FPGA-Based Computed Force Control System
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1238 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 4, APRIL 2009
FPGA-Based Computed Force Control System UsingElman Neural Network for Linear Ultrasonic Motor
Faa-Jeng Lin, Senior Member, IEEE, Ying-Chih Hung, and Syuan-Yi Chen
AbstractA field-programmable gate array (FPGA)-basedcomputed force control system using an Elman neural network(ENN) is proposed to control the mover position of a linearultrasonic motor (LUSM) in this paper. First, the structure andoperating principle of the LUSM are introduced. Then, the dy-namics of the LUSM mechanism with the introduction of a lumpeduncertainty, which include the friction force, are derived. Sincethe dynamic characteristics and motor parameters of the LUSMare nonlinear and time varying, a computed force control systemusing ENN is designed to improve the control performance forthe tracking of various reference trajectories. The ENN with bothonline learning and excellent approximation capabilities is em-
ployed to estimate a nonlinear function including the lumped un-certainty of the moving table mechanism. Moreover, the Lyapunovstability theorem and the projection algorithm are adopted toensure the stability of the control system and the convergence ofthe ENN. Furthermore, an FPGA chip is adopted to implementthe developed control algorithm for possible low-cost and high-performance industrial applications. The experimental resultsshow that excellent positioning and tracking performance areachieved, and the robustness to parameter variations and frictionforce can be obtained as well using the proposed control system.
Index TermsComputed force control, Elman neural network(ENN), field-programmable gate array (FPGA), linear ultrasonicmotor (LUSM).
I. INTRODUCTION
THE TECHNOLOGIES concerning biotechnology,
semiconductor-, nanotechnology, etc., have recently
experienced innovation in high-precision accuracy. Therefore,
the precise positioning technologies are required in many fields
particularly for the advancement of the semiconductor manu-
facturing equipment. These types of manufacturing equipment
require high-precision positioning, multidimensional drive,
miniaturization, and lightweight. Piezoelectric ceramic linear
ultrasonic motors (LUSMs) are one of the new kinds of ultra-
sonic motors which are driven by the ultrasonic vibration force
of piezoelectric ceramic elements and the mechanical friction
effect [1][3]. Different constructions and driving principles ofLUSMs have been reported [3], [4]. They permit high precision,
fast control dynamics, and large driving force in small
dimensions. Thus, some precision motion control stages using
LUSMs, which are small, light, and high-precise positioning,
have been developed for industrial applications [5], [6]. How-
Manuscript received April 23, 2008; revised September 11, 2008. Firstpublished October 31, 2008; current version published April 1, 2009. This workwas supported by the National Science Council, Taiwan, under Grant NSC95-2221-E-008-177-MY3.
The authors are with the Department of Electrical Engineering, NationalCentral University, Chungli 320, Taiwan (e-mail: [email protected];[email protected]; [email protected]).
Digital Object Identifier 10.1109/TIE.2008.2007040
ever, the control accuracy of the LUSMs is much influenced by
the existence of uncertainties, which usually comprises parame-
ter variations, external disturbances, high-order dynamics, etc.
Moreover, the frictional force dynamics between two moving
bodies should also be considered in the linear actuator systems.
Furthermore, the mathematical models of piezoelectric ceramic
LUSMs are complex, and the motor parameters are time vary-
ing due to increasing in temperature and changing in motor
drive operating conditions. In short, the control characteristics
of the LUSMs are complicated and highly nonlinear. Therefore,
the intelligent control approaches are good candidates tocontrol the single-axis motion control stage using LUSMs
for high-performance applications due to their ability of to
approximate nonlinear and time-varying system without using
the mathematical models of the controlled system.
There have been many researchers using intelligent control
approaches to represent complex plants and construct advanced
controllers [7]. Although the Elman neural network (ENN) was
first proposed for speech processing [8] it has been widely
applied in dynamical systems identification and control due to
its distinguished dynamical characteristics [9][11]. Generally,
ENN can be considered as a special kind of feedforward
neural network with additional memory neurons [8]. Due to
the context neurons, it has certain dynamical advantages overstatic neural network, such as multilayer perceptrons and radial-
basis function networks (RBFNs). Furthermore, the ENN can
approximate a high-order system with high precision and fast
convergence speed.
The recurrent neural networks such as recurrent RBFN
and recurrent neural network (RNN), which are always self-
feedback in hidden-layer neurons or in output neurons, have
received increasing attention due to its structural advantage
in nonlinear system modeling and dynamic system control
[5], [12], [13]. The most important characteristic of recurrent
neural networks is its self-connection to memorize feedback
information of the history influence in the same neuron. In thispaper, the adopted ENN can be considered as a special type of
recurrent neural network with feedback connections from the
hidden layer to the context layer in which the context layer is
an addition layer and used as an extra memory to memorize
previous activations of the hidden neurons and feed to all the
hidden neurons after one-step time delay. Therefore, compared
to the general recurrent neural networks, ENN has a special
explicit memory to store the temporal information. Moreover,
in the recurrent RBFN and RNN, the specific self-connection
feedback of the hidden neuron or output neuron is responsible
to memorize the specific previous activation of the hidden
neuron or output neuron and feed to itself only. Therefore,
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the outputs of the other neurons have no ability to affect the
specific neuron. However, in the complicated and nonlinear
dynamic system, the inherent cross-coupled interference and
effect of each state are always existent and serious. Hence,
if each neuron in the recurrent neural networks is considered
as a state in nonlinear dynamic systems, the self-connection
feedback type is unable to approximate the dynamic systemsefficiently. On the other hand, the feedbacks in ENN not only
are self-connection but also store in the context neurons and
feed to all the hidden neurons. Thus, the structure of ENN is
more powerful than general recurrent neural networks to deal
with nonlinear dynamic systems due to the cross-coupled inter-
ference and effect of each state can be approximated efficiently
with the additional context layer [13], [14]. Therefore, since
the nonlinear function including the lumped uncertainty of the
LUSM dynamics is very complicated, the ENN is more suitable
than the other recurrent neural networks to be adopted as a
nonlinear function estimator.
Field-programmable gate array (FPGA) incorporates the ar-
chitecture of gate arrays and the programmability of a program-
mable logic device. It consists of thousands of logic gates, some
of which are combined together to form a configurable logic
block thereby simplifying high-level circuit design. Intercon-
nections between logic gates using software are externally de-
fined through SRAM and ROM, which will provide flexibility
in modifying the designed circuit without altering the hardware.
Moreover, concurrent operation, simplicity, programmability, a
comparatively low cost, and rapid prototyping make it the fa-
vorite choice for prototyping an application-specified integrated
circuit (ASIC) [15], [16]. All the internal logic elements and all
the control procedures of the FPGA are executed continuously
and simultaneously. On the other hand, the control algorithmis executed sequentially using software in a digital signal
processor (DSP) or personal computer (PC), and the minimum
execution time is limited. Therefore, the execution time of the
FPGA is faster than DSP and PC. Furthermore, the circuits
and algorithms can be developed in the Very High Speed
Integrated Circuit Hardware Description Language (VHDL)
[15], [16]. This method is as flexible as any software solution.
Another important advantage of VHDL is that it is technol-
ogy independent. The same algorithm can be synthesized into
any FPGA and even has a direct path to an ASIC to open
interesting possibilities in industrial applications in terms of
performance and cost. However, the major disadvantage of anFPGA-based system for hardware implementation is the limited
capacity of available cells. Therefore, in the past decade, only
research on FPGA-based sliding mode, proportional-integral
differential, and fuzzy controllers can be found in control
application literatures [17][21]. Recently, some FPGA-based
motor applications using neural networks have been found [22],
[23]. Nevertheless, the FPGA-based neural network control
systems proposed by the aforementioned literatures do not
possess the online learning capability. In this paper, the FPGA
chip is adopted to implement the proposed neural network
control system with online learning capability in order to allow
possible low-cost and high-performance industrial applications.
In addition, the developed VHDL code can easily be modifiedand implemented to control any type of ac motors as well.
In this paper, an FPGA-based computed force control system
using ENN is developed to control the mover position of
an LUSM to track periodical step command, sinusoidal, and
trapezoidal reference trajectories with accuracy tracking per-
formance. First, in order to obtain the simplified control design,
the single-axis dynamics of the LUSM with the introduction
of a lumped uncertainty, which includes parameter variations,external disturbances, and friction force, are derived. Then, a
computed force control system using ENN is proposed where
the ENN with accurate approximation capability is employed to
estimate a nonlinear function including the lumped uncertainty
of the moving table mechanism. Moreover, a robust compen-
sator is proposed to confront the minimum approximation error.
Furthermore, an adaptive learning algorithm for the online
training of the ENN is derived using the Lyapunov theorem to
guarantee closed-loop tracking stability. In addition, to ensure
the convergence of the ENN, the adaptive learning algorithm is
further modified using the projection algorithm. Additionally,
the circuits design of the proposed intelligent control system
via an FPGA chip is discussed. Finally, experimentation is
carried out to investigate the effective of the proposed control
scheme.
II. LUSM MOTION CONTROL STAGE
A. Motion Control Stage
The motion control stage can be divided into two parts: the
LUSM servodrive and the motion control stage. The AB1A-
SP-E1 drive manufactured by Nanomotion Corp. is adopted for
the single-axis servodrive. Moreover, the motion control stage
comprises one SP series LUSM, the SP1-02 LUSM, which isalso manufactured by the Nanomotion Corporation. The travel
of the moving table of the motion control stage is linear. The
moving table is directly driven using the spacer of the LUSM.
The structure of the SP series LUSMs is a large face of
a relatively thin rectangular piezoelectric ceramic device, as
shown in Fig. 1(a) [3], [4]. Four electrodes (A, A, B, and B)are bounded to the front face to form a checkerboard pattern
of rectangles, and each substantially covers one quarter of this
face. The rear face is substantially fully covered with a single
electrode. Diagonally located electrodes (A, A, B, and B)are electrically connected by wires. The single electrode on
the rear face is grounded via the tuning inductor that canchange the resonant frequency. The movement of LUSM is
constrained by four support springs with large stiffness. These
support springs along a pair of long edges of the LUSM contact
the piezoelectric ceramic at points of zero movement in the
x-direction. A relatively hard ceramic spacer is attached withcement to a short edge of piezoelectric ceramic at the center
of the edge. A preload spring is preferably pressed against the
middle of a second short edge of piezoelectric ceramic opposite
to the short edge with the spacer. The preload spring supplies
pressure between the spacer and the moving table that causes
the motion of the spacer to be transmitted to the moving table.
A friction force takes place at the surface between the spacer
and the table. The face of the spacer pressed against the table isdesigned to move away from the table during part of the cycle
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Fig. 1. Operating principles of LUSM. (a) Structure of piezoelectric ceramicLUSM. (b) Vibration modes of LUSM.
when the spacer is moving opposite to the direction of motion
applied to the table.
The operation of the SP series LUSMs are based on the
double-mode vibrations, i.e., bending and longitudinal modes,
as shown in Fig. 1(b) [3], [4]. Using the bending mode in the
x-direction and the longitudinal mode in the y-direction leads
to the desired elliptical motion of the surface points in thexy-plane. The left-hand picture in Fig. 1(b) shows the defor-mation of the LUSM for the bending mode. A cross-sectional
area in the xz-plane is displaced in the x-direction and revolvedabout the z-axis. The displacement and the rotation of the cross-sectional area are denoted as x and , respectively. The vi-brating nodes of this mode are in the middle, up, and down parts
of the LUSM. The right-hand picture in Fig. 1(b) shows the
deformation of the LUSM for the longitudinal mode. A cross-
sectional area in the xz-plane is displaced in the y-direction,and the displacement of the cross-sectional area is denoted as
y. The longitudinal mode has a vibrating node in the middleof the LUSM. In order to obtain maximum displacements, the
modes have to be excited in resonance. An elliptical motion canonly be obtained if the resonant frequencies of the two modes
are equal or at least very close to each other. Thus, one has to
choose the length and the width of the piezoelectric ceramic to
determine the resonant frequency.
The output of the controller is the command voltage (con-
trol effort) of the LUSM servodrive. Moreover, the command
voltage with 10 V is applied to the drive AB1A-SP-E1. The
drive generates a fixed frequency (39.6 kHz) sine wave voltagewhose amplitude (0260 Vrms) is a function of the applied
command voltage (010 V). Furthermore, the generated sine
wave voltage drives the LUSM, and then generates thrust force
and velocity to rotate the moving table to reach the desired
position. When the command voltage is positive, the electrodes
A and A, shown in Fig. 1(a), are electrified, and B and B,shown in Fig. 1(a), are left floating (or grounded), and the
moving table moves to the right; when the command voltage
is negative, the electrodes B and B are electrified, and A andA are left floating (or grounded), and the moving table movesto the left.
B. Modeling of Motion Control Stage
For a friction drive system of single-axis LUSM mechanism,
according to the Newtonian law, the dynamic motion equation
can be assumed to take the following form:
FD = Md(t) + Dd(t) + (f(v) + FL) = KfU (1)
where M denotes the equivalent mass of the single-axis mech-anism; D denotes the viscous friction; FL is the externaldisturbance term; d denotes the position of the moving stage;
v denotes the velocity of the moving stage; d denotes thesecond-order derivative of d with respect to time; Kf denotesthe nominal voltage-to-force coefficient of an LUSM drive; Udenotes the control effort, i.e., the thrust voltage command;
and f is the lumped friction force includes the static friction,Coulomb friction, and viscous friction between the moving
table and the sliders. The friction force can be formulated as
follows [24], [25]:
f(v) = FCsgn(v) + (FS FC)e(v/vs)
2
sgn(v) + Kvv (2)
where FC is the Coulomb friction; FS is the static friction; vS is
the Stribeck velocity parameter; Kv is the coefficient of viscousfriction; and sgn() is a sign function. All the parameters in (2)are time varying.
Although the thrust force of LUSM can be simplified, as
shown in (1), however, considering the variation of system
parameters and external disturbances including friction force,
the motion control stage is a nonlinear time-varying system in
practical applications.
III. PROPOSED COMPUTED FORCE CONTROL SYSTEM
In order to control the motion control stage, a computed
force control system with ENN estimator is developed, asshown in Fig. 2. Assuming that the system parameter variations
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Fig. 2. Block diagram of computed force control system with ENN estimator.
and external disturbance are absent, then LUSM drive can be
formulated by rewriting (1) as follows:
d(t) = D
Md(t) +
Kf
MU And(t) + BnU (3)
where An = D/M; Bn = Kf/M > 0. The overbar symbolrepresents the system parameter in the nominal condition. Now,
considering the existence of parameter variations and external
force disturbances including friction force for the LUSM drive
system, then
d(t) = (An+A)d(t)+ (Bn+B)U+(Cn+C) [FL+f(v)]
= And(t)+ BnU+L(t) (4)
where Cn = 1/M; A, B, and C denote the uncertain-ties introduced by system parameters M and D; and L(t) iscalled the lumped uncertainty defined as
L(t) = Ad(t) + BU + (Cn + C) [FL + f(v)] . (5)
Here, the bound of the lumped uncertainty is assumed to be
known, i.e.,
|L(t)| (6)
where is a given positive constant. To confront these unpre-dictable uncertainties existing in the LUSM drive system, a
computed force control system is proposed.
The control problem is to find a control law so that the state
d(t) can track the desired command dm(t) accurately underthe occurrence of the uncertainties. To achieve this control
objective, define the tracking error and its derivative as follows:
e(t) = dm(t) d(t) (7)
e(t) =
dm(t)
d(t) (8)e(t) = dm(t) d(t). (9)
Substitute (9) into (4), then
e(t) = dm(t) And(t) BnU L(t). (10)
According to (10), the perfect equivalent control law U of Ucan be designed as follows:
U = B1n
dm(t) And(t) L(t)
+ z(t) (11)
where z(t) is designed as z(t) = z1e + z2e, in which z1 and z2are nonzero positive constants. Substituting (11) into (10), the
following error dynamic equation can be obtained:
e + Bnz1e + Bnz2e = 0 (12)
which implies limt0 e(t) = 0. However, the products of Bnand zi are difficult to obtain since Bn is an unknown systemparameter. Therefore, an auxiliary proportional-derivative (PD)
controller u(t) is adopted to replace z(t) to obtain the samecontrol performance. The PD controller u(t) is designed asu(t) = k1e + k2e, in which k1 and k2 are nonzero positiveconstants. Moreover, rewrite the perfect equivalent control
law (11) as
U = W + u(t) (13)
where the nonlinear function W is defined as
W = B1n
dm(t) And(t) L(t)
. (14)
Then, the proposed ideal computed force control law is
designed as
Ueq = U
= W + u(t). (15)
However, the ideal computed force control law cannot be
obtained in practical applications since the nonlinear function
W is unknown owing to the existence of the uncertainties.Therefore, the stability of the control system cannot be guar-
anteed. For this reason, the computed force control law is
redesigned to approximate the perfect equivalent control law
via the estimation ofW using ENN.
A. Design of ENN
The nonlinear function W contains the effects of uncer-
tainties including mechanical parametric variations, externaldisturbances, and friction force. Since the parameter variations
of the system are difficult to measure, and the exact values of
the external disturbances and friction force are also difficult
to know in advance for practical applications, the control law
shown in (15) cannot be implemented practically. Therefore,
a practical computed force control law Ueq is proposed toapproximate Ueq as follows:
Ueq = W + u(t) (16)
where the intelligent control law W is adopted to learn thenonlinear function W and defined as
W = WENN + Ur (17)
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Fig. 3. Network structure of ENN.
where WENN is an ENN estimator which is used to learn the
nonlinear equation W, and Ur is a robust compensator whichis designed to compensate the minimum approximation errorbetween W and WENN. Therefore, the practical computed forcecontrol law in (16) can be rewritten as
Ueq = WENN + Ur + u(t). (18)
Therefore, the practical control effort for the LUSM can be
obtained using the equation (18) based on the designed practical
computed force control law as follows:
U = Ueq. (19)
Moreover, using (18), the error dynamic equation (10) can be
rewritten as
e(t) = Bn(W Ueq)
= Bn
W WENN Ur u(t)
. (20)
Thus, an error equation is obtained as follows:
E = E+B(W WENN Ur) (21)
whereE= [e e]T; = [0 1
Bnk2 Bnk1 ] is a stable matrix;
andB = [0 Bn]T.
The structure of the ENN is shown in Fig. 3, including the
input layer (i layer), the hidden layer (j layer), the contextlayer (r layer), and the output layer (o layer). In the network,the hidden layer neurons are fed by the outputs of the context
neurons and the input neurons. Context neurons are known
as memory units as they store the previous output of hidden
neurons. Signal propagation and the basic function of each layer
are introduced in the following:
Layer 1 (Input layer): In the input layer, the node input and
the node output are represented as
ei(k) = fi(neti) = neti, i = 1, 2 (22)
where neti represents the ith input to the input layer. In thispaper, the inputs of the ENN are the tracking error and its
derivative, i.e., [e1(k) e2(k)]T = [e e]T.
Layer 2 (Hidden layer): In the hidden layer, the receptive
field function is a sigmoid function S(x), and the node inputand the node output are represented as
xj(k) = S(netj) =1
1 + enetj, j = 1, 2, . . . , 9. (23)
Moreover
netj =r
xcr(k) +i
W1ij neti, r = 1, 2, . . . , 9
(24)
where netj and xj(k) are the input and the output of the hiddenlayer, respectively; xcr(k) is output of the context layer; W
1ij is
the connective weight of input neuron to hidden neuron.
Layer 3 (Context layer): In the context layer, the node inputand the node output are represented as
xcr(k) = xj(k 1). (25)
Layer 4 (Output layer): In the output layer, the node input
and the node output are represented as
yo(k) = f(neto(k)) = neto(k) = WENN (26)
neto(k) =j
W2jo xj(k) (27)
where yo(k) is the output of the ENN; W2jo is the con-
nective weight of hidden neuron to output neuron; =[W211 W
2j1] R
1j is the adjustable weight vector of W2jo;
and = [x1(k) xj(k)]T Rj1 is the vector ofxj(k).
B. Robust Compensator
According to the universal approximation property, there
exists an optimal ENN estimator WENN to estimate thenonlinear function W such that
W = WENN
+ h = + h (28)
where h is the minimum reconstructed error and the absolutevalue ofh is assumed to be less than a small positive constant ,i.e., |h| < ; and is the optimal parameters of . Re-writing (17), one can obtain
W = WENN + Ur = + Ur (29)
where is the real value of as provided by tuning algorithm
to be introduced. Subtracting (29) from (28), an approximation
error W is defined as
W = W W = + h Ur = + h Ur(30)
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where = . According (21) and (30), the errorequation can be represented as
E=E+B(W WENN Ur)
=E+ BW
=E+B(+ h Ur). (31)
Theorem 1: Consider the LUSM drive system represented
by (4). If the computed force controller is designed as (16),
the intelligent control law is designed as (17), in which the
adaptation law of the ENN is designed as (32), and the robust
compensator is designed as (33) with an estimation algorithm
shown in (34), then the stability of the controlled system can be
guaranteed
= 1E
TPBT (32)
Ur = h(t) (33)
h(t) = 2E
TPB (34)
where 1 and 2 are positive constants; = [W211
W2j1] R1j ; and h(t) is the estimated value ofh.
Proof: Choose a Lyapunov function candidate as
VE, h(t),
=
1
2ETPE+
1
21(
T) +
1
22h2(t)
(35)
where h(t) = h h(t) denote the estimated error and
P = [P1 00 P2
] is a symmetric positive definite matrix which
satisfies the following Lyapunov equation:
TP+ P = Q (36)
and Q > 0. Differentiating (35) with respect to time andusing (31), one can obtain
VE, h(t),
=
1
2ETPE+
1
2ET
PE1
1
T
1
2h(t)
h(t)
=1
2ETP
E+B(+ h Ur)
+1
2
E+B(+ h Ur)
TPE
1
1
T
1
2h(t)
h(t)
=1
2ETPE+
1
2ETTPE
+ETPB(+ h Ur)
11
T 1
2h(t) h(t)
= 1
2ETQE
+
ETPB
1
1
T
+ETPB(hUr)1
2
h(t)h(t). (37)
If the adaptation law of the ENN is chosen as (32), and the
robust compensator is designed as (33) with the estimation
algorithm (34), then (37) can be rewritten as
VE, h(t),
=
1
2ETQE+ETPB
h h(t)
1
2h(t)
h(t)
= 1
2ETQE+ETPBh(t) h(t)ETPB
=
1
2ET
QE 0. (38)
Since V(E, h(t), ) 0, V(E, h(t), ) is negative semi-definite, i.e., V(E, h(t), ) V(E, h(0), ), which impliesthat E, h(t), and are bounded. Define function (t) =1/2ETQE V, and integrate the function (t) with respectto time
t0
()d VE, h(0),
V
E, h(t),
. (39)
Because V(E, h(0), ) is bounded, and V(E, h(t), ) is non-
increasing and bounded, one can obtain
limt
t0
()d < . (40)
Differentiate (t) with respect to time
(t) = ETQE. (41)
Since all the variables in the right-hand side of (31) are
bounded, it implies E is also bounded. Then, (t) is uniformlycontinuous [26]. By using Barbalets lemma [26], it can be
shown that limt (t) = 0. That is, E 0 as t . Asa result, the proposed control system is asymptotically stable.Moreover, the tracking error of the control system will converge
to zero according to E 0.
C. Online Parameters Learning of ENN
In order to train the ENN effectively, an online parameters
learning algorithm, which is derived using Lyapunov stability
theorem and the gradient descent method, is proposed. First,
the connecting weights between the input and the hidden layer
of ENN are adjusted online, and the adaptation law shown in
(32) can be rewritten as follows [27]:
= 1E
TPBT 1eP2BnT. (42)
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Although Bn is unknown for the LUSM drive system, anappropriate positive constant can be selected to replace P2Bn,which is a positive constant, as part of the learning rate in both
(34) and (42). According to the gradient descent method, the
update law of the connecting weights between the hidden and
output layer can be represented as follows:
= 1e
T = 1V
WENN
WENNyo(k)
yo(k)
W2jo
= 1V
WENNxj(k). (43)
Thus, the Jacobian of the controlled system V/WENN =e. The approximated error term needs to be calculated andpropagated by the following equation:
jo = V
WENN
WENNyo(k)
yo(k)
xj(k)
xj(k)
netj
= e W2joxj(k) (1 xj(k)) . (44)
The update law of W1ij can be obtained also by the gradientdescent method, i.e.,
= 1
V
W1ij
= 1 VWENN
WENNyo(k)yo(k)xj(k)
xj(k)netj
netj
W1ij
= 1joei(k) (45)
where = [W111 . . . W 11j , W
121 . . . W
12j ] R
2j1; =
[W111 . . . W11j, W
121 . . . W
12j ] R
2j1 and 1 is thelearning rate.
D. Stability Analysis Using Projection Algorithm
According to the assumption of the bound of the minimum
reconstructed error, the stability proof of the control systemcan be guaranteed using Theorem 1. However, the convergence
condition of the ENN must be satisfied. If the parameters of
the ENN are bounded, the convergence property of the ENN
can be guaranteed. Moreover, according to (26), the output of
the ENN is bounded if the weights between the output layer
and the hidden layer are bounded. Define the constraint set
b for as
b = Mb
(46)
where is a two-norm of vector and Mb is the upperbound of . Therefore, to guarantee b, the adapta-
tion law (32) is modified using the projection algorithm [28]
as follows:
=
1ETPBT
if< Mb or= Mb and E
TPBTT
0
1E
T
PBT
1ET
PB
TT
2
if= Mb and E
TPBTT
> 0
.
(47)
The upper bound is selected to achieve the best transient
control performance in the experimentation considering the
possible variation of operating conditions. According to the
projection algorithm, the convergence property of the ENN
can be guaranteed. Thus, it is reasonable to assume that the
minimum reconstructed error to be bounded. Furthermore, the
asymptotical stability of the proposed control system using
the projection algorithm can be shown by the following
theorem.Theorem 2: Consider the LUSM drive system represented
by (4). If the computed force controller is designed as (16),
the intelligent control law is designed as (17), in which the
adaptation law of the ENN is designed as (47), and the robust
compensator is designed as (33) with an estimation algorithm
shown in (34), then the stability of the controlled system can be
guaranteed.
Proof: When the conditions < Mb or ( = Mb
and ETPBTT 0) hold, the stability analysis is the
same as Theorem 1. On the other hand, when = Mb and
ETPBTT
> 0, the derivative of the Lyapunov function
shown in (37) can be rewritten as (48), which is shown at thebottom of the next page.
Use the property ( )T
= (1/2)(2 2
2) < 0, which is according to = Mb > ,
then
VE, h(t),
=
1
2ETQE+ETPB
( )T
2
T
1
2ETQE+
1
2ETPB
2 2 2
2T
1
2ETQE 0. (49)
Then, by using of the Barbalats lemma, as shown in Theorem 1,
E 0 as t can be obtained as well. Thus, the stabilityproperty also can be guaranteed.
IV. CIRCUITS DESIGN ON FPGA CHI P
The FPGA-based control system for a single-axis motion
control stage is shown in Fig. 4. The proposed control systemis realized on a 24-MHz FPGA (XC2V1000) with 1 million
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Fig. 4. FPGA-based control system for motion control stage using LUSM drive.
gate counts and 10 240 flip-flops from Xilinx, Inc. using VHDL
with the Q-format arithmetic representation. Integrated Soft-
ware Environment version 8.1i from Xilinx, Inc. is adopted to
develop the FPGA chip. A linear scale with resolution 1 mis adopted to detect the position of the moving table. To
implement the computed force control system with the ENN
VE, h(t),
=
1
2ETQE+ETPB(h Ur)
1
2h(t)
h(t) +
ETPB
1
1
T
= 1
2ETQE+ETPB
h h(t)
h(t)ETPB
+
( )
ETPB
1
1
1E
TPBT 1ETPB
T
T
2
= 1
2ETQE+ETPBh(t) h(t)ETPB
+ETPB (
)T
2T
(48)
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1246 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 4, APRIL 2009
Fig. 5. Circuits design on FPGA. (a) Timing control module. (b) Encoder interface module. (c) Auxiliary control, robust compensator, and computed forcecontroller of CFENN module. (d) Input, hidden, and context layer of CFENN module. (e) Output layer of CFENN module. (f) Online parameter learning andadaptation law of CFENN module.
estimator, the timing control module, encoder interface module,
and the computed force control and ENN (CFENN) module are
realized on the FPGA chip, respectively. Moreover, to show
the effectiveness of the control system with small number of
neurons, the ENN that has two, nine, nine, and one neurons at
the input, hidden, context, and output layers, respectively. Therequired processing time of the control algorithm is 0.341 ms
(2929 Hz). Two D/A converters are utilized to display the
reference trajectory dm, the mover position d, the controleffort U, the tracking error e, the estimated value using ENNWENN, and connected weights alternately on the oscilloscopeby changing the definition of I/O pins in VHDL code. The
entire I/O port for this chip includes two pins for the inputports and 36 pins for the output port. Furthermore, 4804 out of
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Fig. 6. Experimental results of computed force control system with ENN estimator for periodical step command reference trajectory at nominal condition.(a) Tracking response. (b) Control effort. (c) Tracking error. (d) Estimated value ofW using ENN. (e) Connected weight W2
51between hidden layer and output
layer. (f) Connected weight W115
between input layer and hidden layer.
10 240 flip-flops (46%) have been used in the FPGA chip. In
addition, the used slices of the encoder interface module, the
data and D/A controllers, and the CFENN module are 102, 37,
and 3417 out of 5120, respectively; the used gate counts of the
encoder interface module, the data and D/A controllers, and theCFENN module are 1964, 711, and 62 162, respectively. Addi-
tionally, the circuits and control algorithm in the FPGA are de-
veloped using VHDL by a PC as the development system. In the
development of the VHDL codes for a 12-bits FPGA proces-
sor, by using fractional numbers between 1 and 1 with theQ-format representation, the results of multiplication can easily
be handled since the product of two numbers is always in the
same range. Besides, the sine function and multiplier are imple-
mented using available intellectual property (IP).
A. Timing Control Module
The block diagram of the timing control module, which iscomposed of one 13-bit counter and one events generator, is
shown in Fig. 5(a). In the timing control module, the counter
is used to generate various counts for the generation of various
control signals to enable (EN) the respective circuit. Moreover,
the sampling frequency 2929 Hz, which is used in the encoder
interface circuit, is also generated via the counter. Furthermore,various control signals are generated using the events generator
to EN the respective hardware circuit in different modules to
meet the specific timing control sequence.
B. Encoder Interface Module
The block diagram of encoder interface module is shown in
Fig. 5(b), which consists of timing control, two digital filters, a
decoder, an updown counter, a register, a command generator,
and one adder. The function of the encoder interface is to obtain
the position and speed values of the mover. The pulse count
signal PLS and the rotating direction signal DIR are obtained
using the A, B pulse input signals from the decoder throughtwo digital filters. The position signal d can be obtained using
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1248 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 4, APRIL 2009
Fig. 7. Experimental results of computed force control system with ENN estimator for periodical sinusoidal reference trajectory at nominal condition.(a) Tracking response. (b) Control effort. (c) Tracking error. (d) Estimated value ofW using ENN. (e) Connected weight W2
51between hidden layer and output
layer. (f) Connected weight W115
between input layer and hidden layer.
the PLS and DIR signals through updown counter. Moreover,
the command generator includes periodical sinusoidal IP and
periodical trapezoidal IP in order to generate the reference
trajectory dm. Furthermore, v is the velocity signal, and resultsfrom the difference between the position signal d and the time
delay of d, ddelay. In addition, the resolution of the encoder is1 mm = 1000 digital value at the sampling frequency 2929 Hz.
C. CFENN Module
To implement the control law effectively, the CFENN mod-
ule is divided into four parts which are shown in Figs. 5(c)(f):
1) Fig. 5(c) shows the block diagram of auxiliary control,
robust compensator, and computed force controller, using dm,d, WENN, and h(k) to obtain the control effort U. First, usingdm and d to obtain e and e. Moreover, the auxiliary controlinput u(t) based on the PD controller is obtained using an adder
and two multipliers. Then, the robust compensator Ur with theestimation algorithm
h(k) shown in (33) and (34) which is
equivalent to h(k) = 2e is obtained using an adder, tworegisters, and two multipliers. Finally, the control effort U basedon (18) is obtained using an adder; 2) in order to reduce the
computational load and facilitate the hardware implementation
using FPGA, a piecewise continuous function is selected as the
receptive field function for the ENN to approximate the sigmoid
function in the following:
xj(k) =
1, if netj > 0.5/a0, if netj < 0.5/aa netj + 0.5, otherwise
j = 1, 2, . . . , 9 (50)
where a is the slope of linear function. Fig. 5(d) shows theblock diagram of the input, hidden, and context layers utilized
to obtain the output of the hidden layer x1(k) x9(k) usinge, e, and xcr(k) based on (22), (24), (25), and (50). First, two
multipliers are utilized to multiply the outputs of the input layer,e and e, with the weights between the input layer and the hidden
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Fig. 8. Experimental results of computed force control system with ENN estimator for periodical trapezoidal reference trajectory at nominal condition.(a) Tracking response. (b) Control effort. (c) Tracking error. (d) Estimated value ofW using ENN. (e) Connected weight W2
51between hidden layer and output
layer. (f) Connected weight W115
between input layer and hidden layer.
layer W111 W119 and W
121 W
129 individually. Then, add the
summation of the output of the context layer to result in net1 net9 based on (24). Moreover, the outputs of each neuron in the
hidden layerx1(k) x9(k)
are generated using the piecewise
function shown in (50) where all the slopes are 1.0; 3) Fig. 5(e)
shows the block diagram of the output layer utilized to obtain
the output of the ENN, WENN, using x1(k) x9(k) based on(26) and (27). First, two multiplexers with a multiplier are uti-
lized to multiply the outputs of the hidden layer x1(k) x9(k)with the weights between the hidden layer and the output layer
W211 W291 individually. Then, the output WENN is obtained
through a register and an adder; and 4) Fig. 5(f) shows the
block diagram of online parameters learning algorithm utilized
to achieve the adaptation law of the weights between the hidden
layer and the output layer based on (42) which is equivalent
to W2j1 = 1e xj(k), and the weights between the input
layer and the hidden layer based on (45). Since the sigmoidfunction has been approximated as (50), (44) is modified to
jo = e W2joa in the experimentation. In Fig. 5(f), first, the
variations of the weights W211 W291 are obtained by a
multiplexer, three multipliers, and a register; the variations of
the weights W1
11 W1
19 and W1
21 W1
29 are obtainedby two multiplexers, four multipliers, and two registers. Then,
the new weights W211(k + 1) W291(k + 1), W
111(k + 1)
W119(k + 1) and W121(k + 1) W
129(k + 1) are obtained by
adding the weights of current iteration W211(k) W291(k) with
W211 W291, W
111(k) W
119(k) with W
111 W
119 and
W121(k) W129(k) with W
121 W
129 individually.
V. EXPERIMENTAL RESULTS
The control objective is to control the mover of the LUSM
to move periodically according to the reference trajectories
including step command, sinusoidal, and trapezoidal com-
mands using the computed force control system with ENNestimator. Moreover, two test conditions are provided in the
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1250 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 4, APRIL 2009
Fig. 9. Experimental results of computed force control system with ENN estimator for periodical step command reference trajectory at parameter variationcondition. (a) Tracking response. (b) Control effort. (c) Tracking error. (d) Estimated value of W using ENN. (e) Connected weight W2
51between hidden layer
and output layer. (f) Connected weight W115
between input layer and hidden layer.
experimentation, which are the nominal condition and the pa-
rameter variation condition. The parameter variation condition
is the addition of one iron disk with the mass 3.66 kg on the
moving table.
Some experimental results are provided to demonstrate the
effectiveness of the proposed FPGA-based control systems.
The control objective is to control the mover to move 1 mm
periodically for step command reference trajectory, 1 mmperiodically for sinusoidal reference trajectory, and 1 mm pe-
riodically for trapezoidal reference trajectory. The step com-
mand reference trajectory is obtained using a first-order transfer
function with periodical step function as input. A first-order
transfer function 2/(s + 2) with rise time 1 s is adopted tosmooth the step function. Figs. 611 show the experimental
results of the command tracking due to the periodical step com-
mand, sinusoidal, and trapezoidal reference trajectories of the
proposed computed force control system with ENN estimator.The tracking responses of the mover position due to periodical
step command reference trajectory at nominal condition and
parameter variation condition are shown in Figs. 6(a) and 9(a);
the associated control efforts are shown in Figs. 6(b) and
9(b); the tracking errors are shown in Figs. 6(c) and 9(c); the
estimated values ofW using ENN are shown in Figs. 6(d) and9(d); the responses of one of the connected weights between the
hidden layer and the output layer of the ENN, W251, are shownin Figs. 6(e) and 9(e); the responses of one of the connected
weights between the input layer and the hidden layer of the
ENN, W115, are shown in Figs. 6(f) and 9(f), respectively. Goodpositioning performance is achieved from the experimental
results, as shown in Figs. 6(a) and 9(a). Moreover, the tracking
responses of the mover position due to the periodical sinusoidal
reference trajectory at nominal condition and parameter varia-
tion condition are shown in Figs. 7(a) and 10(a); the associated
control efforts are shown in Figs. 7(b) and 10(b); the tracking
errors are shown in Figs. 7(c) and 10(c); the estimated values ofW using ENN are shown in Figs. 7(d) and 10(d); the responses
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Fig. 10. Experimental results of computed force control system with ENN estimator for periodicalsinusoidal reference trajectoryat parameter variationcondition.(a) Tracking response. (b) Control effort. (c) Tracking error. (d) Estimated value ofW using ENN. (e) Connected weight W2
51between hidden layer and output
layer. (f) Connected weight W115
between input layer and hidden layer.
of one of the connected weights between the hidden layer and
the output layer of the ENN, W251, are shown in Figs. 7(e) and10(e); the responses of one of the connected weights between
the input layer and the hidden layer of the ENN, W115, are shownin Figs. 7(f) and 10(f), respectively. Furthermore, the tracking
responses of the mover position due to the periodical trape-
zoidal reference trajectory at nominal condition and param-
eter variation condition are shown in Figs. 8(a) and 11(a); the
associated control efforts are shown in Figs. 8(b) and 11(b); the
tracking errors are shown in Figs. 8(c) and 11(c); the estimated
values of W using ENN are shown in Figs. 8(d) and 11(d);the responses of one of the connected weights between the
hidden layer and the output layer of the ENN, W251, are shownin Figs. 8(e) and 11(e); the responses of one of the connected
weights between the input layer and the hidden layer of the
ENN, W115, are shown in Figs. 8(f) and 11(f), respectively.From the experimental results, good tracking responses of the
mover can be obtained at both the nominal and the parametervariation conditions for the proposed computed force control
system with ENN estimator, as shown in Figs. 6(a), 7(a), 8(a),
9(a), 10(a), and 11(a). It also shows that the proposed FPGA-
based computed force control system using ENN has effective
hardware online learning ability of the network parameters and
is robust with regard to the parameter variations and friction
force.
VI. CONCLUSION
Since the dynamic characteristics of the LUSM are non-
linear and time varying, and the precise dynamic model is
difficult to obtain, an FPGA-based computed force control
system using ENN has been proposed to control the position
of the moving table of the LUSM to achieve high-accuracy
position control in this paper. First, the LUSM drive system
was introduced. Next, the dynamics of LUSM mechanism with
the introduction of a lumped uncertainty, which includes the
friction force, was derived. Since the dynamic characteristicsand motor parameters of the LUSM are nonlinear and time
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1252 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 4, APRIL 2009
Fig. 11. Experimental results of computed force control system with ENN estimator for periodical trapezoidal reference trajectory at parameter variationcondition. (a) Tracking response. (b) Control effort. (c) Tracking error. (d) Estimated value of W using ENN. (e) Connected weight W2
51between hidden
layer and output layer. (f) Connected weight W115
between input layer and hidden layer.
varying, a computed force control system with ENN estimator
was designed to improve the control performance in reference
trajectories tracking. Then, the Lyapunov stability theorem and
the projection algorithm were adopted to ensure the stability
of the control system and the convergence of the ENN, and to
derive the adaptation laws of the control system. Moreover, the
online parameters learning algorithm of the ENN was derived
using gradient decent method for the purpose of real-time
estimation. Furthermore, to verify the effectiveness of the pro-
posed control scheme, the computed force control system with
ENN estimator was implemented in an FPGA-based control
system. Finally, the effectiveness of the proposed low-cost high-
performance FPGA-based LUSM drive has been confirmed by
some experimental results. The experimental results show that
excellent positioning and trajectories tracking performance are
achieved. In addition, the robustness to parameter variations
and friction force can be obtained as well using the proposedcontrol system.
REFERENCES
[1] T. Sashida and T. Kenjo, An Introduction to Ultrasonic Motors. Oxford,U.K.: Clarendon, 1993.
[2] M. Zhu, Contact analysis and mathematical modeling of traveling wave
ultrasonic motors, IEEE Trans. Ultrason., Ferroelectr., Freq. Control,vol. 51, no. 6, pp. 668679, Jun. 2004.
[3] J. Zumeris, Ceramic motor, U.S. Patent 5 777 423, Jul. 7, 1998.[4] F. J. Lin, R. J. Wai, and M. P. Chen, Wavelet neural network control for
linear ultrasonic motor drive via adaptive sliding-mode technique, IEEETrans. Ultrason., Ferroelectr., Freq. Control, vol. 50, no. 6, pp. 686698,Jun. 2003.
[5] F. J. Lin and P. H. Shieh, Recurrent RBFN-based fuzzy neural net-work control for X-Y- motion control stage using linear ultrasonicmotors, IEEE Trans. Ultrason., Ferroelectr., Freq. Control, vol. 53,no. 12, pp. 24502464, Dec. 2006.
[6] Y. F. Peng and C. M. Lin, Intelligent motion control of linear ultrasonicmotor withH tracking performance, IET Control Theory Appl., vol. 1,no. 1, pp. 917, Jan. 2007.
[7] J. S. R. Jang, C. T. Sun, and E. Mizutani, Neuro-Fuzzy and Soft Comput-ing: A Computational Approach to Learning and Machine Intelligence.
Upper Saddle River, NJ: Prentice-Hall, 1997.[8] J. Elman, Finding structure in time, Cognit. Sci., vol. 14, no. 2, pp. 179211, 1990.
Authorized licensed use limited to: Steven Sullivan. Downloaded on April 8, 2009 at 23:01 from IEEE Xplore. Restrictions apply.
-
7/31/2019 FPGA-Based Computed Force Control System
16/16
LIN et al.: FPGA-BASED COMPUTED FORCE CONTROL SYSTEM USING ENN FOR LINEAR ULTRASONIC MOTOR 1253
[9] X. Li, G. Chen, Z. Chen, and Z. Yuan, Chaotifying linear Elmannetworks, IEEE Trans. Neural Netw., vol. 13, no. 5, pp. 11931199,Sep. 2002.
[10] T. Sawaragi and T. Kudoh, Self-reflective segmentation of human bodilymotions using recurrent neural networks, IEEE Trans. Ind. Electron.,vol. 50, no. 5, pp. 903911, Oct. 2003.
[11] M. Wlas, Z. Krzeminski, J. Guzinski, H. Abu-Rub, and H. A. Toliyat,Artificial-neural-network-based sensorless nonlinear control of induction
motors, IEEE Trans. Energy Convers., vol. 20, no. 3, pp. 520528,Sep. 2005.[12] F. J. Lin, H. J. Shieh, P. H. Shieh, and P. H. Shen, An adaptive recurrent-
neural-network motion controller for X-Y table in CNC machine, IEEETrans. Syst., Man, Cybern. B, Cybern., vol. 36, no. 2, pp. 286299,Apr. 2006.
[13] X. D. Li, J. K. L. Ho, and T. W. S. Chow, Approximation of dynami-cal time-variant systems by continuous-time recurrent neural networks,
IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 52, no. 10, pp. 656660,Oct. 2005.
[14] S. C. Kremer, On the computational power of Elman-style recurrentnetworks, IEEE Trans. Neural Netw., vol. 6, no. 4, pp. 10001004,Jul. 1995.
[15] L. P. Douglas, VHDL: Programming by Example, 4th ed. Columbus,OH: McGraw-Hill, 2002.
[16] H. C. Roth, Circuit Design with VHDL. Cambridge, MA: MIT Press,2004.
[17] J. Chen and P. C. Tang, A sliding mode current control scheme for PWMbrushless DC motor drives, IEEE Trans. Power Electron., vol. 14, no. 3,pp. 541551, May 1999.
[18] R. X. Chen, L. G. Chen, and L. Chen, System design consideration fordigital wheelchair controller, IEEE Trans. Ind. Electron., vol. 47, no. 4,pp. 898907, Aug. 2000.
[19] D. Kim, An implementation of fuzzy logic controller on the reconfig-urable FPGA system, IEEE Trans. Ind. Electron., vol. 47, no. 3, pp. 703715, Jun. 2000.
[20] T. S. Li, S. J. Chang, and Y. X. Chen, Implementation of human-likedriving skills by autonomous fuzzy behavior control on an FPGA-basedcar-like mobile robot, IEEE Trans. Ind. Electron., vol. 50, no. 5, pp. 867880, Oct. 2003.
[21] S. Sanchez-Solano, A. J. Cabrera, I. Baturone, F. J. Moreno-Velo, andM. Brox, FPGA implementation of embedded fuzzy controllers for ro-botic applications, IEEE Trans. Ind. Electron., vol. 54, no. 4, pp. 1937
1945, Aug. 2007.[22] S. Jung and S. S. Kim, Hardware implementation of a real-time neuralnetwork controller with a DSP and an FPGA for nonlinear systems, IEEETrans. Ind. Electron., vol. 54, no. 1, pp. 265271, Feb. 2007.
[23] D. Zhang and H. Li, A stochastic-based FPGA controller for an inductionmotor drive with integrated neural network algorithms, IEEE Trans. Ind.
Electron., vol. 55, no. 2, pp. 551561, Feb. 2008.[24] T. Yaolong, C. Jie, and T. Hualin, Adaptive backstepping control and
friction compensation for AC servo with inertia and load uncertainties,IEEE Trans. Ind. Electron., vol. 50, no. 5, pp. 944952, Oct. 2003.
[25] G. Ferreti, G. Magnani, and P. Rocco, Single and multistate integralfriction models, IEEE Trans. Autom. Control, vol. 49, no. 12, pp. 22922297, Dec. 2004.
[26] J.-J. E. Slotine and W. Li, Applied Nonlinear Control. Upper SaddleRiver, NJ: Prentice-Hall, 1991.
[27] F. J. Lin, W. J. Hwang, and R. J. Wai, A supervisory fuzzy neural networkcontrol system for tracking periodic inputs, IEEE Trans. Fuzzy Syst.,
vol. 7, no. l, pp. 4152, Feb. 1999.[28] L. X. Wang, A Course in Fuzzy Systems and Control. Englewood Cliffs,
NJ: Prentice-Hall, 1997.
Faa-Jeng Lin (M93SM99) received the Ph.D.degree in electrical engineering from National TsingHua University, Hsinchu, Taiwan, in 1993.
From 1993 to 2001, he was an Associate Pro-fessor and then a Professor with the Department ofElectrical Engineering, Chung Yuan Christian Uni-versity, Chungli, Taiwan. From 2001 to 2003, he wasChairperson and a Professor with the Department
of Electrical Engineering, National Dong Hwa Uni-versity, Hualien, Taiwan. He was Dean of Researchand Development from 2003 to 2005 and Dean of
Academic Affairs from 2006 to 2007 at the same university. Currently, he isa Professor with the Department of Electrical Engineering, National CentralUniversity, Chungli. He is also the Chair, Power Engineering Division, NationalScience Council, Taiwan, from 2007 to 2009. His research interests include acand ultrasonic motor drives, DSP-based computer control systems, fuzzy andneural network control theories, nonlinear control theories, power electronics,and micromechatronics.
Dr. Lin received the Outstanding Research Professor Award from ChungYuan Christian University in 2000; the Crompton Premium Best Paper Awardfrom the Institution of Electrical Engineers (IEE), U.K., in 2002; the Outstand-ing Research Award from the National Science Council, Taiwan, in 2004; theOutstanding Research Professor Award from National Dong Hwa Universityin 2004; and the Outstanding Professor of Electrical Engineering Award in2005 from the Chinese Electrical Engineering Association, Taiwan. He was
also the recipient of the Distinguished Professor Award from National CentralUniversity in 2007. He is a Fellow of the Institution of Engineering andTechnology (formerly IEE).
Ying-Chih Hung was born in Taipei, Taiwan, in1984. He received the B.S. degree in electricalengineering from Chung Yuan Christian University,Chungli, Taiwan, in 2006, and the M.S. degree inelectrical engineering from the National Dong HwaUniversity, Hualien, Taiwan, in 2008. He is currentlyworking toward the Ph.D. degree in electrical engi-neering at National Central University, Chungli.
His research interests include field-programmablegate arrays, linear ultrasonic motors, motion control,and intelligent control theories.
Syuan-Yi Chen was born in Changhua, Taiwan,in 1982. He received the B.S. degree in electricalengineering from National Kaohsiung University ofApplied Science, Kaohsiung, Taiwan, in 2004, andthe M.S. degree in industrial educationfrom NationalTaiwan Normal University, Taipei, Taiwan, in 2006.He is currently working toward the Ph.D. degree inelectrical engineering at National Central University,Chungli, Taiwan.
His research interests include magnetic levitationsystems, active magnetic bearing systems, nonlinear
control theories, and intelligent control theories.