Hypothesizing a bipolar reference signal, it can be assumed that the range Vref > 0 corresponds to thesupply–user connection, while the field Vref < 0 corresponds to the user–discharge c
Trang 1Hypothesizing a bipolar reference signal, it can be assumed that the range Vref > 0 corresponds to the
supply–user connection, while the field Vref < 0 corresponds to the user–discharge connection The appropriate equation of flow above must be rewritten in the same way
Calculation of the conductance of the flow proportional valve is made considering the static and
dynamic link between the reference voltage Vref and the opening of the passage aperture A V in accordance with modeling of the second order of the type:
(20.65)
where ζ is the damping factor, σn is the valve’s natural frequency, and K s is its area static gain
Assuming a static relation of the linear type between the opening A V and the conductance C, as an
initial approximation, we get
(20.66)
where K V is the flow static gain of the valve, function of the maximum conductance Cmax, and of the
maximum value of the reference voltage Vref max:
(20.67)
The complete dynamic relation between reference voltage and conductance is, therefore,
(20.68)
The nonlinear model of the pneumatic servosystem with the position reference xset and the force
disturbance F e as inputs, is made up of a nonlinear system of nine equations, of order eight overall, of the type:
c) G1 = G1(C1, P1) order 0 flow rate of valve V1 (see (20.61)–(20.64))
d) G2 = G2(C2, P2) order 0 flow rate of valve V2 (see (20.61)–(20.64))
e) G1 = G1(P1, 1, x, ) order 1 continuity chamber 1 (see (20.58))
f) G2 = G2(P2, 2, x, ) order 1 continuity chamber 2 (see (20.59))
g) = (F e , P1, P2, ) order 2 piston equilibrium (see (20.60))
h) Vref 1 = Vref 1 (xset, xret) order 0 V1 valve control
i) Vref 2 = Vref 2(xset, xret) order 0 V2 valve control
If we want to carry out a linear analysis, it can be assumed that the equations a), b), g), h), i) are already
written in linear form
As far as the flow rates of valves c) and d) are concerned, it is hypothesized that the flow rate for each
of them is subsonic in feed, with Vref > 0, and sonic in discharge, with Vref < 0 This means that for valve
V1, for example, the pressure P1 must be within the range bP s < P1 ≤ Ps in feed and in the range P1 ≥ Pamb /b
d2AV
dt2
- 2zsndAV
dt
- + sn2AV
C = KcAV = KcKsVref = KVVref
KV Cmax
Vref max
-=
d2C
dt2
- 2zsndC
dt
- + sn2C
P˙ x˙
P˙ x˙
x˙˙ x˙˙ x˙
Trang 2Hypothesizing a bipolar reference signal, it can be assumed that the range Vref > 0 corresponds to the
supply–user connection, while the field Vref < 0 corresponds to the user–discharge connection The appropriate equation of flow above must be rewritten in the same way
Calculation of the conductance of the flow proportional valve is made considering the static and
dynamic link between the reference voltage Vref and the opening of the passage aperture A V in accordance with modeling of the second order of the type:
(20.65)
where ζ is the damping factor, σn is the valve’s natural frequency, and K s is its area static gain
Assuming a static relation of the linear type between the opening A V and the conductance C, as an
initial approximation, we get
(20.66)
where K V is the flow static gain of the valve, function of the maximum conductance Cmax, and of the
maximum value of the reference voltage Vref max:
(20.67)
The complete dynamic relation between reference voltage and conductance is, therefore,
(20.68)
The nonlinear model of the pneumatic servosystem with the position reference xset and the force
disturbance F e as inputs, is made up of a nonlinear system of nine equations, of order eight overall, of the type:
c) G1 = G1(C1, P1) order 0 flow rate of valve V1 (see (20.61)–(20.64))
d) G2 = G2(C2, P2) order 0 flow rate of valve V2 (see (20.61)–(20.64))
e) G1 = G1(P1, 1, x, ) order 1 continuity chamber 1 (see (20.58))
f) G2 = G2(P2, 2, x, ) order 1 continuity chamber 2 (see (20.59))
g) = (F e , P1, P2, ) order 2 piston equilibrium (see (20.60))
h) Vref 1 = Vref 1 (xset, xret) order 0 V1 valve control
i) Vref 2 = Vref 2(xset, xret) order 0 V2 valve control
If we want to carry out a linear analysis, it can be assumed that the equations a), b), g), h), i) are already
written in linear form
As far as the flow rates of valves c) and d) are concerned, it is hypothesized that the flow rate for each
of them is subsonic in feed, with Vref > 0, and sonic in discharge, with Vref < 0 This means that for valve
V1, for example, the pressure P1 must be within the range bP s < P1 ≤ Ps in feed and in the range P1 ≥ Pamb /b
d2AV
dt2
- 2zsndAV
dt
- + sn2AV
C = KcAV = KcKsVref = KVVref
KV Cmax
Vref max
-=
d2C
dt2
- 2zsndC
dt
- + sn2C
P˙ x˙
P˙ x˙
x˙˙ x˙˙ x˙
Trang 3
theory and mechanics comprise the fundamentals for analysis, modeling, simulation, design, and opti-mization, while fabrication is based on the micromachining and high-aspect-ratio techniques and pro-cesses, which are the extension of the CMOS technologies developed to fabricate ICs For many years, the developments in microelectromechanical systems (MEMS) have been concentrated on the fabrica-tion of microstructures adopting, modifying, and redesigning silicon-based processes and technologies commonly used in integrated microelectronics The reason for refining of conventional processes and technologies as well as application of new materials is simple: in general, microstructures are three-dimensional with high aspect ratios and large structural heights in contrast to two-three-dimensional planar microelectronic devices Silicon structures can be formed from bulk silicon micromachining using wet
or dry processes, or through surface micromachining Metallic micromolding techniques, based upon photolithographic processes, are also widely used to fabricate microstructures Molds are created in polymer films (usually photoresist) on planar surfaces, and then filled by electrodepositing metal (elec-trodeposition plays a key role in the fabrication of the microstructures and microdevices, which are the components of MEMS) High-aspect ratio technologies use optical, e-beam, and x-ray lithography to create trenches up to 1 mm deep in polymethylmethacrylate resist on the electroplating base (called seed layer) Electrodeposition of magnetic materials and conductors, electroplating, electroetching, and lift-off are extremely important processes to fabricate microscale structures and devices Though it is recog-nized that the ability to use and refine existing microelectronics fabrication technologies and materials
is very important, and the development of novel processes to fabricate MEMS is a key factor in the rapid growth of affordable MEMS, other emerging areas arise In particular, devising, design, modeling, analysis, and optimization of novel MEMS are extremely important Therefore, recently, the MEMS theory and microengineering fundamentals have been expanded to thoroughly study other critical prob-lems such as the system-level synthesis and integration, synergetic classification and analysis, modeling and design, as well as optimization This chapter studies the fabrication, analysis, and design problems for electromagnetic microstructures and microdevices (microtransducers with ICs) The descriptions of the fabrication processes are given, modeling and analysis issues are emphasized, and the design is performed
Design and Fabrication
In MEMS, the fabrication of thin film magnetic components and microstructures requires deposition of conductors, insulators, and magnetic materials Some available bulk material constants (conductivity σ, resistivity ρ at 20°C, relative permeability µr, thermal expansion t e, and dielectric constant—relative permittivity r) in SI units are given in Table 20.12
Aluminum 3.82 × 107 0.26 × 10−7 1.00000065 25
Nickel 1.45 × 107 0.69 × 10−7 600 nonlinear NA
0066_Frame_C20.fm Page 97 Wednesday, January 9, 2002 1:44 PM