phd-simscape-nano-hexapod/simscape-nano-hexapod.org

#+TITLE: Simscape Model - Nano Hexapod
:DRAWER:
#+LANGUAGE: en
#+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas

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* Notes                                                             :noexport:
** Notes
Prefix is =nhexa=

Based on:
- [ ] Stewart platform presentation: [[file:~/Cloud/meetings/group-meetings-me/2020-01-27-Stewart-Platform-Simscape/2020-01-27-Stewart-Platform-Simscape.org]]
- [ ] Add some sections from here: [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/index.org]]
  For instance:
  - [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/stewart-architecture.org][stewart architecture]]
  - [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/stewart_platform.org::+TITLE: Stewart Platform - Simscape Model]]
  - [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/kinematic-study.org][kinematic study]]
  - [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/identification.org][stewart platform - dynamics]]
  - [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/cubic-configuration.org][cubic configuration]]
- [ ] Look at the [[file:~/Cloud/work-projects/ID31-NASS/documents/state-of-thesis-2020/index.org][NASS 2020 report]]
  Sections 5.1, 5.4
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/amplified_piezoelectric_stack.org][amplified_piezoelectric_stack]] (Just use 2DoF here)
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/nano_hexapod.org][nano_hexapod]] (it seems this report is already after the detailed design phase: yes but some parts could be interesting)
- [ ] Should the study of effect of flexible joints be included here?
- [X] file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/control-vibration-isolation.org

Questions:
- [ ] The APA model should maybe not be used here, same for the nice top and bottom plates. Here the detailed design is not yet performed

** TODO [#A] Copy relevant parts of reports

- [ ] Stewart platform presentation: [[file:~/Cloud/meetings/group-meetings-me/2020-01-27-Stewart-Platform-Simscape/2020-01-27-Stewart-Platform-Simscape.org]]
- [ ] Add some sections from here: [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/index.org]]
  For instance:
  - [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/stewart-architecture.org][stewart architecture]]
  - [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/stewart_platform.org::+TITLE: Stewart Platform - Simscape Model]]
  - [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/kinematic-study.org][kinematic study]]
  - [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/identification.org]]
         Effect of joints stiffnesses
  - [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/cubic-configuration.org][cubic configuration]]
- [ ] Look at the [[file:~/Cloud/work-projects/ID31-NASS/documents/state-of-thesis-2020/index.org][NASS 2020 report]]
  Sections 5.1, 5.4
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/amplified_piezoelectric_stack.org][amplified_piezoelectric_stack]] (Just use 2DoF here)
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/nano_hexapod.org][nano_hexapod]] (it seems this report is already after the detailed design phase: yes but some parts could be interesting)
- [ ] Should the study of effect of flexible joints be included here?
- [X] file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/control-vibration-isolation.org

** DONE [#A] Make a nice outline
CLOSED: [2025-02-05 Wed 17:45]

*Introduction*
- Choice of architecture to do 5DoF control
- Stewart platform
- Need to model the active vibration platform
- Control

*1 - Active Vibration Platforms*:
Introduction:
Maybe no sections, just a review discussing several aspect of the platforms.
1. Review of active vibration platforms (focused on Synchrotron applications)
2. Serial and Parallel Architecture: advantages and disadvantages of both
3. Which architecture => Parallel manipulator? Why *Stewart platform*?

*2 - The Stewart Platform*:
Introduction: some history about Stewart platform and why it is so used
1. Architecture (plates, struts, joints)
2. Kinematics and Jacobian
4. Static Analysis
5. Dynamic Analysis: very complex => multi-body model
   For instance, compute the plant for massless struts and perfect joints (will be compared with Simscape model).
   But say that if we want to model more complex cases, it becomes impractical (cite papers).

*3 - Multi-Body model of the Stewart platform*:
Introduction: Complex dynamics => analytical formulas can be complex =>  Choose to study the dynamics using a multi-body model
1. Model definition: (Matlab Toolbox), frames, inertias of parts, stiffnesses, struts, etc...
2. Joints: perfect 2dof/3dof (+ mass-less)
3. Actuators: APA + Encoder (mass-less)
4. Nano-Hexapod: definition of each part + Plant with defined inputs/outputs (force sensor, relative displacement sensor, etc...)
   Compare with analytical formulas (see number of states)

*4 - Control of the Stewart Platform*:
Introduction: MIMO control => much more complex than SISO control because of interaction. Possible to ignore interaction when good decoupling (important to have tools to study interaction)
1. Centralized and Decentralized Control
2. Decoupling Control / Choice of control space file:~/Cloud/research/matlab/decoupling-strategies/svd-control.org
   Estimate coupling: RGA
   - Jacobian matrices, CoK, CoM, control in the frame of the struts, ...
   - Discussion of cubic architecture (quick, as it is going to be in detailed in chapter 2)
   - SVD, Modal, ...
3. Active Damping: decentralized IFF
   Guaranteed stability?
   For decentralized control: "MIMO root locus"
   How to optimize the added damping to all modes?
4. HAC-LAC
   Stability of closed-loop: Nyquist (main advantage: possible to do with experimental FRF)

*Conclusion*:
- Configurable Stewart platform model
- Will be included in the multi-body model of the micro-station => nass multi body model

** DONE [#A] Location of this report in the complete thesis
CLOSED: [2025-02-05 Wed 16:04]

*Before the report* (assumptions):
- Uniaxial model: no stiff actuator, HAC-LAC strategy
- Rotating model:
  Soft actuators are problematic due to gyroscopic effects
  Use moderately stiff (1um/N).
  IFF can be applied with APA architecture
- Model of Micro-station is ready

*In this report*:
- Goal: build a flexible (i.e. configurable) multi-body model of a Stewart platform that will be used in the next section to perform dynamical analysis and simulate experiments with the complete NASS
- Here, I propose to work with "perfect" stewart platforms:
  - almost mass-less struts
  - joints with zero stiffness in free DoFs (i.e. 2-DoF and 3-DoF joints)
- Presentation of Stewart platforms (Literature review about stewart platforms will be done in chapter 2)
- Presentation of the Simscape model

*After the report* (NASS-Simscape):
- nano-hexapod on top of micro-station
- control is performed
- simulations => validation of the concept

** TODO [#C] First time in the report that we speak about MIMO control ? Or maybe next section!

Maybe should introduce:
- "MIMO" Root locus
- "MIMO" Nyquist plot / characteristic loci

Or should this be in annexes?

Maybe say that in this phd-thesis, the focus is not on the control.
I tried multiple architectures (complementary filters, etc.), but the focus is not on that.

** QUES [#C] Cubic architecture should be the topic here or in the detailed design?

I suppose that it should be in the detailed design phase.
(Review about Stewart platform design should be made in Chapter two.)

Here, just use simple control architecture for general validation (and not optimization).

** QUES [#C] Should I make a review of control strategies?

Yes it seems to good location for review related to control.

Jacobian matrix.
Control is the frame of the struts, in the cartesian frame (CoM, CoK), modal control, etc...

[[file:~/Cloud/research/matlab/decoupling-strategies/svd-control.org][file:~/Cloud/research/matlab/decoupling-strategies/svd-control.org]]

** TODO [#C] Compare simscape =linearize= and analytical formula

- [X] OK for $\omega=0$ (using just the Stiffness matrix)
- [ ] Should add the mass matrix and compare for all frequencies

The analytical dynamic model is taken from cite:taghirad13_paral

** TODO [#C] Output the cubic configuration with clear display of the cube and center of the cube

[[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/cubic-configuration.org][cubic configuration]]

** TODO [#C] Make sure the Simulink file for the Stewart platform is working well

It should be the exact model reference that will be included in the NASS model.

** TODO [#C] Maybe make an appendix to present the developed toolbox?

* Introduction                                                        :ignore:

Introduction:
- Choice of architecture to do 5DoF control (Section ref:sec:nhexa_platform_review)
- Stewart platform (Section ref:sec:nhexa_stewart_platform)
  Show what is an hexapod, how we can define its geometry, stiffness, etc...
  Some kinematics: stiffness matrix, mass matrix, etc...
- Need to model the active vibration platform: multi-body model (Section ref:sec:nhexa_model)
  Explain what we want to capture with this model
  Key elements (plates, joints, struts): for now simplistic model (rigid body elements, perfect joints, ...), but in next section, FEM will be used
- Control (Section ref:sec:nhexa_control)

* Active Vibration Platforms
<<sec:nhexa_platform_review>>
** Introduction                                                      :ignore:

*Goals*:
- Explain why Stewart platform architecture is chosen
- Explain what is a Stewart platform (quickly as it will be shown in details in the next section)
- Quick review of active vibration platforms (5 or 6DoF)

Active vibration platform with 5DoF or 6DoF?
Synchrotron applications?


- Literature review? (*maybe more suited for chapter 2*)
  - file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/bibliography.org
  - Talk about flexible joint? Maybe not so much as it should be topic of second chapter.
    Just say that we must of flexible joints that can be defined as 3 to 6DoF joints, and it will be optimize in chapter 2.
- [[cite:&taghirad13_paral]]
- For some systems, just XYZ control (stack stages), example: holler
- For other systems, Stewart platform (ID16a), piezo based
- Examples of Stewart platforms for general vibration control, some with Piezo, other with Voice coil. IFF, ...
  Show different geometry configuration
- DCM: tripod?

** Active vibration control of sample stages

[[file:~/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/A0-nass-introduction/nass-introduction.org::*Review of stages with online metrology for Synchrotrons][Review of stages with online metrology for Synchrotrons]]

- [ ] Talk about external metrology?
- [ ] Talk about control architecture?
- [ ] Comparison with the micro-station / NASS

** Serial and Parallel Manipulators

*Goal*:
- Explain why a parallel manipulator is here preferred
- Compact, 6DoF, higher control bandwidth, linear, simpler

- Show some example of serial and parallel manipulators

- A review of Stewart platform will be given in Chapter related to the detailed design of the Nano-Hexapod

* The Stewart platform
:PROPERTIES:
:HEADER-ARGS:matlab+: :tangle matlab/nhexa_1_stewart_platform.m
:END:
<<sec:nhexa_stewart_platform>>
** Introduction                                                      :ignore:

# Most of this section is based on [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/kinematic-study.org][kinematic-study.org]]

- Some history about Stewart platforms
- What is so special and why it is so used in different fields: give examples
  Explain advantages compared to serial architecture
- Little review (very quick: two extreme sizes, piezo + voice coil)
  Complete review of Stewart platforms will be made in Chapter 2
- Presentation of tools used to analyze the properties of the Stewart platform => useful for design and control


** Matlab Init                                              :noexport:ignore:
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** Mechanical Architecture
<<ssec:nhexa_stewart_platform_architecture>>

file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/stewart-architecture.org

Presentation of the typical architecture
- Explain the different frames, etc...
- explain key elements:
  - two plates
  - joints
  - actuators

Make well defined notations.
- {F}, {M}
- si, li, ai, bi, etc.

- [ ] Make figure with defined frames, joints, etc...
  Maybe can use this figure as an example:
  [[file:/home/thomas/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/A0-nass-introduction/figs/introduction_stewart_du14.svg]]

** Kinematic Analysis
<<ssec:nhexa_stewart_platform_kinematics>>
**** Inverse Kinematics

**** Forward Kinematics

**** Jacobian Matrix

- Velocity Loop Closure
- Static Forces

**** Singularities

- Briefly mention singularities, and say that for small stroke, it is not an issue, the Jacobian matrix may be considered constant

** Static Analysis
<<ssec:nhexa_stewart_platform_static>>

How stiffness varies with orientation of struts.
Same with stroke?
Or maybe in the detailed chapter?

** Dynamic Analysis
<<ssec:nhexa_stewart_platform_dynamics>>

Very complex => multi-body model
For instance, compute the plant for massless struts and perfect joints (will be compared with Simscape model).
But say that if we want to model more complex cases, it becomes impractical (cite papers).

** Conclusion
:PROPERTIES:
:UNNUMBERED: t
:END:

All depends on the geometry.
Reasonable choice of geometry is made in chapter 1.
Optimization of the geometry will be made in chapter 2.

* Multi-Body Model
:PROPERTIES:
:HEADER-ARGS:matlab+: :tangle matlab/nhexa_2_model.m
:END:
<<sec:nhexa_model>>
** Introduction                                                      :ignore:

*Goal*:
- Study the dynamics of Stewart platform
- Instead of working with complex analytical models: a multi-body model is used.
  Complex because has to model the inertia of the struts.
  Cite papers that tries to model the stewart platform analytically
  Advantage: it will be easily included in the model of the NASS

- Mention the Toolbox (maybe make a DOI for that)

- [ ] Have a table somewhere that summarizes the main characteristics of the nano-hexapod model
  - location of joints
  - size / mass of platforms, etc...

** Matlab Init                                              :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
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#+begin_src matlab :exports none :results silent :noweb yes
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** Model Definition
<<ssec:nhexa_model_def>>

- [ ] Make a schematic of the definition process (for instance knowing the ai, bi points + {A} and {B} allows to compute Jacobian, etc...)

- What is important for the model:
  - Inertia of plates and struts
  - Positions of joints / Orientation of struts
  - Definition of frames (for Jacobian, stiffness analysis, etc...)

Then, several things can be computed:
- Kinematics, stiffness, platform mobility, dynamics, etc...


- Joints: can be 2dof to 6dof
- Actuators: can be modelled as wanted

** Nano Hexapod
<<ssec:nhexa_model_nano_hexapod>>

Start simple:
- Perfect joints, massless actuators

Joints: perfect 2dof/3dof (+ mass-less)
Actuators: APA + Encoder (mass-less)
- k = 1N/um
- Force sensor

Definition of each part + Plant with defined inputs/outputs (force sensor, relative displacement sensor, etc...)

** Model Dynamics
<<ssec:nhexa_model_dynamics>>

- If all is perfect (mass-less struts, perfect joints, etc...), maybe compare analytical model with simscape model?
- Say something about the model order
  Model order is 12, and that we can compute modes from matrices M and K, compare with the Simscape model
- Compare with analytical formulas (see number of states)

** Conclusion
:PROPERTIES:
:UNNUMBERED: t
:END:

- Validation of multi-body model in a simple case
- Possible to increase the model complexity when required
  - If considered 6dof joint stiffness, model order increases
  - Can have an effect on IFF performances: [[cite:&preumont07_six_axis_singl_stage_activ]]
  - Conclusion: during the conceptual design, we consider a perfect, but will be taken into account later
  - Optimization of the Flexible joint will be performed in Chapter 2.2
- MIMO system: how to control? => next section

* Control of Stewart Platforms
:PROPERTIES:
:HEADER-ARGS:matlab+: :tangle matlab/nhexa_3_control.m
:END:
<<sec:nhexa_control>>
** Introduction                                                      :ignore:

MIMO control: much more complex than SISO control because of interaction.
Possible to ignore interaction when good decoupling is achieved.
Important to have tools to study interaction
Different ways to try to decouple a MIMO plant.

Reference book: [[cite:&skogestad07_multiv_feedb_contr]]

** Matlab Init                                              :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
#+end_src

#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src

#+begin_src matlab :tangle no :noweb yes
<<m-init-path>>
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#+begin_src matlab :eval no :noweb yes
<<m-init-path-tangle>>
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#+begin_src matlab :noweb yes
<<m-init-other>>
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** Centralized and Decentralized Control
<<ssec:nhexa_control_centralized_decentralized>>

- Explain what is centralized and decentralized:
  - linked to the sensor position relative to the actuators
  - linked to the fact that sensors and actuators pairs are "independent" or each other (related to the control architecture, not because there is no coupling)
- When can decentralized control be used and when centralized control is necessary?
  Study of interaction: RGA

** Choice of the control space
<<ssec:nhexa_control_space>>

- [ ] file:~/Cloud/research/matlab/decoupling-strategies/svd-control.org

- Jacobian matrices, CoK, CoM, control in the frame of the struts, SVD, Modal, ...
- Combined CoM and CoK => Discussion of cubic architecture ? (quick, as it is going to be in detailed in chapter 2)
- Explain also the link with the setpoint: it is interesting to have the controller in the frame of the performance variables
  Also speak about disturbances? (and how disturbances can be mixed to different outputs due to control and interaction)
- Table that summarizes the trade-off for each strategy
- Say that in this study, we will do the control in the frame of the struts for simplicity (even though control in the cartesian frame was also tested)

** Active Damping with Decentralized IFF
<<ssec:nhexa_control_iff>>

Guaranteed stability: [[cite:&preumont08_trans_zeros_struc_contr_with]]
- [ ] I think there is another paper about that

For decentralized control: "MIMO root locus" can be used to estimate the damping / optimal gain
Poles and converging towards /transmission zeros/

How to optimize the added damping to all modes?
- [ ] Add some papers citations

Compute:
- [ ] Plant dynamics
- [ ] Root Locus

** MIMO High-Authority Control - Low-Authority Control
<<ssec:nhexa_control_hac_lac>>

Compute:
- [ ] compare open-loop and damped plant (outputs are the encoders)
- [ ] Implement decentralized control?
- [ ] Check stability:
  - Characteristic Loci: Eigenvalues of $G(j\omega)$ plotted in the complex plane
  - Generalized Nyquist Criterion: If $G(s)$ has $p_0$ unstable poles, then the closed-loop system with return ratio $kG(s)$ is stable if and only if the characteristic loci of $kG(s)$, taken together, encircle the point $-1$, $p_0$ times anti-clockwise, assuming there are no hidden modes
- [ ] Show some performance metric? For instance compliance?

** Conclusion
:PROPERTIES:
:UNNUMBERED: t
:END:


* Conclusion
:PROPERTIES:
:UNNUMBERED: t
:END:
<<sec:nhexa_conclusion>>

- Configurable Stewart platform model
- Will be included in the multi-body model of the micro-station => nass multi body model
- Control: complex problem, try to use simplest architecture

* Bibliography                                                        :ignore:
#+latex: \printbibliography[heading=bibintoc,title={Bibliography}]

* Helping Functions                                                 :noexport:
** Initialize Path
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%% Path for functions, data and scripts
addpath('./matlab/mat/'); % Path for data
addpath('./matlab/');     % Path for scripts
#+END_SRC

#+NAME: m-init-path-tangle
#+BEGIN_SRC matlab
%% Path for functions, data and scripts
addpath('./mat/'); % Path for data
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** Initialize other elements
#+NAME: m-init-other
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%% Colors for the figures
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