Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Structural and Multidisciplinary Optimization
Published in: Structural and Multidisciplinary Optimization 3/2019

21-03-2019 | Research Paper

Integrated optimization of 3D structural topology and actuator configuration for vibration control in ultra-precision motion systems

Authors: Jing Wang, Ming Zhang, Yu Zhu, Kaiming Yang, Xin Li, Leijie Wang, Jinchun Hu, Chuxiong Hu

Published in: Structural and Multidisciplinary Optimization | Issue 3/2019

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Ever-increasing demands for precision and efficiency in ultra-precision motion systems will result in a lightweight and flexible motion system with complex dynamics. In this paper, integrated optimization of 3D structural topology and actuator configuration is investigated to achieve better vibration control performance in ultra-precision motion systems. A material interpolation model with high accuracy is proposed for the integrated optimization; a simple integral equation utilizing R-functions and level-set functions is established to represent non-overlapping constraints of actuators. Over-actuation degrees are utilized to actively control the dominant flexible modes. The objective function is the weighted sum of natural frequencies of the selected flexible modes. Controllability of the controlled flexible modes is guaranteed, and controllability of residual (uncontrolled) flexible modes is restricted in optimization. Mechanical requirements on thrust to mass ratios and currents in actuators are also considered as design constraints. A two-loop solving strategy combining the genetic algorithm and the modified optimal criteria method is adopted for optimization solving. The proposed method is verified by designing a simplified fine stage in the wafer stage; the optimized result proved its effectiveness.
previous article Co-optimization of color and mechanical properties by volumetric voxel control
next article A performance measure approach for risk optimization

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Appendix
Available only for authorised users
Literature
Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Multidiscip Optim 1(4):193–202
Bendsøe MP (2004) Topology optimization: theory, methods, and applications. 2nd edn corrected printing. Springer
Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224MathSciNetMATHCrossRef
Biyikli E, To AC (2015) Proportional topology optimization: a new non-sensitivity method for solving stress constrained and minimum compliance problems and its implementation in matlab. PLoS One 10(12):e0145041CrossRef
Brauer JR (2014) Magnetic actuators and sensors. Wiley-IEEE
Bruns TE, Tortorelli DA (2001) Topology optimization of non-linear elastic structures and compliant mechanisms. Comput Methods Appl Mech Eng 190(26):3443–3459MATHCrossRef
Butler H (2013) Adaptive feedforward for a wafer stage in a lithographic tool. IEEE Trans Control Syst Technol 21(3):875–881CrossRef
de Roover D (1997) Motion control of a wafer stage: a design approach for speeding up ic production. Mechanical Maritime & Materials Engineering, Delft
Díaz AR, Lipton R, Soto CA (1995) A new formulation of the problem of optimum reinforcement of reissner-mindlin plates. Comput Methods Appl Mech Eng 123(1–4):121–139MathSciNetMATHCrossRef
Du J, Olhoff N (2007) Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps. Struct Multidiscip Optim 34(2):91–110MathSciNetMATHCrossRef
Eldred MS, Venkayya VB, Anderson WJ (1995) Mode tracking issues in structural optimization. AIAA J 33(10):1926–1933MATHCrossRef
Gawronski WK (1998) Dynamics and Control of Structures. Springer, New York
Herpen RV, Oomen T, Kikken E, Wal MVD, Aangenent W, Steinbuch M (2014) exploiting additional actuators and sensors for nano-positioning robust motion control. American Control Conference
Jensen JS, Pedersen NL (2006) On maximal eigenfrequency separation in two-material structures: the 1d and 2d scalar cases. J Sound Vib 289(4):967–986CrossRef
Jensen JS, Sigmund O (2005) Topology optimization of photonic crystal structures: a high-bandwidth low-loss t-junction waveguide. J Opt Soc Am B 22(6):1191–1198CrossRef
Kailath T (1980) Linear systems. Prentice-Hall, Englewood Cliffs
Kang Z, Wang Y (2013) Integrated topology optimization with embedded movable holes based on combined description by material density and level sets. Comput Methods Appl Mech Eng 255(255):1–13MathSciNetMATHCrossRef
Kim TS, Kim YY (2000) Mac-based mode-tracking in structural topology optimization. Comput Struct 74(3):375–383CrossRef
Laro D, Boshuizen R, Van Eijk J (2010) design and control of over-actuated lightweight 450 mm fine stage. Proceedings of the ASPE control topical meeting
Liu K (2014) An efficient 3d topology optimization code written in matlab. Springer-Verlag, Inc, New YorkCrossRef
Lu X, Usman IUR (2012) 6d direct-drive technology for planar motion stages. CIRP Ann Manuf Technol 61(1):359–362CrossRef
Ma ZD, Cheng HC, Kikuchi N (1994) Structural design for obtaining desired eigenfrequencies by using the topology and shape optimization method. Comput Syst Eng 5(1):77–89CrossRef
Ma ZD, Kikuchi N, Cheng HC, Hagiwara I (1995) Topological optimization technique for free vibration problems. J Appl Mech 62(62):357–358MathSciNetMATH
Ma ZD, Kikuchi N, Pierre C, Raju B (2006) Multidomain topology optimization for structural and material designs. J Appl Mech 73(4):565–573MathSciNetMATHCrossRef
Maeda Y, Nishiwaki S, Izui K, Yoshimura M, Matsui K, Terada K (2010) Structural topology optimization of vibrating structures with specified eigenfrequencies and eigenmode shapes. Int J Numer Methods Eng 67(5):597–628MathSciNetMATHCrossRef
Mei Y, Wang X (2004) A level set method for structural topology optimization and its applications. Elsevier Science Ltd, AmsterdamMATH
Onoda J, Haftka R (2013) Simultaneous structure/control optimization of large flexible spacecraft. Structures, Structural Dynamics and Materials Conference
Oomen T (2010) System identification for robust and inferential control: with applications to ILC and precision motion systems. Technische Universiteit Eindhoven
Oomen T, Herpen R van, Quist S, Wal M van de, Bosgra O, Steinbuch M (2012) next-generation wafer stage motion control: connecting system identification and robust control. American Control Conference
Pedersen NL (2000) Maximization of eigenvalues using topology optimization. Struct Multidiscip Optim 20(1):2–11CrossRef
Rankers AM (1997) Machine dynamics in mechatronic systems: an engineering approach. Universiteit Twente, Enschede
Ronde MJC, Schneiders MGE, Kikken E, Molengraft RVD, Steinbuch M (2014) Model-based spatial feedforward for over-actuated motion systems. Mechatronics 24(4):307–317CrossRef
Schneiders MGE, Molengraft RVD, Steinbuch M (2004) Modal framework for closed-loop analysis of over-actuated motion systems. Hal Archives 53(7)
Shapiro V (1991) Theory of r-functions and applications: a primer. Cornell University
Sigmund O (2001) A 99 line topology optimization code written in matlab. Struct Multidiscip Optim 21(2):120–127CrossRef
Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Multidiscip Optim 16(1):68–75
Sontag ED (1988) Mathematical control theory: deterministic finite dimensional systems. Texts Appl Math 40(92):28–30
Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373MathSciNetMATHCrossRef
Svanberg K, Werme M (2007) Sequential integer programming methods for stress constrained topology optimization. Struct Multidiscip Optim 34(34):277–299MathSciNetMATHCrossRef
van der Veen G, Langelaar M, van Keulen F (2014) Integrated topology and controller optimization of motion systems in the frequency domain. Struct Multidiscip Optim 51(3)
van der Veen G, Langelaar M, van der Meulen S, Laro D, Aangenent W, van Keulen F (2017) Integrating topology optimization in precision motion system design for optimal closed-loop control performance. Mechatronics 47:1–13
Venkayya VB (1989) Optimality criteria: a basis for multidisciplinary design optimization. Comput Mech 5(1):1–21MATHCrossRef
Xia L, Zhu J, Zhang W (2012) Sensitivity analysis with the modified heaviside function for the optimal layout design of multi-component systems. Comput Methods Appl Mech Eng 241-244(3):142–154MathSciNetMATHCrossRef
Xia L, Zhu J, Zhang W, Breitkopf P (2013) An implicit model for the integrated optimization of component layout and structure topology. Comput Methods Appl Mech Eng 257(257):87–102MathSciNetMATHCrossRef
Zhang W, Zhong W, Guo X (2015) Explicit layout control in optimal design of structural systems with multiple embedding components. Comput Methods Appl Mech Eng 290:290–313MathSciNetMATHCrossRef
Zhao Y, Zheng S, Wang H, Yang L (2015) Simultaneous optimization of photostrictive actuator locations, numbers and light intensities for structural shape control using hierarchical genetic algorithm. Adv Eng Softw 88(C):21–29CrossRef
Metadata
Title
Integrated optimization of 3D structural topology and actuator configuration for vibration control in ultra-precision motion systems
Authors
Jing Wang
Ming Zhang
Yu Zhu
Kaiming Yang
Xin Li
Leijie Wang
Jinchun Hu
Chuxiong Hu
Publication date
21-03-2019
Publisher
Springer Berlin Heidelberg
Published in
Structural and Multidisciplinary Optimization / Issue 3/2019
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-019-02244-4

Other articles of this Issue 3/2019

Structural and Multidisciplinary Optimization 3/2019 Go to the issue

Research Paper

Optimum design of large steel skeletal structures using chaotic firefly optimization algorithm based on the Gaussian map

Research Paper

Modified parameter-setting-free harmony search (PSFHS) algorithm for optimizing the design of reinforced concrete beams

Brief Note

Topology optimization under topologically dependent material uncertainties

Research Paper

Co-optimization of color and mechanical properties by volumetric voxel control

Industrial Application

Cavitation optimization of a throttle orifice plate based on three-dimensional genetic algorithm and topology optimization

Research Paper

A novel model modification method for support vector regression based on radial basis functions

Premium Partners

    Image Credits