IEEJ Journal of Industry Applications
Vol.8 No.2 pp.263–270
DOI: 10.1541/ieejjia.8.263

Paper

Perfect Tracking Control Considering Generalized Controllability Indicesand Application for High-Precision Stage in Translation and Pitching
Masahiro Mae∗a)
Hiroshi Fujimoto∗

Wataru Ohnishi∗
Yoichi Hori∗

Student Member,
Senior Member,

Member
Fellow(Manuscript received May 2, 2018, revised Sep. 28, 2018)

High-precision stages are widely used for manufacturing semiconductors and flat panels. These high-precision stages
have become multi-input multi-output (MIMO) systems with six-degrees-of-freedom (DOF); hence, the coupling between the translation and pitching motion deteriorates the control performance. This study proposes the multirate
feedforward control for MIMO systems and applies it to these high-precision stages. The multirate feedforward control designs the stable inversion for the unstable discretization zero problem. In addition, the design of the MIMO
multirate feedforward controllers has a degree of freedom to design the B matrix according to the selection of thegeneralized controllability indices. In conventional control methods such as precompensated decoupling controllers,
it is theoretically impossible to achieve perfect tracking because unstable discretization zeros are generated. In thisstudy, the proposed method is applied to the translation and pitching motion of a high-precision stage, and it achieves
perfect tracking in the simulation. The eﬀectiveness of the proposed method is verified experimentally.
Keywords: multirate feedforward, multi-input multi-output system, high-precision stage

1.

with zero tracking error at every sampling point” (4) . In the
proposed method, we use discretized plant models and design the controller in the discrete-time domain. Using thisapproach, PTC is achieved theoretically by considering theinterference between axes using the MIMO multirate feedforward controller. The consideration of the input multiplicities
in the digital control for the MIMO system is the important
point.
In this study, the authors control a high-precision stage
with six-DOF, as shown in Fig. 1(a). The authors consider
two-DOF of translation in the x axis direction and pitchingaround the y axis, as shown in Fig. 1(b). The eﬀectivenessof the proposed method is demonstrated by simulations andexperiments.

Introduction

A high-precision scan stage is critical in manufacturing
semiconductors and flat panels (1) . The circuit configurationof semiconductors and flat panels becomes finer exponentially annually (2) . The conventional high-precision stage isa one-degree-of-freedom (DOF) system mechanically constrained to move only one direction. Recently, to decrease
the disturbance of vibration from the floor and friction fromthe mechanical restraint, the high-precision stage is a sixDOF (x, y, z, θ x , θy , θz ) system by the gravity canceller thatcompensates for the gravitational force experienced by thefine stage (1) . In the stage with six-DOF, the interference
forces between the axes worsen the positioning accuracy ofthe stage. Many studies have been conducted on the decoupling. The precompensator for decoupling is typically used
to apply the single-input single-output (SISO) controllers to
the coupled multi-input multi-output (MIMO) system (1) . The
MIMO feedback controller and the integrated design of themechanism and the controller are also used for decoupling,e.g., using the Direct Nyquist Array method and changing
the height of the actuation point virtually (3) .
From the viewpoint of designing the feedforward controller, the controller is designed in the continuous-time domain and discretized in the conventional method. In this approach, the controller cannot achieve perfect tracking control(PTC) theoretically because of the discretized unstable zeros. The word “perfect tracking control (PTC)” is definedas “the plant output perfectly tracks the desired trajectory2.

2.1 Multirate Feedforward for Single-Input SingleOutput System
Multirate feedforward control achieves
PTC (6) . A digital tracking control system typically has two
samplers for the reference signal r(t) and the output y(t), andone holder on the input u(t), as shown in Fig. 2. Therefore,
three time periods exist: T r , T y , and T u , representing the periods of r(t), y(t), and u(t), respectively, as shown in Fig. 3.
Additionally, the longer period of T r or T y is defined as theframe period T f . In the case of the SISO nth-order plant,
T r = nT y = nT u = T f .
Consider the continuous-time nth-order plant described by
the state equation (1) and the output equation (2).

ẋ(t) = Ac x(t) + bc u(t) · · · · · · · · · · · · · · · · · · · · · · · · · · · (1)y(t) = cc x(t) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (2)a) Correspondence to: Masahiro Mae. E-mail: mmae@ieee.org∗
The University of Tokyo
5-1-5, Kashiwanoha, Kashiwa, Chiba 227-8561, Japanc 2019 The Institute of Electrical Engineers of Japan.
⃝

Proposed Method

From the discretization of (1) and (2) by the zero-order hold263

PTC Considering GCI and Application for High-Precision Stage（Masahiro Mae et al.）(a) Photograph of the six-DOF high-precision stage.

(b) Coupling problem between xm and θy .

(c) Block diagram of the plant.

Fig. 1. Details of the plantFig. 2. Block diagram of the controller with the plant that does not contain unstable intrinsic zeros. S, H, and L
denote a sampler, holder, and lifting operator (5) , respectively; z and z s denote e sTr and e sTu , respectivelyt = iT r = kT u and t = (i + 1)T r = (k + n)T u . The input andoutput vectors u[i] (7) and y[i] (8) are given by"#Tu[i]= u1 [i] u2 [i] · · · un [i]"= u(kT u ) u((k + 1)T u ) · · ·#Tu((k + n − 1)T u ) ,· · · · · · · · · · · · · · · · · · · · · · · (7)"#Ty[i]= y1 [i] y2 [i] · · · yn [i]"= y(kT y ) y((k + 1)T y ) · · ·· · · · · · · · · · · · · · · · · · · · · · · (8)Fig. 3. SISO multirate sampling control at the same interval

From (5), the control input uﬀ [i] to achieve PTC are given by
uﬀ [i] = B−1 (I − z−1 A)x[i + 1]. · · · · · · · · · · · · · · · · · · · (9)in the sampling period T u , the discrete-time plant becomes
the state equation (3) and output equation (4).

The block diagram of the control system is shown in Fig. 2.
L is a discrete-time lifting operator (5) . L−1 outputs the elements of the nth dimensional vector uﬀ [i], which is input at
every period T r , in the order from 1 to n by T u = T r /n.
2.2 Multirate Feedforward for Multi-Input MultiOutput System
In an m-input p-output nth order MIMO
system, the state equation (10) and the output equation (11)of the continuous-time plant are given byx[k + 1] = A s x[k] + b s u[k] · · · · · · · · · · · · · · · · · · · · · (3)y[k] = c s x[k] · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (4)where the matrices A s , b s , and c s are given by! Tu
Ac T uAs = e, bs =e Ac τ bc dτ, c s = cc .
0ẋ(t) = Ac x(t) + Bc u(t), · · · · · · · · · · · · · · · · · · · · · · · · (10)y(t) = Cc x(t), · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (11)""##T
Bc = bc1 · · · bcm , Cc = cc1 · · · ccp ,By lifting the discrete-time state equation (3) and the output
equation (4), the state equation (5) and the output equation(6) are given by

where the plant state is x ∈ Rn , the plant input is u ∈ Rm , andthe plant output is u ∈ R p .
The generalized controllability indices are defined as follows (7) :Definition (Generalized Controllability Indices). The generalized controllability indices of ( Ac , Bc ) are defined as follows for Ac ∈ Rn×n and Bc = [bc1 , · · · , bcm ] ∈ Rn×m , respectively. If ( Ac , Bc ) is a controllable pair, n linearly independent vectors including the linear combination can be selectedx[i + 1] = Ax[i] + Bu[i], · · · · · · · · · · · · · · · · · · · · · · · (5)y[i] = cx[i], · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (6)where the matrices A, B, and c, and i are given by
"
An−2
As bs
A = Ans , B = An−1
s bs
s bs · · ·c = c s , x[i] = x(iT r ).

#Ty((k + n − 1)T y ) .

#bs ,Equations (5) and (6) are given from the interval between
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PTC Considering GCI and Application for High-Precision Stage（Masahiro Mae et al.）Table 1. Model parametersfrom {bc1 , · · · , bcm , Ac bc1 , · · · , Ac bcm , · · · , An−1
c bcm }.

Symbol
xm
xg1
xg2
θy
fx
τy
M x1
C x1
K x1
M x2
Jθy
Cθy
Kθy
Lm
Lg2
Lfx

Setting ϕ as a set of these n vectors, σl and N are definedbyσl = number{k| Ak−1
c bcl ∈ ϕ}, · · · · · · · · · · · · · · · · · · · (12)m$σl = n, · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13)l=1

N = max(σl ). · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (14)Meaning
Measured position of the fine stage
Position of the CoG of the planar air bearing and the air gyro
Position of the CoG of the fine stage
Measured attitude angle of the fine stage
Input force of the fine stage in the x direction
Input torque of the fine stage in the θy direction
Mass of the planar air bearing and the air gyro
Viscosity coeﬃcient in the xg1 motion
Spring coeﬃcient in the xg1 motion
Mass of the fine stage
Moment of inertia of the fine stage
Viscosity coeﬃcient of the fine stage in the θy motion
Spring coeﬃcient of the fine stage in the θy motion
Distance between the measurement point of xm and the CoRDistance between the CoR and the CoG of the fine stage
Distance between the CoR of the fine stage and the actuation point

Value
–
–
–
–
–
–
0.077 kg
300 N/(m/s)
6000 N/m
5.3 kg0.10 kgm2
1.6 Nm/(rad/s)
1200 Nm/rad−0.028 m−0.051 m−0.0026 m

In the MIMO system, n (= plant order) number of vectors
are selected from the generalized controllability indices, andthe full row rank matrix B are designed for almost all sampling period of the discretization† . Therefore, the feedforward controllers designed according to their diﬀerent forms.
From (15), the control input uﬀ [i] to achieve PTC are givenby (16).

The state equations (27) and output equations (28) of thecontinuous-time plant are given byx[i + 1] = Ax[i] + Bu[i], · · · · · · · · · · · · · · · · · · · · · · (15)uﬀ [i] = B−1 (I − z−1 A)x[i + 1], · · · · · · · · · · · · · · · · · (16)ẋ(t) = Ac x(t) + Bc u(t), · · · · · · · · · · · · · · · · · · · · · · · · (27)y(t) = Cc x(t), · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (28)where the matrices A, x[i], u[i], z and T f are given by
A=e

3.

Ac T fwhere the vectors x(t), u(t), and y(t), and the matrices Ac ,Bc , and Cc are given by⎡ ⎤⎢⎢⎢ xm ⎥⎥⎥+ ,+ ,⎢⎢⎢ ẋ ⎥⎥⎥
x
fx
m⎥
⎢
⎥
⎢
x(t) = ⎢⎢ ⎥⎥ , u(t) =, y(t) = m ,τyθy⎢⎣⎢ θy ⎥⎦⎥
θ̇y
⎡
⎤
1
0
0 ⎥⎥
⎢⎢⎢ 0
+
,
⎥
⎢⎢⎢a
1 0 0 0a22 a23 a24 ⎥⎥⎥⎥⎥⎥⎥ , Cc =Ac = ⎢⎢⎢⎢ 21,
0 0 1 0
0
0
1 ⎥⎥⎦
⎢⎢⎣ 0
a41 a42 a43 a44
⎡
⎤
0 ⎥⎥
⎢⎢⎢ 0
⎥
#
⎢⎢⎢b
b22 ⎥⎥⎥⎥ "⎥⎥⎥ = bc1 bc2 .
Bc = ⎢⎢⎢⎢ 21
0 ⎥⎥⎦
⎢⎢⎣ 0
b41 b42sT fx[i] = x(iT f ), z = e , T f = NT u ,#Tu[i] = u1 [i] · · · um [i]"#T= u11 [i] · · · u1σ1 [i] u21 [i] · · · umσm [i] .
",Modeling

In the simulation and experiment, the authors controlled
the fine stage of the six-DOF high-precision stage shown in
Fig. 1(a). This fine stage is supported by a six-DOF air bearing gravity canceller. In this study, the two-DOF of the translation x along the x axis and the pitching θy around the y axis
are controlled, as shown in Fig. 1(b).
3.1 System Identification
The equations of motionof the translation and pitching of the stage are given by (17)and (18) (8) .

By using the zero-order hold in the state equation (27) andthe output equation (28) of the continuous-time plant withthe sampling period T u , the state equation (29) and the output
equation (30) of the discrete-time plant are given by(M x1 + M x2 ) ẍg1 + C x1 ẋg1 + K x1 xg1 + M x2 Lg2 θ̈y = f x · · · · (17)(M x2 L2g2 + Jθy )θ̈y +Cθy θ̇y +Kθy θy + M x2 Lg2 ( ẍg1 − gθy )=τy + f x L f x · · · · (18)x[k + 1] = A s x[k] + B s u[k], · · · · · · · · · · · · · · · · · · · (29)y[k] = C s x[k], · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (30)

Convert xg1 to observable xm by (19).
xm (s) = xg1 (s) + Lm θy (s)· · · · · · · · · · · · · · · · · · · · · · · ·(19)where x[k], u[k], y[k], and B s are given by⎤⎡⎢⎢⎢ xm [k]⎥⎥⎥,+,+⎢⎢⎢ ẋ [k]⎥⎥⎥xm [k]
f x [k]m⎥⎢⎥ , u[k] =x[k] = ⎢⎢⎢, y[k] =,τy [k]
θy [k]⎢⎣⎢ θy [k] ⎥⎥⎥⎦⎥
θ̇y [k]"#B s = b s1 b s2 .

From the expressions (17), (18), and (19), the transfer functions g11 to g22 are given by (20) to (23).
The parameters of the stage are shown in Table 1, which is
given from fitting in the frequency domain, shown in Fig. 6.
3.2 State Space Realization
ai j , bik (i ∈ {2, 4}, j ∈{1, 2, 3, 4}, k ∈ {1, 2}) from the expressions (17), (18), and(19), ( ẍm , θ̈y ) explained by (xm , ẋm , θy , θ̇y ) are given by (25)and (26).

When constructing the square matrix B, the generalized
controllability indices are given byẍm =a21 xm +a22 ẋm +a23 θy +a24 θ̇y +b21 f x +b22 τy · · · · · (25){b s1 , b s2 , A s b s1 , A s b s2 , A2s b s1 , A2s b s2 , A3s b s1 , A3s b s2 }.

θ̈y =a41 xm +a42 ẋm +a43 θy +a44 θ̇y +b41 f x +b42 τy · · · · · · (26)

† This is possible because the controllability of the continuous-time system is not preserved in the discrete system only if the two poles ηi andη jhave the same real parts, and the discretizing sampling period T satisfies
ηi = η j + j 2kπ
T (k = ±1, ±2, . . .); further, it is limited to only several cases.

When the plant order is n = 4, four elements are chosen fromthe generalized controllability indices to construct the squarematrix B.
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PTC Considering GCI and Application for High-Precision Stage（Masahiro Mae et al.）(a) Conventional method 1.

(b) Conventional method 2.

(c) Proposed method.

Fig. 4. Block diagram of the control methods. These show only feedforward controllers(a) (σ1 , σ2 ) = (2, 2)(b) (σ1 , σ2 ) = (3, 1)(c) (σ1 , σ2 ) = (4, 0)

Fig. 5. MIMO multirate sampling control at the same interval

xm (s) [Jθy +L f x Lm M x1 −(L f x −Lg2 )(Lg2 −Lm )M x2 ]s2 +(Cθy +L f x LmC x1 )s+L f x Lm K x1 −Lg2 M x2 g=
· · · · · · · · · · · (20)f x (s)D(s)xm (s) [Lm M x1 +(Lm −Lg2 )M x2 ]s2 +Lm C x1 s+Lm K x1
g12 (s)==· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (21)τy (s)D(s)g11 (s)=θy (s) [L f x M x1 +(L f x −Lg2 )M x2 ]s2 +L f x C x1 s+L f x K x1=
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (22)f x (s)D(s)θy (s) (M x1 + M x2 )s2 +C x1 s+K x1=· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (23)g22 (s)=τy (s)D(s)g21 (s)=D(s)=[(M x1 + M x2 )Jθy + M x1 M x2 L2g2 ]s4 +[(M x1 + M x2 )Cθy +(Jθy + M x2 L2g2 )C x1 ]s3+[(Jθy + M x2 L2g2 )K x1 +(M x1 + M x2 )(Kθy − M x2 Lg2 g)+CθyC x1 ]s2 +[Cθy K x1 +C x1 (Kθy −Lg2 M x2 g)]s+K x1 (Kθy −Lg2 M x2 g)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (24)4.

In Fig. 6, G4 is used for the MIMO plant model of the proposed method, and G2 is used for the SISO plant model of theconventional methods 1 and 2. The nominal plant g12 and g21
contain some gaps with the frequency response data because
these four transfer functions, g11 to g22 , are correlated in thissystem and a trade oﬀ exists in the fitting. In this model, we
focus on the fitting of the transfer function g21 representing
the coupling from the translational force f x along the x axis
to the rotation θy around the y axis to prevent pitching.
In the simulation, C f b [z s ], which is the feedback controller,
is 0 in all the methods. In the experiment, C f b [z s ] is a PID
controller designed as 20 Hz closed-loop pole for all six-DOF(x, y, z, θ x , θy , θz ) in all the methods.
The seventh-order polynomial trajectory of 0 µm to 100 µm
in 0 ms to 20 ms is given for xref
m , and a zero constant reference is given for θyref . T u = 200 µs, N = max(σ1 , σ2 ), andT r = NT y = NT u = T f .
4.2 Simulation Result
In this study, the simulation of
the proposed method, in which the generalized controllability indices can be selected in three ways, as shown in Fig. 5,
is conducted with the conventional method.

Experiment

4.1 Condition
The block diagram of the simulationis shown in Fig. 2. Generally, a dual-input dual-output plantwith a coupling problem is represented by a block diagram, as
shown in Fig. 1(c). g11 to g22 represent the transfer functionof each path. Conventional method 1 ignores the interferenceby g12 and g21 and the multirate feedforward controllers aredesigned for each SISO system g11 and g22 , respectively, as
shown in Fig. 4(a). Coupling is suppressed by the feedback
controller. Conventional method 2 designs a precompensatorfor continuous-time plants that cancels the interference between axes by g12 and g21 , and the multirate feedforward controllers are designed for each decoupled SISO system g11 andg22 , respectively, as shown in Fig. 4(b). In this method, theprecompensator is discretized by the bilinear transformation.
Because the problem of the unstable discretization zero is notconsidered, PTC cannot be achieved, theoretically. In the
proposed method, a dual-input dual-output multirate feedforward controller is designed for a dual-input dual-output plant,as shown in Fig. 4(c).
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PTC Considering GCI and Application for High-Precision Stage（Masahiro Mae et al.）(a) g11(b) g12(c) g21(d) g22

Fig. 6. Frequency responses of the plant. G4 and G2 denote a 4th order MIMO nominal plant and a 2nd order
SISO nominal plant, respectively"#(σ1 , σ2 )=(2, 2) : B = A s b s1 b s1 A s b s2 b s2
· · · · · · · · · · · · · · · · · · · (31)"#(σ1 , σ2 )=(3, 1) : B = A2s b s1 A s b s1 b s1 A2s b s2 + A s b s2 + b s2

· · · · · · · · · · · · · · · · · · · (32)"#(σ1 , σ2 )=(4, 0) : B = A3s b s1 A2s b s1 A s b s1 b s1
· · · · · · · · · · · · · · · · · · · (33)The simulation result is shown in Fig. 7 to Fig. 11. Fig. 12
and Fig. 13 show the tracking error of each output. Fromthe simulation results, PTC cannot be achieved with the conventional method, but it can be achieved in all three casesof the proposed method. The eﬀectiveness of the proposed
method is verified. It is noteworthy that the second-order relative degree plant moves the second-order polynomial trajectory between the sampling points. Therefore, the errors occur
between the sampling points because of the diﬀerence in theorder between the second-order polynomial trajectory and theseventh-order polynomial trajectory. This is an error becauseof the physical model, and not a mechanical vibration.
4.3 Experimental Results
In the experiment, theproposed method of (σ1 , σ2 ) = (2, 2), conventional method
1, and conventional method 2 are compared under the same
conditions as the simulation.
The experimental result is shown in Fig. 14. From the experimental results, the tracking error of θy in the proposed
method is the smallest compared with that in the conventional
methods. The tracking error of xm in the proposed method
is not clearly smaller than that of other conventional methods, because we focus on the fitting of the transfer function
g21 representing the coupling from the translational force f xalong the x axis to the rotation θy around the y axis to prevent
pitching in this model. Therefore, the modeling error of g12
may worse the tracking error of xm . The coupling of the feedback controllers is also a problem. Because it is verified thatthe tracking error becomes smaller and the control performance improves in the simulation that has no modeling error,
it appears that the modeling error influences the experiment.
From the simulation and experimental results, the applicability of the proposed method is verified and the improvementin the modeling error will be future work.
5.

(a) xm(b) θy(c) e xm(d) eθy(e) f xﬀ(f) τyﬀ

Fig. 7. Simulation results of the conventional method 1

as using a precompensator have been employed, and the system was controlled as a SISO system. However, when theprecompensator and SISO multirate feedforward controller
were used, it was theoretically impossible to achieve PTC
because the unstable zeros were generated by discretization.
In the proposed method, the MIMO multirate feedforward
controller achieved PTC. In this study, the eﬀectiveness ofthe proposed method was shown in the simulation and experiment of controlling two-DOF (x, θy ) of the high-precision
stage. The diﬀerences in the control performance dependingon the selection of the generalized controllability indices will
be considered in future studies. The proposed method loosened the restrictions of the mechanical design to suppress thecoupling problem; therefore, the freedom of the mechanicaldesign was improved.

Conclusion

The six-DOF high-precision stage has the coupling problem. In the conventional methods, decoupling methods such
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PTC Considering GCI and Application for High-Precision Stage（Masahiro Mae et al.）(a) xm(b) θy(a) xm(b) θy(c) e xm(d) eθy(c) e xm(d) eθy(e) f xﬀ(f) τyﬀ(e) f xﬀ(f) τyﬀ

Fig. 10. Simulation results of the proposed method(σ1 , σ2 ) = (3, 1)

Fig. 8. Simulation results of the conventional method 2(a) xm(b) θy(a) xm(b) θy(c) e xm(d) eθy(c) e xm(d) eθy(e) f xﬀ(f) τyﬀ(e) f xﬀ(f) τyﬀ

Fig. 9. Simulation results of the proposed method(σ1 , σ2 ) = (2, 2)

Fig. 11. Simulation results of the proposed method(σ1 , σ2 ) = (4, 0)

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PTC Considering GCI and Application for High-Precision Stage（Masahiro Mae et al.）(a) Conventional method 1.

(b) Conventional method 2. (c) Proposed method (σ1 , σ2 ) = (d) Proposed method (σ1 , σ2 ) = (e) Proposed method (σ1 , σ2 ) =(2, 2).
(3, 1).
(4, 0).

Fig. 12. Simulation result of e xm (zoom)(a) Conventional method 1.

(b) Conventional method 2. (c) Proposed method (σ1 , σ2 ) = (d) Proposed method (σ1 , σ2 ) = (e) Proposed method (σ1 , σ2 ) =(2, 2).
(3, 1).
(4, 0).

Fig. 13. Simulation result of eθy (zoom)(a) xm(b) e xm(c) f xﬀ(d) f x f b(e) θy(f) eθy(g) τyﬀ(h) τy f b

Fig. 14. Experimental results(7)

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(4)

(5)
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(8)

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PTC Considering GCI and Application for High-Precision Stage（Masahiro Mae et al.）Masahiro Mae (Student Member) received the B.E. degree from the
University of Tokyo, Japan in 2018. He is currently
working towards the M.S. degree in the Departmentof Advanced Energy, Graduate School of Frontier
Sciences, the University of Tokyo. His interests arein control engineering, motion control, and nanoscaleservo systems. He is a student member of the Instituteof Electrical and Electronics Engineers.

Yoichi Hori (Fellow) received the B.S., M.S., and Ph.D. degrees inelectrical engineering from the University of Tokyo,
Tokyo, Japan, in 1978, 1980, and 1983, respectively.
In 1983, he joined the Department of Electrical Engineering, the University of Tokyo, as a Research Associate. He later became an Assistant Professor, an
Associate Professor, and, in 2000, a Professor at thesame university. In 2002, he transitioned to the Institute of Industrial Science as a Professor in the Information and System Division, and in 2008, to the
Department of Advanced Energy, Graduate School of Frontier Sciences, theUniversity of Tokyo. From 1991 to 1992, he was a visiting researcher at
the University of California at Berkeley. His research fields are control theory and its industrial applications to motion control, mechatronics, robotics,
electric vehicles, and wireless power transfer. He has been the Treasurer of
the IEEE Japan Council and Tokyo Section since 2001. He was the winnerof the Best Transactions Paper Award from the IEEE Transactions on Industrial Electronics in 1993 and 2001, of the 2000 Best Transactions Paper
Award from the Institute of Electrical Engineers of Japan (IEEJ), and of the2011 Achievement Award of the IEEJ. He is an AdCom member of the IEEE
Industrial Electronics Society. He is also a member of the Society of Instrument and Control Engineers, Robotics Society of Japan, Japan Society of
Mechanical Engineers, and the Society of Automotive Engineers of Japan.
He is the past president of the Industry Applications Society of the IEEJ, thepresident of the Capacitors Forum, the chairman of the Motor Technology
Symposium of the Japan Management Association, and the director of Technological Development of the Society of Automotive Engineers of Japan.

Wataru Ohnishi (Member) received the B.E., M.S., and Ph.D. degrees from the University of Tokyo, Japan in 2013,2015, and 2018, respectively. Presently, he is a
research associate with the Department of Electrical Engineering and Information Systems, Graduate
School of Engineering, the University of Tokyo. His
research interest includes high-precision motion control. He is a member of the Institute of Electrical andElectronics Engineers.

Hiroshi Fujimoto (Senior Member) received the Ph.D. degree in the
Department of Electrical Engineering from the University of Tokyo in 2001. In 2001, he joined the Department of Electrical Engineering, Nagaoka University of Technology, Niigata, Japan, as a research associate. From 2002 to 2003, he was a visiting scholar in
the School of Mechanical Engineering, Purdue University, U.S.A. In 2004, he joined the Department ofElectrical and Computer Engineering, Yokohama National University, Yokohama, Japan, as a lecturer andhe became an associate professor in 2005. He has been an Associate Professor of the University of Tokyo since 2010. He received the Best Paper
Awards from the IEEE Transactions on Industrial Electronics in 2001 and2013, Isao Takahashi Power Electronics Award in 2010, Best Author Prizeof SICE in 2010, the Nagamori Grand Award in 2016, and First Prize Paper
Award IEEE Transactions on Power Electronics in 2016. His interests are incontrol engineering, motion control, nano-scale servo systems, electric vehicle control, motor drive, visual servoing, and wireless motors. He is a senior
member of IEE of Japan and IEEE. He is also a member of the Society of
Instrument and Control Engineers, the Robotics Society of Japan, and theSociety of Automotive Engineers of Japan. He is an associate editor of theIEEE/ASME Transactions on Mechatronics from 2010 to 2014, the IEEE Industrial Electronics Magazine from 2006, the IEE of Japan Transactions on
Industrial Application from 2013, and the Transactions on SICE from 2013
to 2016. He is a chairperson of the JSAE vehicle electrification committee
from 2014 and a past chairperson of the IEEE/IES Technical Committee on
Motion Control from 2012 to 2013.

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