Nonlinear Control of MEMSindividual.utoronto.ca/quanyan/docs/thesispresentation.pdf · 3 0 27 8 Aε...
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Nonlinear Control of MEMS: Modeling, Analysis and Design Quanyan Zhu, IEEE Member Software for Analysis and Design Department of Electrical and Computer Engineering Faculty of Engineering McGill University Montreal, Canada Presentation details on http://www.ece.mcgill.ca/~qzhu4 Contact: [email protected] or [email protected]
Transcript of Nonlinear Control of MEMSindividual.utoronto.ca/quanyan/docs/thesispresentation.pdf · 3 0 27 8 Aε...
Nonlinear Control of MEMS: Modeling, Analysis and Design
Quanyan Zhu, IEEE Member
Software for Analysis and DesignDepartment of Electrical and Computer Engineering
Faculty of Engineering
McGill UniversityMontreal, Canada
Presentation details on http://www.ece.mcgill.ca/~qzhu4Contact: [email protected] or [email protected]
Outline
1. Introduction2. Modeling and Analysis3. Finite Element Analysis4. Issues of Control5. Future Work6. Conclusion
MEMS: Micro-Electro-Mechanical Systems
MEMS RF Tunable Filter
Wide Applications:• Signal Processing• Biomimetic Sensors• Mass Data Storage• Integrated micro-optomechanicalcomponents• Embedded sensors• Integrated RF Circuit, etc.
airborne surveillance dust
Boeing Pressure Belt using MEMS
Sensor/Actuator
Introduction
Analysis
Design
Modeling1. Classical Mechanics2. Thermal Physics3. Electromagnetism4. Fluid Dynamics5. Quantum Physicsetc.
Fabrication
Control
1. Analytical Approach2. Semi-Analytical Approach3. Numerical Analysis:
Finite Element Method
1. Robust Control2. Distributed Control3. Hybrid ControlEtc.
• Design Software • Prototype Design
MEMS Fabrication
• Bulk micromachining• Surface micromachining• Go beyond microelectronics
fabricationMicrofabrication lab, Berkeley
Fundamental Fabrication Procedures
J. Bardeen, W.H. Brattain, “The first transistor, a semiconductor triode”, Phys. Rev., 74, 230 (1948).
Fundamental Structures: Beam
Cantilever-based devices:
2 2 2 2
2 2 2 2( ) ( , )u u uA EI f x tt x x x
ρ µ∂ ∂ ∂ ∂− + =
∂ ∂ ∂ ∂
• Versatile for a variety of applications• Fabrication simplicity• Better Sensitivity
Governing equation:
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x 10-4
-3
-2
-1
0
1
2
3
x 10-5
X - horizontal [m]
Y -
verti
cal
[m]
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x 10-4
-3
-2
-1
0
1
2
3
x 10-5
X - horizontal [m]
Y -
verti
cal
[m]
2µN on the tip produces a displacement of 3.0 µm
Material: PolysiliconE=165 GPa
•Electro-elastic problem•Thermo-elastic problem•Thermo-magnetic problem, etc
How about Coupling?
Simulation of a Linear Multiple Mode Resonator
102
103
104
105
106
-10
-9
-8
-7
-6
-5
Frequency (Hz)
log1
0(m
agni
tude
)
102
103
104
105
106
-200
-100
0
100
200
Frequency (Hz)
phas
e(de
gree
)
The response of vertical displacement of mass
102
103
104
105
106
-15
-14
-13
-12
-11
Frequency (Hz)
log1
0(m
agni
tude
)
102
103
104
105
106
-100
-50
0
50
100
Frequency (Hz)
phas
e(de
gree
)
The response of induced current in lower comb
From MEMS to NEMS
On
Off
SWNT Cantilever Van der Waals Force per unit length:
rLEq vdW
vdW d)/(d
=
∫∫=21 ,
2121
6621 dd
),()(
VVvdW VV
VVrCnnrEwhere
Simple Model of Electro-mechanical Coupling problem
1-D Governing equation
AtQGtGktGbtGm
ε2)())(()()(
2
0 −=−++ &&&
))()()((1)(A
tGtQtVR
tQ s ε−=&
Mechanical:
Electrical:
Coupled term
Coupled, Nonlinear, Second-order set of Equations: Potentially Unstable beyond a critical point: pull-in Voltage
0
30
278
εAkGV inpull =−
1/3 G0
V
x
G0
Vpull-in
1-D Simplified Analytical Solution stable
unstable
u
rxqr
qxvv
qvx
+
−−
+−−
=
3200
)1(1312 2ζ
&&& Normalized State-Space form of the dynamics
Some Nonlinear Control Scheme Might be Necessary!
( )kx
xsVF =−
= 20
20
2ε
Simulation of Simplified Model
40 60 80 100 120 140 160 180 200 220 2402
4
6
8
10
12
14
16
18
20
22
Pull-i
n Volt
ages
(V)
Length of the beam L (um)
O Experimental results
Simulation results
6 6.5 7 7.5 8 8.5 9 9.5 100
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Voltage V (v)
Gap d
istan
ce at
node
6 (u
m)
v1 a1
b1 g1
a2 a3
g
n1 n2 n3
n4 n5
•Beam: Nominal Lb=100um, w=2um, h=2um. Measured : L=100um, w=1.74um, h=2.003um(Error of 0.13%)•Gap plate: Lg=100um, w=10um, h=2.003um.
•Young’s Modulus: assume 165GPa.
•Fringing Effects Considered
•Pull-in Voltage Predicted at 8.56V
How to make this prediction more precise to include fringing effects, beam nonlinearity, and manufacturing error?
Finite Element Analysis
Strong Coupling procedure:
Simultaneous analysis in one solver
Conventional Week coupling procedure:
Iterative Finite Element Analysis in separate solves for different physics domain
Finite Element Analysis (Cont’d)Discretization of Element:
Monolithic Formulation:
MEMS Control Challenges• Single Device Stability
– Nonlinearity from the device– Ensure the device operate in stability– Manage the manufacture uncertainty and chaotic behavior
• Increasing Complexity of Device
– Conventional model-based optimization process sensitive to modeling errors.
– Learning-based approaches, such as neural network: hard to know the model.
– Both model-based and learning-based
Multi-variable Robust Control
P
∆
K
Model-based Neural Networks Control
MEMS Control Challenges (Cont’d)• Multi-device System Stability
– Distributed nature of MEMS: many embedded sensors and actuators interaction
– Need robust coordination: may elements can exhibit failures, delays and limited modeling ability in stochastic environment
Distributed Market-based Control (Game Theoretically Based Control) http://ho.seas.ucla.edu.
(local) (hierarchy)
Multivariable Robust Control• Present Control Design of the parallel-plate micro-actuator
– Simple feedback with a capacitor may stabilize the system
• Proposed Robust Control Design of the benchmark problem– Provide more feedback control perspective for more sophisticated
control– Directly deal with state-space of a control system – Deal with parametric uncertainty arising from manufacturing process
• Strong coupled finite element analysis for parameter identification
+V Device
Cf
Conclusion
• Study of MEMS involves the multidisciplinary study of multi-physics problems. Finite element analysis is a flexible tool for solving physical quantities.
• Different levels of control problem exist, both on device level and system-network level. Intelligent schemes such as market-based control and neural networks are worthy of investigation
• We will establish a link between finite element analysis and control design, which will be used for parameter identification
• Some Prospective Future Work– Other control scheme:
• Hybrid system optimal control• Neural Network based control• Game-theoretically based control
– Adaptive finite element scheme– Nano-beam structure
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