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Journal ArticleDOI

Integrated Design and Control of Flexure-Based Nanopositioning Systems — Part I: Methodology

01 Jan 2011-IFAC Proceedings Volumes (Elsevier)-Vol. 44, Iss: 1, pp 9406-9412

Abstract: Flexure-based mechanisms, also referred to as flexures, are widely being used as motion-guidance, or bearing, elements in applications requiring multi-degree-of-freedom positioning and alignment. Unlike friction-bearings (such as sliding or rolling contact bearings), flexures can be designed to offer, to a large extent, reliable linear elastic motion with a high resolution (on the order of nanometers) over small ranges of motion (on order of micrometers). Example applications include positioning a probe or sample in atomic force microscopy, alignment of tool and sample in stamping processes, and fine-positioning of wafers and masks in semiconductor manufacturing. These applications are often required satisfy critical functional requirements, such as load-capacity, bandwidth, resolution, and range. A systematic approach is needed to simultaneously address the design and control challenges involved, starting from the initial design concept generation stage to the final control implementation and testing. In this paper, we present an integrated design and control method for implementing flexure-based nanopositioning systems. We discuss the need for varying design topology and order of a controller in design and control optimization. An automation engine generates a set of flexure-based design topologies and also controllers of varying order in the optimization. A simple 1-DOF example is worked out to illustrate the steps involved in using this methodology. The outcome of the exercise is a novel design topology, with it shape and size optimized, and a controller synthesized such that a desired control bandwidth and design requirements of strength and modal separation are met.
Topics: Integrated design (60%), Automation (52%)

Summary (3 min read)

1. INTRODUCTION

  • Precision positioning applications built around conventional bearings (such as sliding contact or rolling contact bearings) are often hindered by friction, backlash, hysteresis, and other motion non-linearities.
  • In Part I of this paper, a novel methodology integrating design and control considerations was presented.
  • The topology generation is aimed as a valuable addition to the design toolkit, facilitating novel designs that could not have been conceived otherwise.
  • The authors present a generic problem description, and then specify a set of critical Preprint submitted to 18th IFAC World Congress.
  • A piezoelectric stack actuator with a lever amplification mechanism is suggested for generating a large displacement range on the order of 100 μm required for the gap z.

2. INTEGRATED DESIGN AND CONTROL

  • Integrated design and control has been an active area of research spanning applications such as robotic manipulator design and control [17]-[22], motion stages developed using lead-screw drives [24], passive and active vibration isolation platforms [25, 26], and chemical process control [27].

2.1 Varying Design and/or Control Parameters

  • In what follows, the authors first review works reported on optimizing a or controller so that a desired performance metric ( or control) is met under physical constraints, and state/output and control constraints.
  • Different approaches for integrated design and control have been studied from an optimization theory standpoint in [17] and [15].
  • External damping such as squeeze film damping and foamdamping have been suggested and explored for flexures in the past.
  • The design and control performance space in terms of performance requirements, such as (i) the positioning error and (ii) control bandwidth of the drive and (iii) the maximum acceleration of the carriage, were captured for the entire range of geometry, material, and other parameters.
  • Preprint submitted to 18th IFAC World Congress.

2.2 Varying Design Topology

  • Unlike most of the methods reported above, few references address changing the design structure or configuration (referred to as the topology) itself, so that control performance is enhanced.
  • The authors examine here two specific cases from the literature that illustrate the importance of selecting an appropriate design topology before deploying any optimization routine.
  • Since the actuator and the sensor are not at the same location in space, i.e. the system is non-collocated.
  • In order to avoid the occurrence of the non-minimum phase zero, the actuation point shown in Fig. 1 (a) can be moved away from the motor closer to the end-point, as shown in Fig. 1(b).
  • The presence of the bearing translation mode is undesirable for two reasons: (i) the translation shows up in the displacement at the read head and (ii) the transfer function between the applied force and the measured displacement at read head can be non-minimum phase under certain 2.

3. PROPOSED METHOD

  • Based on the examples of integrated design and control described in Section 2, the authors identify the four possible cases for integrated design and control in Table 1.
  • In Case II, for a fixed design topology, the controller is allowed to vary.
  • The primitives are then subjected to these operations generate building blocks that meet the desired performance requirement.
  • Step 5: Optimization: Given that the nominal design and the nominal controller have passed the screening test, the authors now feed them to an optimization procedure.
  • If the performance requirements are not met at the end of the optimization procedure and the maximum number of iterations has not been reached, the nominal design topology is revised.

5. SUMMARY

  • The authors presented a method for iterating on design topologies and controller order to achieve a desired closed-loop system specification.
  • Instead, the authors need to iterate over design topologies and controller order.
  • An automated topology generation engine is discussed.
  • Further, a novel controller parameterization is used to vary the controller order while directly tuning the sensitivity function to a desired form.
  • The first author is thankful to Xerox Foundation and MIT Dean School of Engineering for fellowship support.

2.2 Problem Statement

  • The problem statement for applying the proposed integrated design and control methodology to the example of the positioning system of Fig. 2 is as follows: Given a lever amplification mechanism of Fig. 2 with the following parameters: (ii) output displacement yout measured at a distance Ls = 2.
  • The authors approach of integrated design and control is implemented for achieving this feature.
  • In the example of disk drive actuator system given in [4], altering geometry of the given topology eliminates nonminimum phase zeros.
  • In a actual multi-DOF system, given many constraints on geometry, and design requirements, both (i) varying parameters within a topology and (ii) varying the topology (and parameters within each topology) should be explored.
  • Preprint submitted to 18th IFAC World Congress.

2 in from the pivot.

  • Design a flexure-based pivot that meets the performance requirements given in Table 1.

3. IMPLEMENTATION OF METHODOLOGY

  • Given the above parameters for the lever and the piezoelectric stack actuator, the authors examine the topology, shape-size optimization and control performance of the system when a flexure-based mechanism is used as a pivot for the lever.
  • While the notch flexure joint in Fig. 5(a) has a localized compliance around its neck, the beam flexure of Fig. 5(b) has a compliance distributed over its length.
  • The rest of the design topologies shown in Figs. 5(c)(j) are obtained as follows.
  • The transfer function Yout(s)F (s) between the applied force input F (s) from the piezoelectric stack actuator to the output displacement Yout(s) is given by: Yout(s) F (s) =− { 1 ms2 + 2bys + 2ky } + Ls { La Js2 + 2bθs + 2kθ } (8) The first term in Eq. (8) corresponds to the contribution of the fundamental vertical (y) mode of the flexural pivot as seen at the output displacement measurement.
  • The details of the controller optimization are as follows: Control Parameter.

6. RESULTS AND DISCUSSION

  • An optimal solution was found for the case of flexurebased pivots of Fig. 5(g)-(j) for both the design and control optimization problems.
  • The design topologies of Fig. 5(c)-(f) turn out to be infeasible, the reason for which is discussed as follows.
  • Hence, the flexure-based pivots of Fig. 5(c)-(f) need to be discarded in their integrated design and control methodology.
  • The nominal sensitivity transfer function resulting from a nominal controller C0(s) = 1000s has a low bandwidth, while the desired sensitivity has a bandwidth of 1000 Hz, a rollon of 40db/dec.
  • Avoiding the non-minimum phase zero may require reconsidering where to measure relative to where the authors actuate the system.

7. SUMMARY

  • The authors presented a flow chart for iterating on design and controller to achieve a desired closedloop system specification.
  • An example of a flexure-based 1-DOF positioning system was worked out to show the integrated design and control methodology.
  • The methodology was worked out step-by-step to cover (i) generation of design topologies (ii) screening of topologies for obvious design choices that cannot work for the given application, (iii) optimization formulation in terms of design parameters, cost functions, and equality and inequality constraints, and (iv) controller generation based on model-matching of a sensitivity transfer function.
  • White JR, “The nanogate: nanoscale flow control,” Ph.D. dissertation, Cambridge, MA: Massachusetts Institute of Technology, Department of Mechanical Engineering, June 2003. [2].
  • Shilpiekandula V, “Progress through Mechanics: Small-scale Gaps,” Mechanics (Publication of the American Academy of Mechanics), vol. 35, no.

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MITSUBISHI ELECTRIC RESEARCH LABORATORIES
http://www.merl.com
Integrated Design and Control of
Flexure-Based Nanopositioning Systems -
Part I: Methodology
Shilpiekandula, V.; Youcef-Toumi, K.
TR2011-053 August 2011
Abstract
Flexure-based mechanisms, also referred to as flexures, are widely being used as motion-guidance,
or bearing, elements in applications requiring multi-degree-of-freedom positioning and align-
ment. Unlike friction-bearings (such as sliding or rolling contact bearings), flexures can be
designed to offer, to a large extent, reliable linear elastic motion with a high resolution (on the
order of nanometers) over small ranges of motion (on order of micrometers). Example applica-
tions include positioning a probe or sample in atomic force microscopy, alignment of tool and
sample in stamping processes, and fine-positioning of wafer steppers in semiconductor manu-
facturing. These applications are often required satisfy critical functional requirements, such as
load-capacity, bandwidth, resolution, and range. A systematic approach is needed to simultane-
ously address the design and control challenges involved, starting from the initial design concept
generation stage to the final control implementation and testing. In this paper, we present an
integrated design and control method for implementing flexurebased nanopositioning systems.
We discuss the need for varying design topology and order of a controller in design and con-
trol optimization. An automation engine generates a set of flexurebased design topologies and
also controllers of varying order in the optimization. A simple 1-DOF example is worked out to
illustrate the steps involved in using this methodology. The outcome of the exercise is a novel de-
sign topology, with it shape and size optimized, and a controller synthesized such that a desired
control bandwidth and design requirements of strength and modal separation are met.
World Congress of the International Federation of Automatic Control
This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part
without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include
the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of
the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or
republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All
rights reserved.
Copyright
c
Mitsubishi Electric Research Laboratories, Inc., 2011
201 Broadway, Cambridge, Massachusetts 02139

MERLCoverPageSide2

Integrated Design and Control of
Flexure-Based Nanopositioning Systems
Part I: Methodology
Vijay Shilpiekandula
1
and Kamal Youcef-Toumi
Mechatronics Research Laboratory,
Department of Mechanical Engineering,
77 Massachusetts Avenue, Cambridge MA 02139
Abstract: Flexure-based mechanisms, also referred to as flexures, are widely being used
as motion-guidance, or bearing, elements in applications requiring multi-degree-of-freedom
positioning and alignment. Unlike friction-bearings (such as sliding or rolling contact bearings),
flexures can be designed to offer, to a large extent, reliable linear elastic motion with a high
resolution (on the order of nanometers) over small ranges of motion (on order of micrometers).
Example applications include positioning a probe or sample in atomic force microscopy,
alignment of tool and sample in stamping processes, and fine-positioning of wafer steppers in
semiconductor manufacturing. These applications are often required satisfy critical functional
requirements, such as load-capacity, bandwidth, resolution, and range. A systematic approach
is needed to simultaneously address the design and control challenges involved, starting from
the initial design concept generation stage to the final control implementation and testing.
In this paper, we present an integrated design and control method for implementing flexure-
based nanopositioning systems. We discuss the need for varying design topology and order of a
controller in design and control optimization. An automation engine generates a set of flexure-
based design topologies and also controllers of varying order in the optimization. A simple 1-DOF
example is worked out to illustrate the steps involved in using this methodology. The outcome
of the exercise is a novel design topology, with it shape and size optimized, and a controller
synthesized such that a desired control bandwidth and design requirements of strength and
modal separation are met.
Keywords: Flexure-based mechanisms, Nanopositioning, Topology Generation, Synthesis.
1. INTRODUCTION
Precision linear positioning and angular (rotary) align-
ment at nanoscale resolutions are often referred to as
“nanopositioning.” Many applications for nanoposition-
ing systems have emerged over the past few decades in
various contexts, such as semiconductor manufacturing,
metrology, x-ray crystallography, and biological imaging.
From among the many different methods of implement-
ing nanopositioning systems, those involving compliant
flexure-based mechanisms have gained popularity over the
years. Flexure-based mechanisms are composed of slender
beam-like spring elements in their mechanical design; they
are close to being ideal motion bearings with minimal
friction, backlash, and other uncertainties. These advan-
tages make flexure-based mechanisms, also referred to
as flexures, ideal candidates for precision motion control
implementations.
1
Corresponding author: svijay@mit.edu
The drive for better performance steers high-resolution
designs towards satisfying stringent specifications in terms
of functional parameters such as range, load-capacity, and
bandwidth. While flexure-based nanopositioning systems
for such advanced nanotechnology applications have been
around for the past few decades [8], designing them for dy-
namic performance has received little attention. Kinematic
arrangement of parallel flexure systems using projection
geometry theory has been worked out in [9]. Analysis of the
statics [7] and dynamics of flexure-based mechanisms have
been extensively studied [11, 33]. However, few publica-
tions [12, 13] have appeared in the context of design for dy-
namic performance. The design of flexures in the context of
mechanical advantage is detailed in [12]. A finite-element
approach based on Euler-Bernoulli beam bending theory is
formulated for analyzing dynamics in [13] and optimizing
the design space for precision flexure-based applications
in [14].
While dynamic performance of just the flexure-based
mechanism or ‘plant’ presents one of the performance
requirements, a more challenging and critical requirement
CONFIDENTIAL. Limited circulation. For review only.
Preprint submitted to 18th IFAC World Congress. Received October 18, 2010.

is achieving an overall desired closed-loop control perfor-
mance [15] of a system assembled with the mechanism,
and suitable actuator and sensor subsystems. A poten-
tially useful approach in this context should be based on
integrating design and control methods right from design
conception and validation phase before hardware imple-
mentations are tested out. To the best of our knowledge, an
integrated approach for the design and control of flexure-
based nanopositioning systems is lacking in the existing
literature. A common systems-based methodology can fa-
cilitate developing valuable synthesis tools for achieving
the desired closed-loop control performance.
In this paper, we tackle the “co-design” problem, inte-
grating design and control for achieving a desired closed-
loop control performance of flexure-based nanopositioning
systems. In Section 2 we provide a detailed review of rele-
vant literature that tackle the co-design problem, while (i)
motivating the need for co-design from two practical servo-
hardware examples, and (ii) highlighting the deficiencies
in current approaches in the field of nanopositioning sys-
tems. A novel method for integrated design and control
is presented in Section 3, and tailored for flexure-based
mechanisms. A detailed set of steps needed to implement
the method is analyzed in Section 4. The paper concludes
with a summary in Section 5. The reader is referred to
Part II of this paper for an application case study of a
1-DOF alignment mechanism that is worked out in detail
using the proposed method.
2. INTEGRATED DESIGN AND CONTROL
Integrated design and control has been an active area of re-
search spanning applications such as robotic manipulator
design and control [17]-[22], motion stages developed using
lead-screw drives [24], passive and active vibration isola-
tion platforms [25, 26], and chemical process control [27].
In this section, we cover a detailed survey of relevant
methods in the literature.
2.1 Varying Design and/or Control Parameters
In what follows, we first review works reported on op-
timizing a design (plant) or controller so that a desired
performance metric (design or control) is met under phys-
ical (design) constraints, and state/output and control
constraints.
Optimal design and control of flexible structures has been
studied for (i) improving a mass efficiency metric (defined
as mass moved per unit work output) in [3], (ii) a quadratic
control performance index in [6], and (iii) a weighted
sum of structural mass and the energy of the controlled
mechanism in [26]. The integrated design and control prob-
lem was formulated as a multi-objective optimization in-
volving design and proportional-integral-derivative (PID)
controller parameters in [28] for mechatronic systems. A
similar approach optimizing proportional-derivative (PD)
controller parameters and design parameters for four-bar
linkages was studied in [18]. A non-linear optimization
formulation including design costs and a robust perfor-
mance constraint on the weighted sum of sensitivity and
complementary sensitivity functions is considered for a
chemical distillation column in [27]. Decentralized control
techniques were used to solve for the optimization of
passive (design parameters) and active (control param-
eters) for vibration isolation platforms in [25]. Different
approaches for integrated design and control have been
studied from an optimization theory standpoint in [17]
and [15]. These approaches include (i)sequential optimiza-
tion with design optimization followed by control opti-
mization, (ii)simultaneous design and control optimiza-
tion, and (iii)an iterative combination where the design
is initially optimized without affecting the controller, then
the controller is optimized, and such a cycle is iterated
until performance requirements are met.
Optimal locations for embedded actuators and sensors in
a mechanism with distributed compliance are discussed
in [16] for satisfying controllability and observability condi-
tions. However, neither the design of the controller nor the
influence of a poor design choice on control performance is
addressed in this reference. A related critical issue is one
of lightly damped flexible modes of flexure-based mech-
anisms. Physical damping is low in flexures made from
metals such as aluminium (used in development stages
of the design process for ease of machining), or titanium
(used in the implementation and testing phase because
of its high fatigue strength and other material properties).
External damping such as squeeze film damping and foam-
damping have been suggested and explored for flexures in
the past. Active damping through appropriate selection
of control strategies needs to be addressed to tackle the
lightly damped resonances in these structures. Since the
level of damping in an assembled mechanism is hard to
predict before the fabricated product is available for test-
ing, it becomes necessary to iterate the design process with
thorough system identification and testing of hardware
mechanism implementations.
Motion stages developed using lead-screw drives were char-
acterized for their dynamics and controlled with classical
lead-lag compensators in [24]. In this reference, the design
and control performance space in terms of performance
requirements, such as (i) the positioning error and (ii)
control bandwidth of the drive and (iii) the maximum
acceleration of the carriage, were captured for the entire
range of geometry, material, and other parameters. Since
lightly damped harmonics hinder control performance,
achieving robust passive damping with foam-based ma-
terials is proposed by the same research group in [38]. An
integrated design and control methodology for high-speed
control of robotic manipulators is presented in [21, 22].
Since unmodeled dynamics in the control bandwidth can
adversely affect the performance, it is necessary to account
for model-truncation errors in the design and control op-
timization. In this context, a constraint condition on the
Hankel norm of the truncated modes is formulated in the
optimization problem [21].
CONFIDENTIAL. Limited circulation. For review only.
Preprint submitted to 18th IFAC World Congress. Received October 18, 2010.

2.2 Varying Design Topology
Unlike most of the methods reported above, few refer-
ences address changing the design structure or configu-
ration (referred to as the topology) itself, so that control
performance is enhanced. We examine here two specific
cases from the literature that illustrate the importance of
selecting an appropriate design topology before deploying
any optimization routine.
Consider the example of a robotic system shown in Fig. 1
addressing the end-point control of a flexible link. The
actuator is a rotary servomotor that generates a torque
required for moving the end-point of the link. The feedback
signal is the end-point position, which can be recorded
by a sensor such as an accelerometer. Since the actuator
and the sensor are not at the same location in space,
i.e. the system is non-collocated. For the non-collocated
system, the flexibility of the link is known to cause non-
minimum phase zeros in the transfer function between the
voltage applied to the motor and the measured end-point
displacement [36].
In order to avoid the occurrence of the non-minimum phase
zero, the actuation point shown in Fig. 1 (a) can be moved
away from the motor closer to the end-point, as shown
in Fig. 1(b). With the actuation location moved closer
to the end-point, the portion of the link from the new
actuation point to the sensor location is shorter, and hence
stiffer. It is shown in [36] that, under certain geometry
conditions, this topology change results in moving the
zeros from the real-axis on to the imaginary axis, making
the system minimum-phase. The design topology change
shown in Fig. 1(b) is implemented in Fig. 1(c) using a
cable transmission from the motor.
Without this topology change, with the actuator just
as the motor and sensor at the end-point, the system
would be non-minimum phase and pose critical control
challenges.
2
We next consider the example of a hard disk drive actuator
subsystem in Fig. 2. As shown in Fig. 2 (a), this subsystem
positions the read (or write) head at the end of an
arm pivoting about a rotary bearing. A lorentz-force F
m
generated by voice coil motor at an distance R
e
causes
the arm to rotate about the pivot. However, the applied
force F
m
also exerts a force F
r
at the bearing, exciting
its translation mode. The displacement at the read head
is composed of the difference of modal responses arising
from the rigid body rotation and the bearing translation
mode.
The presence of the bearing translation mode is undesir-
able for two reasons: (i) the translation shows up in the
displacement at the read head and (ii) the transfer function
between the applied force and the measured displacement
at read head can be non-minimum phase under certain
2
The constraint on control bandwidth imposed by non-minimum
phase zeros is worked out for an example positioning system in Part
II of this pap er.
(a)
(b)
(c)
Point of
torque application
End point
Inner hub
Outer hub
Motor shaft
Arm
Link
Elastic
Coupler
Joint
Axle
Belt/
Cable
Actuator
(Motor)
τ
τ
Fig. 1. Design for control example from [36]. (a) Moving
the torque application point away from the hub and
closer to the end point of the flexible manipulator
results in minimum-phase dynamics, and hence allows
for higher control bandwidths. (b) A belt transmission
is used on a motor to vary the location of the torque
application point.
geometry conditions [37]. A novel actuator (see Fig. 2(b))
based on a set of magnetic arrays called Hallbach arrays is
designed in [35] to form a voice coil motor that generates
only a torque and now net translational force. The new
design topology is shown in Fig. 2(c) with the purely-
torque motor mounted in the pivot itself, without the need
for the linear force F
m
applied at the arm distance R
e
.
Without this design topology change, the translation of
the bearing and the non-minimum phase zero would limit
the performance of the read head.
In summary, the two examples discussed above emphasize
the need for developing suitable design topologies before
any optimization is attempted. An interesting extension
of this problem is one of identifying a set or library
of topologies from which we can select an appropriate
topology.
In what follows, we discuss our integrated design and
control method that is based on optimizing over a library
of topologies, not just dimensional (and other) parameters
within a given topology.
CONFIDENTIAL. Limited circulation. For review only.
Preprint submitted to 18th IFAC World Congress. Received October 18, 2010.

Figures (17)
Citations
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Journal ArticleDOI
Mojtaba Moradi1, Mahyar Naraghi1Institutions (1)
20 Jun 2016-
Abstract: Minimisation of shaking forces in mechanisms is an important issue in industry due to its destructive vibrations and acoustical disturbances. Practically, it may be impossible to eliminate the shaking forces because of many factors such as unfeasible counterweights and/or counter-rotators. However, it can be minimised. This paper presents a novel method, based on the closed-loop optimal control theory to indirectly minimise the shaking forces and input torques. To this end, the integrated design method is extended to closed-chain mechanisms. The proposed method is applied on a nonlinear position control problem. A slider-crank mechanism is utilised to validate the control algorithms. However, the proposed method can be simply extended to other mechanisms. The results indicate an impressive improvement in the shaking force reduction with an insignificant change in the control performance.

2 citations


Cites methods from "Integrated Design and Control of Fl..."

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Journal ArticleDOI
Brian P. Trease1, Yong Mo Moon2, Sridhar Kota1Institutions (2)
Abstract: Flexure joints are widely used to approximate the function of traditional mechanical joints, while offering the benefits of high precision, long life, and ease of manufacture. This paper investigates and catalogs the drawbacks of typical flexure connectors and presents several new designs for highly-effective, kinematically-behaved compliant joints. A revolute and a translational compliant joint are proposed (Figure 1), both of which offer great improvements over existing flexures in the qualities of (1) large range of motion, (2) minimal axis drift, (3) increased off-axis stiffness, and (4) reduced stress-concentrations. Analytic stiffness equations are developed for each joint and parametric computer models are used to verify their superior stiffness properties. A catalog of design charts based on the parametric models is also presented, allowing for rapid sizing of the joints for custom performance. Finally, two multi-degree-of-freedom joints are proposed as modifications to the revolute joint. These include a compliant universal joint and a compliant spherical joint, both designed to provide high degrees of compliance in the desired direction of motion and high stiffness in other directions.Copyright © 2002 by ASME

326 citations