similarly, at the Sirius facility, a tripod configuration based on voice coil actuators has been implemented for XYZ position control, achieving feedback bandwidths of approximately 100 Hz (Figure\nbsp{}ref:fig:nhexa_stages_sapoti). Similarly, at the Sirius facility, a tripod configuration based on voice coil actuators has been implemented for XYZ position control, achieving feedback bandwidths of approximately 100 Hz (Figure\nbsp{}ref:fig:nhexa_stages_sapoti).
#+name: fig:nhexa_stages_translations #+name: fig:nhexa_stages_translations
@ -4786,7 +4786,7 @@ Furthermore, hybrid architectures combining both serial and parallel elements ha
After evaluating the different options, the Stewart platform architecture was selected for several reasons. After evaluating the different options, the Stewart platform architecture was selected for several reasons.
In addition to providing control over all required degrees of freedom, its compact design and predictable dynamic characteristics make it particularly suitable for nano-positioning when combined with flexible joints. In addition to providing control over all required degrees of freedom, its compact design and predictable dynamic characteristics make it particularly suitable for nano-positioning when combined with flexible joints.
Stewart platforms have been implemented in a wide variety of configurations, as illustrated in Figure\nbsp{}ref:fig:nhexa_stewart_examples, which shows two distinct implementations: one utilizing piezoelectric actuators for nano-positioning applications, and another based on voice coil actuators for vibration isolation. Stewart platforms have been implemented in a wide variety of configurations, as illustrated in Figure\nbsp{}ref:fig:nhexa_stewart_examples, which shows two distinct implementations: one implementing piezoelectric actuators for nano-positioning applications, and another based on voice coil actuators for vibration isolation.
These examples demonstrate the architecture's versatility in terms of geometry, actuator selection, and scale, all of which can be optimized for specific applications. These examples demonstrate the architecture's versatility in terms of geometry, actuator selection, and scale, all of which can be optimized for specific applications.
Furthermore, the successful implementation of Integral Force Feedback (IFF) control on Stewart platforms has been well documented\nbsp{}[[cite:&abu02_stiff_soft_stewar_platf_activ;&hanieh03_activ_stewar;&preumont07_six_axis_singl_stage_activ]], and the extensive body of research on this architecture enables thorough optimization specifically for the NASS. Furthermore, the successful implementation of Integral Force Feedback (IFF) control on Stewart platforms has been well documented\nbsp{}[[cite:&abu02_stiff_soft_stewar_platf_activ;&hanieh03_activ_stewar;&preumont07_six_axis_singl_stage_activ]], and the extensive body of research on this architecture enables thorough optimization specifically for the NASS.
@ -5349,7 +5349,7 @@ The choice between these approaches depends significantly on the degree of inter
For instance, when using external metrology systems that measure the platform's global position, centralized control becomes necessary because each sensor measurement depends on all actuator inputs. For instance, when using external metrology systems that measure the platform's global position, centralized control becomes necessary because each sensor measurement depends on all actuator inputs.
In the context of the nano-hexapod, two distinct control strategies were examined during the conceptual phase: In the context of the nano-hexapod, two distinct control strategies were examined during the conceptual phase:
- Decentralized Integral Force Feedback (IFF), which utilizes collocated force sensors to implement independent control loops for each strut (Section\nbsp{}ref:ssec:nhexa_control_iff) - Decentralized Integral Force Feedback (IFF), which uses collocated force sensors to implement independent control loops for each strut (Section\nbsp{}ref:ssec:nhexa_control_iff)
- High-Authority Control (HAC), which employs a centralized approach to achieve precise positioning based on external metrology measurements (Section\nbsp{}ref:ssec:nhexa_control_hac_lac) - High-Authority Control (HAC), which employs a centralized approach to achieve precise positioning based on external metrology measurements (Section\nbsp{}ref:ssec:nhexa_control_hac_lac)
#+name: fig:nhexa_stewart_decentralized_control #+name: fig:nhexa_stewart_decentralized_control
@ -6183,7 +6183,7 @@ Finally, Section\nbsp{}ref:sec:detail_kinematics_nano_hexapod presents the optim
The first parallel platform similar to the Stewart platform was built in 1954 by Gough\nbsp{}[[cite:&gough62_univer_tyre_test_machin]], for a tyre test machine (shown in Figure\nbsp{}ref:fig:detail_geometry_gough_paper). The first parallel platform similar to the Stewart platform was built in 1954 by Gough\nbsp{}[[cite:&gough62_univer_tyre_test_machin]], for a tyre test machine (shown in Figure\nbsp{}ref:fig:detail_geometry_gough_paper).
Subsequently, Stewart proposed a similar design for a flight simulator (shown in Figure\nbsp{}ref:fig:detail_geometry_stewart_flight_simulator) in a 1965 publication\nbsp{}[[cite:&stewart65_platf_with_six_degrees_freed]]. Subsequently, Stewart proposed a similar design for a flight simulator (shown in Figure\nbsp{}ref:fig:detail_geometry_stewart_flight_simulator) in a 1965 publication\nbsp{}[[cite:&stewart65_platf_with_six_degrees_freed]].
Since then, the Stewart platform (sometimes referred to as the Stewart-Gough platform) has been utilized across diverse applications\nbsp{}[[cite:&dasgupta00_stewar_platf_manip]], including large telescopes\nbsp{}[[cite:&kazezkhan14_dynam_model_stewar_platf_nansh_radio_teles;&yun19_devel_isotr_stewar_platf_teles_secon_mirror]], machine tools\nbsp{}[[cite:&russo24_review_paral_kinem_machin_tools]], and Synchrotron instrumentation\nbsp{}[[cite:&marion04_hexap_esrf;&villar18_nanop_esrf_id16a_nano_imagin_beaml]]. Since then, the Stewart platform (sometimes referred to as the Stewart-Gough platform) has been used across diverse applications\nbsp{}[[cite:&dasgupta00_stewar_platf_manip]], including large telescopes\nbsp{}[[cite:&kazezkhan14_dynam_model_stewar_platf_nansh_radio_teles;&yun19_devel_isotr_stewar_platf_teles_secon_mirror]], machine tools\nbsp{}[[cite:&russo24_review_paral_kinem_machin_tools]], and Synchrotron instrumentation\nbsp{}[[cite:&marion04_hexap_esrf;&villar18_nanop_esrf_id16a_nano_imagin_beaml]].
#+name: fig:detail_geometry_stewart_origins #+name: fig:detail_geometry_stewart_origins
#+caption: Two of the earliest developments of Stewart platforms #+caption: Two of the earliest developments of Stewart platforms
@ -6252,7 +6252,7 @@ Although less frequently encountered, magnetostrictive actuators have been succe
The sensors integrated in these platforms are selected based on specific control requirements, as different sensors offer distinct advantages and limitations\nbsp{}[[cite:&hauge04_sensor_contr_space_based_six]]. The sensors integrated in these platforms are selected based on specific control requirements, as different sensors offer distinct advantages and limitations\nbsp{}[[cite:&hauge04_sensor_contr_space_based_six]].
Force sensors are typically integrated within the struts in a collocated arrangement with actuators to enhance control robustness. Force sensors are typically integrated within the struts in a collocated arrangement with actuators to enhance control robustness.
Stewart platforms incorporating force sensors are frequently utilized for vibration isolation\nbsp{}[[cite:&spanos95_soft_activ_vibrat_isolat;&rahman98_multiax]] and active damping applications\nbsp{}[[cite:&geng95_intel_contr_system_multip_degree;&abu02_stiff_soft_stewar_platf_activ]], as exemplified in Figure\nbsp{}ref:fig:detail_kinematics_ulb_pz. Stewart platforms incorporating force sensors are frequently used for vibration isolation\nbsp{}[[cite:&spanos95_soft_activ_vibrat_isolat;&rahman98_multiax]] and active damping applications\nbsp{}[[cite:&geng95_intel_contr_system_multip_degree;&abu02_stiff_soft_stewar_platf_activ]], as exemplified in Figure\nbsp{}ref:fig:detail_kinematics_ulb_pz.
Inertial sensors (accelerometers and geophones) are commonly employed in vibration isolation applications\nbsp{}[[cite:&chen03_payload_point_activ_vibrat_isolat;&chi15_desig_exper_study_vcm_based]]. Inertial sensors (accelerometers and geophones) are commonly employed in vibration isolation applications\nbsp{}[[cite:&chen03_payload_point_activ_vibrat_isolat;&chi15_desig_exper_study_vcm_based]].
These sensors are predominantly aligned with the struts\nbsp{}[[cite:&hauge04_sensor_contr_space_based_six;&li01_simul_fault_vibrat_isolat_point;&thayer02_six_axis_vibrat_isolat_system;&zhang11_six_dof;&jiao18_dynam_model_exper_analy_stewar;&tang18_decen_vibrat_contr_voice_coil]], although they may also be fixed to the top platform\nbsp{}[[cite:&wang16_inves_activ_vibrat_isolat_stewar]]. These sensors are predominantly aligned with the struts\nbsp{}[[cite:&hauge04_sensor_contr_space_based_six;&li01_simul_fault_vibrat_isolat_point;&thayer02_six_axis_vibrat_isolat_system;&zhang11_six_dof;&jiao18_dynam_model_exper_analy_stewar;&tang18_decen_vibrat_contr_voice_coil]], although they may also be fixed to the top platform\nbsp{}[[cite:&wang16_inves_activ_vibrat_isolat_stewar]].
@ -7053,7 +7053,7 @@ Regarding dynamical properties, particularly for control in the frame of the str
Consequently, the geometry was selected according to practical constraints. Consequently, the geometry was selected according to practical constraints.
The height between the two plates is maximized and set at $95\,mm$. The height between the two plates is maximized and set at $95\,mm$.
Both platforms utilize the maximum available size, with joints offset by $15\,mm$ from the plate surfaces and positioned along circles with radii of $120\,mm$ for the fixed joints and $110\,mm$ for the mobile joints. Both platforms take the maximum available size, with joints offset by $15\,mm$ from the plate surfaces and positioned along circles with radii of $120\,mm$ for the fixed joints and $110\,mm$ for the mobile joints.
The positioning angles, as shown in Figure\nbsp{}ref:fig:detail_kinematics_nano_hexapod_top, are $[255,\ 285,\ 15,\ 45,\ 135,\ 165]$ degrees for the top joints and $[220,\ 320,\ 340,\ 80,\ 100,\ 200]$ degrees for the bottom joints. The positioning angles, as shown in Figure\nbsp{}ref:fig:detail_kinematics_nano_hexapod_top, are $[255,\ 285,\ 15,\ 45,\ 135,\ 165]$ degrees for the top joints and $[220,\ 320,\ 340,\ 80,\ 100,\ 200]$ degrees for the bottom joints.
#+name: fig:detail_kinematics_nano_hexapod #+name: fig:detail_kinematics_nano_hexapod
@ -7137,7 +7137,7 @@ This led to a practical design approach where struts were oriented more vertical
*** Introduction :ignore: *** Introduction :ignore:
During the nano-hexapod's detailed design phase, a hybrid modeling approach combining finite element analysis with multi-body dynamics was developed. During the nano-hexapod's detailed design phase, a hybrid modeling approach combining finite element analysis with multi-body dynamics was developed.
This methodology, utilizing reduced-order flexible bodies, was created to enable both detailed component optimization and efficient system-level simulation, addressing the impracticality of a full FEM for real-time control scenarios. This methodology, using reduced-order flexible bodies, was created to enable both detailed component optimization and efficient system-level simulation, addressing the impracticality of a full FEM for real-time control scenarios.
The theoretical foundations and implementation are presented in Section\nbsp{}ref:sec:detail_fem_super_element, where experimental validation was performed using an Amplified Piezoelectric Actuator. The theoretical foundations and implementation are presented in Section\nbsp{}ref:sec:detail_fem_super_element, where experimental validation was performed using an Amplified Piezoelectric Actuator.
The framework was then applied to optimize two critical nano-hexapod elements: the actuators (Section\nbsp{}ref:sec:detail_fem_actuator) and the flexible joints (Section\nbsp{}ref:sec:detail_fem_joint). The framework was then applied to optimize two critical nano-hexapod elements: the actuators (Section\nbsp{}ref:sec:detail_fem_actuator) and the flexible joints (Section\nbsp{}ref:sec:detail_fem_joint).
@ -7917,7 +7917,7 @@ Such model reduction, guided by detailed understanding of component behavior, pr
<<sec:detail_control>> <<sec:detail_control>>
*** Introduction :ignore: *** Introduction :ignore:
Three critical elements for the control of parallel manipulators such as the Nano-Hexapod were identified: effective utilization and combination of multiple sensors, appropriate plant decoupling strategies, and robust controller design for the decoupled system. Three critical elements for the control of parallel manipulators such as the Nano-Hexapod were identified: effective use and combination of multiple sensors, appropriate plant decoupling strategies, and robust controller design for the decoupled system.
During the conceptual design phase of the NASS, pragmatic approaches were implemented for each of these elements. During the conceptual design phase of the NASS, pragmatic approaches were implemented for each of these elements.
The High Authority Control-Low Authority Control (HAC-LAC) architecture was selected for combining sensors. The High Authority Control-Low Authority Control (HAC-LAC) architecture was selected for combining sensors.
@ -7925,7 +7925,7 @@ Control was implemented in the frame of the struts, leveraging the inherent low-
For these decoupled plants, open-loop shaping techniques were employed to tune the individual controllers. For these decoupled plants, open-loop shaping techniques were employed to tune the individual controllers.
While these initial strategies proved effective in validating the NASS concept, this work explores alternative approaches with the potential to further enhance the performance. While these initial strategies proved effective in validating the NASS concept, this work explores alternative approaches with the potential to further enhance the performance.
Section\nbsp{}ref:sec:detail_control_sensor examines different methods for combining multiple sensors, with particular emphasis on sensor fusion techniques that utilize complementary filters. Section\nbsp{}ref:sec:detail_control_sensor examines different methods for combining multiple sensors, with particular emphasis on sensor fusion techniques that are based on complementary filters.
A novel approach for designing these filters is proposed, which allows optimization of the sensor fusion effectiveness. A novel approach for designing these filters is proposed, which allows optimization of the sensor fusion effectiveness.
Section\nbsp{}ref:sec:detail_control_decoupling presents a comparative analysis of various decoupling strategies, including Jacobian decoupling, modal decoupling, and Singular Value Decomposition (SVD) decoupling. Section\nbsp{}ref:sec:detail_control_decoupling presents a comparative analysis of various decoupling strategies, including Jacobian decoupling, modal decoupling, and Singular Value Decomposition (SVD) decoupling.
@ -7971,8 +7971,8 @@ From the literature, three principal approaches for combining sensors have been
#+end_subfigure #+end_subfigure
#+end_figure #+end_figure
The HAC-LAC approach employs a dual-loop control strategy in which two control loops utilize different sensors for distinct purposes (Figure\nbsp{}ref:fig:detail_control_sensor_arch_hac_lac). The HAC-LAC approach employs a dual-loop control strategy in which two control loops are using different sensors for distinct purposes (Figure\nbsp{}ref:fig:detail_control_sensor_arch_hac_lac).
In\nbsp{}[[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\nbsp{}[[cite:&li01_simul_vibrat_isolat_point_contr]], vibration isolation is provided by accelerometers collocated with the voice coil actuators, while external rotational sensors are used to achieve pointing control.
In\nbsp{}[[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\nbsp{}[[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\nbsp{}[[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\nbsp{}[[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\nbsp{}[[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\nbsp{}[[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.
@ -7992,7 +7992,7 @@ A "two-sensor control" approach was proven to perform better than controllers ba
A Linear Quadratic Regulator (LQG) was employed to optimize the two-input/one-output controller. A Linear Quadratic Regulator (LQG) was employed to optimize the two-input/one-output controller.
Beyond these three main approaches, other control architectures have been proposed for different purposes. Beyond these three main approaches, other control architectures have been proposed for different purposes.
For instance, in\nbsp{}[[cite:&yang19_dynam_model_decoup_contr_flexib]], a first control loop utilizes force sensors and relative motion sensors to compensate for parasitic stiffness of the flexible joints. For instance, in\nbsp{}[[cite:&yang19_dynam_model_decoup_contr_flexib]], a first control loop based on force sensors and relative motion sensors is implemented to compensate for parasitic stiffness of the flexible joints.
Subsequently, the system is decoupled in the modal space (facilitated by the removal of parasitic stiffness) and accelerometers are employed for vibration isolation. Subsequently, the system is decoupled in the modal space (facilitated by the removal of parasitic stiffness) and accelerometers are employed for vibration isolation.
The HAC-LAC architecture was previously investigated during the conceptual phase and successfully implemented to validate the NASS concept, demonstrating excellent performance. The HAC-LAC architecture was previously investigated during the conceptual phase and successfully implemented to validate the NASS concept, demonstrating excellent performance.
@ -8016,7 +8016,7 @@ By carefully selecting the sensors to be fused, a "super sensor" is obtained tha
In some applications, sensor fusion is employed to increase measurement bandwidth\nbsp{}[[cite:&shaw90_bandw_enhan_posit_measur_using_measur_accel;&zimmermann92_high_bandw_orien_measur_contr;&min15_compl_filter_desig_angle_estim]]. In some applications, sensor fusion is employed to increase measurement bandwidth\nbsp{}[[cite:&shaw90_bandw_enhan_posit_measur_using_measur_accel;&zimmermann92_high_bandw_orien_measur_contr;&min15_compl_filter_desig_angle_estim]].
For instance, in\nbsp{}[[cite:&shaw90_bandw_enhan_posit_measur_using_measur_accel]], the bandwidth of a position sensor is extended by fusing it with an accelerometer that provides high-frequency motion information. For instance, in\nbsp{}[[cite:&shaw90_bandw_enhan_posit_measur_using_measur_accel]], the bandwidth of a position sensor is extended by fusing it with an accelerometer that provides high-frequency motion information.
In other applications, sensor fusion is utilized to obtain an estimate of the measured quantity with reduced noise\nbsp{}[[cite:&hua05_low_ligo;&hua04_polyp_fir_compl_filter_contr_system;&plummer06_optim_compl_filter_their_applic_motion_measur;&robert12_introd_random_signal_applied_kalman]]. In other applications, sensor fusion is used to obtain an estimate of the measured quantity with reduced noise\nbsp{}[[cite:&hua05_low_ligo;&hua04_polyp_fir_compl_filter_contr_system;&plummer06_optim_compl_filter_their_applic_motion_measur;&robert12_introd_random_signal_applied_kalman]].
More recently, the fusion of sensors measuring different physical quantities has been proposed to enhance control properties\nbsp{}[[cite:&collette15_sensor_fusion_method_high_perfor;&yong16_high_speed_vertic_posit_stage]]. More recently, the fusion of sensors measuring different physical quantities has been proposed to enhance control properties\nbsp{}[[cite:&collette15_sensor_fusion_method_high_perfor;&yong16_high_speed_vertic_posit_stage]].
In\nbsp{}[[cite:&collette15_sensor_fusion_method_high_perfor]], an inertial sensor used for active vibration isolation is fused with a sensor collocated with the actuator to improve the stability margins of the feedback controller. In\nbsp{}[[cite:&collette15_sensor_fusion_method_high_perfor]], an inertial sensor used for active vibration isolation is fused with a sensor collocated with the actuator to improve the stability margins of the feedback controller.
@ -8036,7 +8036,7 @@ In early implementations of complementary filtering, analog circuits were used t
While analog complementary filters remain in use today\nbsp{}[[cite:&yong16_high_speed_vertic_posit_stage;&moore19_capac_instr_sensor_fusion_high_bandw_nanop]], digital implementation is now more common as it provides greater flexibility. While analog complementary filters remain in use today\nbsp{}[[cite:&yong16_high_speed_vertic_posit_stage;&moore19_capac_instr_sensor_fusion_high_bandw_nanop]], digital implementation is now more common as it provides greater flexibility.
Various design methods have been developed to optimize complementary filters. Various design methods have been developed to optimize complementary filters.
The most straightforward approach utilizes analytical formulas, which depending on the application may be first order\nbsp{}[[cite:&corke04_inert_visual_sensin_system_small_auton_helic;&yeh05_model_contr_hydraul_actuat_two;&yong16_high_speed_vertic_posit_stage]], second order\nbsp{}[[cite:&baerveldt97_low_cost_low_weigh_attit;&stoten01_fusion_kinet_data_using_compos_filter;&jensen13_basic_uas]], or higher orders\nbsp{}[[cite:&shaw90_bandw_enhan_posit_measur_using_measur_accel;&zimmermann92_high_bandw_orien_measur_contr;&stoten01_fusion_kinet_data_using_compos_filter;&collette15_sensor_fusion_method_high_perfor;&matichard15_seism_isolat_advan_ligo]]. The most straightforward approach is based on analytical formulas, which depending on the application may be first order\nbsp{}[[cite:&corke04_inert_visual_sensin_system_small_auton_helic;&yeh05_model_contr_hydraul_actuat_two;&yong16_high_speed_vertic_posit_stage]], second order\nbsp{}[[cite:&baerveldt97_low_cost_low_weigh_attit;&stoten01_fusion_kinet_data_using_compos_filter;&jensen13_basic_uas]], or higher orders\nbsp{}[[cite:&shaw90_bandw_enhan_posit_measur_using_measur_accel;&zimmermann92_high_bandw_orien_measur_contr;&stoten01_fusion_kinet_data_using_compos_filter;&collette15_sensor_fusion_method_high_perfor;&matichard15_seism_isolat_advan_ligo]].
Since the characteristics of the super sensor depend on proper complementary filter design\nbsp{}[[cite:&dehaeze19_compl_filter_shapin_using_synth]], several optimization techniques have emerged—ranging from optimizing parameters for analytical formulas\nbsp{}[[cite:&jensen13_basic_uas;&min15_compl_filter_desig_angle_estim;&fonseca15_compl]] to employing convex optimization tools\nbsp{}[[cite:&hua04_polyp_fir_compl_filter_contr_system;&hua05_low_ligo]] such as linear matrix inequalities\nbsp{}[[cite:&pascoal99_navig_system_desig_using_time]]. Since the characteristics of the super sensor depend on proper complementary filter design\nbsp{}[[cite:&dehaeze19_compl_filter_shapin_using_synth]], several optimization techniques have emerged—ranging from optimizing parameters for analytical formulas\nbsp{}[[cite:&jensen13_basic_uas;&min15_compl_filter_desig_angle_estim;&fonseca15_compl]] to employing convex optimization tools\nbsp{}[[cite:&hua04_polyp_fir_compl_filter_contr_system;&hua05_low_ligo]] such as linear matrix inequalities\nbsp{}[[cite:&pascoal99_navig_system_desig_using_time]].
As demonstrated in\nbsp{}[[cite:&plummer06_optim_compl_filter_their_applic_motion_measur]], complementary filter design can be linked to the standard mixed-sensitivity control problem, allowing powerful classical control theory tools to be applied. As demonstrated in\nbsp{}[[cite:&plummer06_optim_compl_filter_their_applic_motion_measur]], complementary filter design can be linked to the standard mixed-sensitivity control problem, allowing powerful classical control theory tools to be applied.
For example, in\nbsp{}[[cite:&jensen13_basic_uas]], two gains of a Proportional Integral (PI) controller are optimized to minimize super sensor noise. For example, in\nbsp{}[[cite:&jensen13_basic_uas]], two gains of a Proportional Integral (PI) controller are optimized to minimize super sensor noise.
@ -8354,7 +8354,7 @@ Certain applications necessitate the fusion of more than two sensors\nbsp{}[[cit
At LIGO, for example, a super sensor is formed by merging three distinct sensors: an LVDT, a seismometer, and a geophone\nbsp{}[[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\nbsp{}[[cite:&matichard15_seism_isolat_advan_ligo]].
For merging $n>2$ sensors with complementary filters, two architectural approaches are possible, as illustrated in Figure\nbsp{}ref:fig:detail_control_sensor_fusion_three. For merging $n>2$ sensors with complementary filters, two architectural approaches are possible, as illustrated in Figure\nbsp{}ref:fig:detail_control_sensor_fusion_three.
Fusion can be implemented either "sequentially," utilizing $n-1$ sets of two complementary filters (Figure\nbsp{}ref:fig:detail_control_sensor_fusion_three_sequential), or "in parallel," employing a single set of $n$ complementary filters (Figure\nbsp{}ref:fig:detail_control_sensor_fusion_three_parallel). Fusion can be implemented either "sequentially," using $n-1$ sets of two complementary filters (Figure\nbsp{}ref:fig:detail_control_sensor_fusion_three_sequential), or "in parallel," employing a single set of $n$ complementary filters (Figure\nbsp{}ref:fig:detail_control_sensor_fusion_three_parallel).
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. 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.
Previous literature has offered only simple analytical formulas for this purpose\nbsp{}[[cite:&stoten01_fusion_kinet_data_using_compos_filter;&fonseca15_compl]]. Previous literature has offered only simple analytical formulas for this purpose\nbsp{}[[cite:&stoten01_fusion_kinet_data_using_compos_filter;&fonseca15_compl]].
@ -8477,7 +8477,7 @@ For instance,\nbsp{}[[cite:&furutani04_nanom_cuttin_machin_using_stewar]] implem
A similar control architecture was proposed in\nbsp{}[[cite:&du14_piezo_actuat_high_precis_flexib]] using strain gauge sensors integrated in each strut. A similar control architecture was proposed in\nbsp{}[[cite:&du14_piezo_actuat_high_precis_flexib]] using strain gauge sensors integrated in each strut.
An alternative strategy involves decoupling the system in the Cartesian frame using Jacobian matrices. An alternative strategy involves decoupling the system in the Cartesian frame using Jacobian matrices.
As demonstrated during the study of Stewart platform kinematics, Jacobian matrices can be utilized to map actuator forces to forces and torques applied on the top platform. As demonstrated during the study of Stewart platform kinematics, Jacobian matrices can be used to map actuator forces to forces and torques applied on the top platform.
This approach enables the implementation of controllers in a defined frame. This approach enables the implementation of controllers in a defined frame.
It has been applied with various sensor types including force sensors\nbsp{}[[cite:&mcinroy00_desig_contr_flexur_joint_hexap]], relative displacement sensors\nbsp{}[[cite:&kim00_robus_track_contr_desig_dof_paral_manip]], and inertial sensors\nbsp{}[[cite:&li01_simul_vibrat_isolat_point_contr;&abbas14_vibrat_stewar_platf]]. It has been applied with various sensor types including force sensors\nbsp{}[[cite:&mcinroy00_desig_contr_flexur_joint_hexap]], relative displacement sensors\nbsp{}[[cite:&kim00_robus_track_contr_desig_dof_paral_manip]], and inertial sensors\nbsp{}[[cite:&li01_simul_vibrat_isolat_point_contr;&abbas14_vibrat_stewar_platf]].
The Cartesian frame in which the system is decoupled is typically chosen at the point of interest (i.e., where the motion is of interest) or at the center of mass. The Cartesian frame in which the system is decoupled is typically chosen at the point of interest (i.e., where the motion is of interest) or at the center of mass.
@ -8504,7 +8504,7 @@ Finally, a comparative analysis with concluding observations is provided in Sect
**** Test Model **** Test Model
<<ssec:detail_control_decoupling_model>> <<ssec:detail_control_decoupling_model>>
Instead of utilizing the Stewart platform for comparing decoupling strategies, a simplified parallel manipulator is employed to facilitate a more straightforward analysis. Instead of using the Stewart platform for comparing decoupling strategies, a simplified parallel manipulator is employed to facilitate a more straightforward analysis.
The system illustrated in Figure\nbsp{}ref:fig:detail_control_decoupling_model_test is used for this purpose. The system illustrated in Figure\nbsp{}ref:fig:detail_control_decoupling_model_test is used for this purpose.
It possesses three degrees of freedom (DoF) and incorporates three parallel struts. It possesses three degrees of freedom (DoF) and incorporates three parallel struts.
Being a fully parallel manipulator, it is therefore quite similar to the Stewart platform. Being a fully parallel manipulator, it is therefore quite similar to the Stewart platform.
@ -8953,7 +8953,7 @@ The phenomenon potentially relates to previous research on SVD controllers appli
While the three proposed decoupling methods may appear similar in their mathematical implementation (each involving pre-multiplication and post-multiplication of the plant with constant matrices), they differ significantly in their underlying approaches and practical implications, as summarized in Table\nbsp{}ref:tab:detail_control_decoupling_strategies_comp. While the three proposed decoupling methods may appear similar in their mathematical implementation (each involving pre-multiplication and post-multiplication of the plant with constant matrices), they differ significantly in their underlying approaches and practical implications, as summarized in Table\nbsp{}ref:tab:detail_control_decoupling_strategies_comp.
Each method employs a distinct conceptual framework: Jacobian decoupling is "topology-driven", relying on the geometric configuration of the system; modal decoupling is "physics-driven", based on the system's dynamical equations; and SVD decoupling is "data-driven", utilizing measured frequency response functions. Each method employs a distinct conceptual framework: Jacobian decoupling is "topology-driven", relying on the geometric configuration of the system; modal decoupling is "physics-driven", based on the system's dynamical equations; and SVD decoupling is "data-driven", using measured frequency response functions.
The physical interpretation of decoupled plant inputs and outputs varies considerably among these methods. The physical interpretation of decoupled plant inputs and outputs varies considerably among these methods.
With Jacobian decoupling, inputs and outputs retain clear physical meaning, corresponding to forces/torques and translations/rotations in a specified reference frame. With Jacobian decoupling, inputs and outputs retain clear physical meaning, corresponding to forces/torques and translations/rotations in a specified reference frame.
@ -9004,7 +9004,7 @@ SVD decoupling can be implemented using measured data without requiring a model,
Once the system is properly decoupled using one of the approaches described in Section\nbsp{}ref:sec:detail_control_decoupling, SISO controllers can be individually tuned for each decoupled "directions". Once the system is properly decoupled using one of the approaches described in Section\nbsp{}ref:sec:detail_control_decoupling, SISO controllers can be individually tuned for each decoupled "directions".
Several ways to design a controller to obtain a given performance while ensuring good robustness properties can be implemented. Several ways to design a controller to obtain a given performance while ensuring good robustness properties can be implemented.
In some cases "fixed" controller structures are utilized, such as PI and PID controllers, whose parameters are manually tuned\nbsp{}[[cite:&furutani04_nanom_cuttin_machin_using_stewar;&du14_piezo_actuat_high_precis_flexib;&yang19_dynam_model_decoup_contr_flexib]]. In some cases "fixed" controller structures are used, such as PI and PID controllers, whose parameters are manually tuned\nbsp{}[[cite:&furutani04_nanom_cuttin_machin_using_stewar;&du14_piezo_actuat_high_precis_flexib;&yang19_dynam_model_decoup_contr_flexib]].
Another popular method is Open-Loop shaping, which was used during the conceptual phase. Another popular method is Open-Loop shaping, which was used during the conceptual phase.
Open-loop shaping involves tuning the controller through a series of "standard" filters (leads, lags, notches, low-pass filters, ...) to shape the open-loop transfer function $G(s)K(s)$ according to desired specifications, including bandwidth, gain and phase margins\nbsp{}[[cite:&schmidt20_desig_high_perfor_mechat_third_revis_edition, chapt. 4.4.7]]. Open-loop shaping involves tuning the controller through a series of "standard" filters (leads, lags, notches, low-pass filters, ...) to shape the open-loop transfer function $G(s)K(s)$ according to desired specifications, including bandwidth, gain and phase margins\nbsp{}[[cite:&schmidt20_desig_high_perfor_mechat_third_revis_edition, chapt. 4.4.7]].
@ -9032,7 +9032,7 @@ Finally, in Section\nbsp{}ref:ssec:detail_control_cf_simulations, a numerical ex
The idea of using complementary filters in the control architecture originates from sensor fusion techniques\nbsp{}[[cite:&collette15_sensor_fusion_method_high_perfor]], where two sensors are combined using complementary filters. The idea of using complementary filters in the control architecture originates from sensor fusion techniques\nbsp{}[[cite:&collette15_sensor_fusion_method_high_perfor]], where two sensors are combined using complementary filters.
Building upon this concept, "virtual sensor fusion"\nbsp{}[[cite:&verma20_virtual_sensor_fusion_high_precis_contr]] replaces one physical sensor with a model $G$ of the plant. Building upon this concept, "virtual sensor fusion"\nbsp{}[[cite:&verma20_virtual_sensor_fusion_high_precis_contr]] replaces one physical sensor with a model $G$ of the plant.
The corresponding control architecture is illustrated in Figure\nbsp{}ref:fig:detail_control_cf_arch, where $G^\prime$ represents the physical plant to be controlled, $G$ is a model of the plant, $k$ is the controller, and $H_L$ and $H_H$ are complementary filters satisfying $H_L(s) + H_H(s) = 1$. The corresponding control architecture is illustrated in Figure\nbsp{}ref:fig:detail_control_cf_arch, where $G^\prime$ represents the physical plant to be controlled, $G$ is a model of the plant, $k$ is the controller, and $H_L$ and $H_H$ are complementary filters satisfying $H_L(s) + H_H(s) = 1$.
In this arrangement, the physical plant is controlled at low frequencies, while the plant model is utilized at high frequencies to enhance robustness. In this arrangement, the physical plant is controlled at low frequencies, while the plant model is used at high frequencies to enhance robustness.
#+name: fig:detail_control_cf_arch_and_eq #+name: fig:detail_control_cf_arch_and_eq
#+caption: Control architecture for virtual sensor fusion (\subref{fig:detail_control_cf_arch}). An equivalent architecture is shown in (\subref{fig:detail_control_cf_arch_eq}). The signals are the reference signal $r$, the output perturbation $d_y$, the measurement noise $n$ and the control input $u$. #+caption: Control architecture for virtual sensor fusion (\subref{fig:detail_control_cf_arch}). An equivalent architecture is shown in (\subref{fig:detail_control_cf_arch_eq}). The signals are the reference signal $r$, the output perturbation $d_y$, the measurement noise $n$ and the control input $u$.
@ -9277,7 +9277,7 @@ To implement the proposed control architecture in practice, the following proced
***** Plant :ignore: ***** Plant :ignore:
To evaluate this control architecture, a simple test model representative of many synchrotron positioning stages is utilized (Figure\nbsp{}ref:fig:detail_control_cf_test_model). To evaluate this control architecture, a simple test model representative of many synchrotron positioning stages is used (Figure\nbsp{}ref:fig:detail_control_cf_test_model).
In this model, a payload with mass $m$ is positioned on top of a stage. In this model, a payload with mass $m$ is positioned on top of a stage.
The objective is to accurately position the sample relative to the X-ray beam. The objective is to accurately position the sample relative to the X-ray beam.
@ -9442,7 +9442,7 @@ Figure\nbsp{}ref:fig:detail_instrumentation_plant illustrates the control diagra
The selection process follows a three-stage methodology. The selection process follows a three-stage methodology.
First, dynamic error budgeting is performed in Section\nbsp{}ref:sec:detail_instrumentation_dynamic_error_budgeting to establish maximum acceptable noise specifications for each instrumentation component (ADC, DAC, and voltage amplifier). First, dynamic error budgeting is performed in Section\nbsp{}ref:sec:detail_instrumentation_dynamic_error_budgeting to establish maximum acceptable noise specifications for each instrumentation component (ADC, DAC, and voltage amplifier).
This analysis utilizes the multi-body model with a 2DoF APA model, focusing particularly on the vertical direction due to its more stringent requirements. This analysis is based on the multi-body model with a 2DoF APA model, focusing particularly on the vertical direction due to its more stringent requirements.
From the calculated transfer functions, maximum acceptable amplitude spectral densities for each noise source are derived. From the calculated transfer functions, maximum acceptable amplitude spectral densities for each noise source are derived.
Section\nbsp{}ref:sec:detail_instrumentation_choice then presents the selection of appropriate components based on these noise specifications and additional requirements. Section\nbsp{}ref:sec:detail_instrumentation_choice then presents the selection of appropriate components based on these noise specifications and additional requirements.
@ -9871,7 +9871,7 @@ The resulting amplifier noise amplitude spectral density $\Gamma_{n_a}$ and the
**** Digital to Analog Converters **** Digital to Analog Converters
***** Output Voltage Noise ***** Output Voltage Noise
To measure the output noise of the DAC, the setup schematically represented in Figure\nbsp{}ref:fig:detail_instrumentation_dac_setup was utilized. To measure the output noise of the DAC, the setup schematically represented in Figure\nbsp{}ref:fig:detail_instrumentation_dac_setup was used.
The DAC was configured to output a constant voltage (zero in this case), and the gain of the pre-amplifier was adjusted such that the measured amplified noise was significantly larger than the noise of the ADC. The DAC was configured to output a constant voltage (zero in this case), and the gain of the pre-amplifier was adjusted such that the measured amplified noise was significantly larger than the noise of the ADC.
The Amplitude Spectral Density $\Gamma_{n_{da}}(\omega)$ of the measured signal was computed, and verification was performed to confirm that the contributions of ADC noise and amplifier noise were negligible in the measurement. The Amplitude Spectral Density $\Gamma_{n_{da}}(\omega)$ of the measured signal was computed, and verification was performed to confirm that the contributions of ADC noise and amplifier noise were negligible in the measurement.
@ -13425,7 +13425,7 @@ The scanning range is constrained $\pm 100\,\mu m$ due to the limited acceptance
***** Slow scan ***** Slow scan
Initial testing utilized a scanning velocity of $10\,\mu m/s$, which is typical for these experiments. Initial testing were made with a scanning velocity of $10\,\mu m/s$, which is typical for these experiments.
Figure\nbsp{}ref:fig:test_id31_dy_10ums compares the positioning errors between open-loop (without NASS) and closed-loop operation. Figure\nbsp{}ref:fig:test_id31_dy_10ums compares the positioning errors between open-loop (without NASS) and closed-loop operation.
In the scanning direction, open-loop measurements reveal periodic errors (Figure\nbsp{}ref:fig:test_id31_dy_10ums_dy) attributable to the $T_y$ stage's stepper motor. In the scanning direction, open-loop measurements reveal periodic errors (Figure\nbsp{}ref:fig:test_id31_dy_10ums_dy) attributable to the $T_y$ stage's stepper motor.
These micro-stepping errors, which are inherent to stepper motor operation, occur 200 times per motor rotation with approximately $1\,\text{mrad}$ angular error amplitude. These micro-stepping errors, which are inherent to stepper motor operation, occur 200 times per motor rotation with approximately $1\,\text{mrad}$ angular error amplitude.
@ -13499,7 +13499,7 @@ For applications requiring small $D_y$ scans, the nano-hexapod can be used exclu
In diffraction tomography experiments, the micro-station performs combined motions: continuous rotation around the $R_z$ axis while performing lateral scans along $D_y$. In diffraction tomography experiments, the micro-station performs combined motions: continuous rotation around the $R_z$ axis while performing lateral scans along $D_y$.
For this validation, the spindle maintained a constant rotational velocity of $6\,\text{deg/s}$ while the nano-hexapod performs the lateral scanning motion. For this validation, the spindle maintained a constant rotational velocity of $6\,\text{deg/s}$ while the nano-hexapod performs the lateral scanning motion.
To avoid high-frequency vibrations typically induced by the stepper motor, the $T_y$ stage was not utilized, which constrained the scanning range to approximately $\pm 100\,\mu m/s$. To avoid high-frequency vibrations typically induced by the stepper motor, the $T_y$ stage was not used, which constrained the scanning range to approximately $\pm 100\,\mu m/s$.
The system performance was evaluated at three lateral scanning velocities: $0.1\,mm/s$, $0.5\,mm/s$, and $1\,mm/s$. Figure\nbsp{}ref:fig:test_id31_diffraction_tomo_setpoint presents both the $D_y$ position setpoints and the corresponding measured $D_y$ positions for all tested velocities. The system performance was evaluated at three lateral scanning velocities: $0.1\,mm/s$, $0.5\,mm/s$, and $1\,mm/s$. Figure\nbsp{}ref:fig:test_id31_diffraction_tomo_setpoint presents both the $D_y$ position setpoints and the corresponding measured $D_y$ positions for all tested velocities.
#+name: fig:test_id31_diffraction_tomo_setpoint #+name: fig:test_id31_diffraction_tomo_setpoint
@ -13541,7 +13541,7 @@ Alternatively, a feedforward controller could improve the lateral positioning ac
<<ssec:test_id31_cf_control>> <<ssec:test_id31_cf_control>>
# TODO - Add link to section # TODO - Add link to section
A control architecture utilizing complementary filters to shape the closed-loop transfer functions was proposed during the detail design phase. A control architecture based on complementary filters to shape the closed-loop transfer functions was proposed during the detail design phase.
Experimental validation of this architecture using the NASS is presented herein. Experimental validation of this architecture using the NASS is presented herein.
Given that performance requirements are specified in the Cartesian frame, decoupling of the plant within this frame was achieved using Jacobian matrices. Given that performance requirements are specified in the Cartesian frame, decoupling of the plant within this frame was achieved using Jacobian matrices.
@ -13692,7 +13692,7 @@ Moreover, the systematic approach to system development and validation, along wi
:END: :END:
<<sec:test_conclusion>> <<sec:test_conclusion>>
The experimental validation detailed in this chapter confirms that the Nano Active Stabilization System successfully augments the positioning capabilities of the micro-station, thereby enabling full utilization of the ESRF's new light source potential. The experimental validation detailed in this chapter confirms that the Nano Active Stabilization System successfully augments the positioning capabilities of the micro-station, thereby enabling full use of the ESRF's new light source potential.
A methodical approach was employed—first characterizing individual components and subsequently testing the integrated system—to comprehensively evaluate the NASS performance. A methodical approach was employed—first characterizing individual components and subsequently testing the integrated system—to comprehensively evaluate the NASS performance.
Initially, the Amplified Piezoelectric Actuators (APA300ML) were characterized, revealing consistent mechanical and electrical properties across multiple units. Initially, the Amplified Piezoelectric Actuators (APA300ML) were characterized, revealing consistent mechanical and electrical properties across multiple units.
@ -13736,7 +13736,7 @@ Through progressive modeling, from simplified uniaxial representations to comple
It was determined that an active platform with moderate stiffness offered an optimal compromise, decoupling the system from micro-station dynamics while mitigating gyroscopic effects from continuous rotation. It was determined that an active platform with moderate stiffness offered an optimal compromise, decoupling the system from micro-station dynamics while mitigating gyroscopic effects from continuous rotation.
The multi-body modeling approach, informed by experimental modal analysis of the micro-station, was essential for capturing the system's complex dynamics. The multi-body modeling approach, informed by experimental modal analysis of the micro-station, was essential for capturing the system's complex dynamics.
The Stewart platform architecture was selected for the active stage, and its viability was confirmed through closed-loop simulations employing a High-Authority Control / Low-Authority Control (HAC-LAC) strategy. The Stewart platform architecture was selected for the active stage, and its viability was confirmed through closed-loop simulations employing a High-Authority Control / Low-Authority Control (HAC-LAC) strategy.
This strategy incorporated a modified form of Integral Force Feedback (IFF), adapted to provide robust active damping despite the platform rotation and varying payloads. This strategy used a modified form of Integral Force Feedback (IFF), adapted to provide robust active damping despite the platform rotation and varying payloads.
These simulations demonstrated the NASS concept could meet the nanometer-level stability requirements under realistic operating conditions. These simulations demonstrated the NASS concept could meet the nanometer-level stability requirements under realistic operating conditions.
Following the conceptual validation, the detailed design phase focused on translating the NASS concept into an optimized, physically realizable system. Following the conceptual validation, the detailed design phase focused on translating the NASS concept into an optimized, physically realizable system.
@ -13749,7 +13749,7 @@ Instrumentation selection (sensors, actuators, control hardware) was guided by d
The final phase of the project was dedicated to the experimental validation of the developed NASS. The final phase of the project was dedicated to the experimental validation of the developed NASS.
Component tests confirmed the performance of the selected actuators and flexible joints, validated their respective models. Component tests confirmed the performance of the selected actuators and flexible joints, validated their respective models.
Dynamic testing of the assembled nano-hexapod on an isolated test bench provided essential experimental data that correlated well with the predictions of the multi-body model. Dynamic testing of the assembled nano-hexapod on an isolated test bench provided essential experimental data that correlated well with the predictions of the multi-body model.
The final validation was performed on the ID31 beamline, utilizing a short-stroke metrology system to assess performance under realistic experimental conditions. The final validation was performed on the ID31 beamline, using a short-stroke metrology system to assess performance under realistic experimental conditions.
These tests demonstrated that the NASS, operating with the implemented HAC-LAC control architecture, successfully achieved the target positioning stability – maintaining residual errors below $30\,\text{nm RMS}$ laterally, $15\,\text{nm RMS}$ vertically, and $250\,\text{nrad RMS}$ in tilt – during various experiments, including tomography scans with significant payloads. These tests demonstrated that the NASS, operating with the implemented HAC-LAC control architecture, successfully achieved the target positioning stability – maintaining residual errors below $30\,\text{nm RMS}$ laterally, $15\,\text{nm RMS}$ vertically, and $250\,\text{nrad RMS}$ in tilt – during various experiments, including tomography scans with significant payloads.
Crucially, the system's robustness to variations in payload mass and operational modes was confirmed. Crucially, the system's robustness to variations in payload mass and operational modes was confirmed.
@ -13762,7 +13762,7 @@ Although this research successfully validated the NASS concept, it concurrently
The manual tuning process employed to match the multi-body model dynamics with experimental measurements was found to be laborious. The manual tuning process employed to match the multi-body model dynamics with experimental measurements was found to be laborious.
Systems like the micro-station can be conceptually modeled as interconnected solid bodies, springs, and dampers, with component inertia readily obtainable from CAD models. Systems like the micro-station can be conceptually modeled as interconnected solid bodies, springs, and dampers, with component inertia readily obtainable from CAD models.
An interesting perspective is the development of methods for the automatic tuning of the multi-body model's stiffness matrix (representing the interconnecting spring stiffnesses) directly from experimental modal analysis data. An interesting perspective is the development of methods for the automatic tuning of the multi-body model's stiffness matrix (representing the interconnecting spring stiffnesses) directly from experimental modal analysis data.
Such a capability would enable the rapid generation of accurate dynamic models for existing end-stations, which could subsequently be utilized for detailed system analysis and simulation studies. Such a capability would enable the rapid generation of accurate dynamic models for existing end-stations, which could subsequently be used for detailed system analysis and simulation studies.
***** Better addressing plant uncertainty coming from a change of payload ***** Better addressing plant uncertainty coming from a change of payload
@ -13789,7 +13789,7 @@ Nevertheless, a more rigorous analysis of this control architecture and its comp
While the HAC-LAC approach demonstrated a simple and comprehensive methodology for controlling the NASS, sensor fusion represents an interesting alternative that is worth investigating. While the HAC-LAC approach demonstrated a simple and comprehensive methodology for controlling the NASS, sensor fusion represents an interesting alternative that is worth investigating.
While the synthesis method developed for complementary filters facilitates their design (Section ref:sec:detail_control_sensor), their application specifically for sensor fusion within the NASS context was not examined in detail. While the synthesis method developed for complementary filters facilitates their design (Section ref:sec:detail_control_sensor), their application specifically for sensor fusion within the NASS context was not examined in detail.
One potential approach involves fusing external metrology (utilized at low frequencies) with force sensors (employed at high frequencies). One potential approach involves fusing external metrology (used at low frequencies) with force sensors (employed at high frequencies).
This configuration could enhance robustness through the collocation of force sensors with actuators. This configuration could enhance robustness through the collocation of force sensors with actuators.
The integration of encoder feedback into the control architecture could also be explored. The integration of encoder feedback into the control architecture could also be explored.
@ -13803,11 +13803,11 @@ Yet, the development of such metrology systems is considered critical for future
Promising approaches have been presented in the literature. Promising approaches have been presented in the literature.
A ball lens retroreflector is used in [[cite:&schropp20_ptynam]], providing a $\approx 1\,\text{mm}^3$ measuring volume, but does not fully accommodate complete rotation. A ball lens retroreflector is used in [[cite:&schropp20_ptynam]], providing a $\approx 1\,\text{mm}^3$ measuring volume, but does not fully accommodate complete rotation.
In [[cite:&geraldes23_sapot_carnaub_sirius_lnls]], an interesting metrology approach is presented, utilizing interferometers for long stroke/non-rotated movements and capacitive sensors for short stroke/rotated positioning. In [[cite:&geraldes23_sapot_carnaub_sirius_lnls]], an interesting metrology approach is presented, using interferometers for long stroke/non-rotated movements and capacitive sensors for short stroke/rotated positioning.
***** Alternative Architecture for the NASS ***** Alternative Architecture for the NASS
The original micro-station design was driven by optimizing positioning accuracy, utilizing dedicated actuators for different DoFs (leading to simple kinematics and a stacked configuration), and maximizing stiffness. The original micro-station design was driven by optimizing positioning accuracy, using dedicated actuators for different DoFs (leading to simple kinematics and a stacked configuration), and maximizing stiffness.
This design philosophy ensured that the micro-station would remain functional for micro-focusing applications even if the NASS project did not meet expectations. This design philosophy ensured that the micro-station would remain functional for micro-focusing applications even if the NASS project did not meet expectations.
Analyzing the NASS as an complete system reveals that the positioning accuracy is primarily determined by the metrology system and the feedback control. Analyzing the NASS as an complete system reveals that the positioning accuracy is primarily determined by the metrology system and the feedback control.
@ -13857,7 +13857,7 @@ However, implementations of such magnetic levitation stages on synchrotron beaml
The application of dynamic error budgeting and the mechatronic design approach to an entire beamline represents an interesting direction for future work. The application of dynamic error budgeting and the mechatronic design approach to an entire beamline represents an interesting direction for future work.
During the early design phases of a beamline, performance metrics are typically expressed as integrated values (usually RMS values) rather than as functions of frequency. During the early design phases of a beamline, performance metrics are typically expressed as integrated values (usually RMS values) rather than as functions of frequency.
However, the frequency content of these performance metrics (such as beam stability, energy stability, and sample stability) is crucial, as factors like detector integration time can filter out high-frequency components. However, the frequency content of these performance metrics (such as beam stability, energy stability, and sample stability) is crucial, as factors like detector integration time can filter out high-frequency components.
Therefore, adopting a design approach utilizing dynamic error budgets, cascading from overall beamline requirements down to individual component specifications, is considered a potentially valuable direction for future investigation. Therefore, adopting a design approach using dynamic error budgets, cascading from overall beamline requirements down to individual component specifications, is considered a potentially valuable direction for future investigation.
* Bibliography :ignore: * Bibliography :ignore:
#+latex: \printbibliography[heading=bibintoc,title={Bibliography}] #+latex: \printbibliography[heading=bibintoc,title={Bibliography}]