KAYABATECHNICAL OCT. 2022
65
REVIEWKAYABA TECHNICAL REVIEW No. 65 OCT. 2022

No.

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KAYABA TECHNICAL REVIEW
No. 65 OCT. 2022
CONTENTS
Foreword
Rethink of Hydraulics for Sustainable Robotics

HYON Sang Ho

1

Technology Introduction
Making Plating Thickness Constant by Simulation


MIZUNO Yuuki
TERADO Ayuko

3

MATSUMOTO Daisuke

8Technology Explanation
Control Technologies for In-Vehicle Electric Actuators
ENOMOTO DaisukeProduct Introduction
Development of Vane Pump for Medium Passenger Vehicle CVT



Essay
Essay from Expatriate at HKEEssay from Expatriate at KMEX
Glossary⑴ Hard Chrome Plating⑵ Compensators in Control Systems
⑶ PV Values of Vane Pumps
Editors Script

KENJO Kazunori
FUKUSHI Natsuru
HAGIWARA Takahiro

26

OOTAKI Masashi
KONDO Hirotoshi
SHINDOU Shota
HATTORI Koji
KAWAI Hiroshi

32
36

MOCHIZUKI Yoshitaka

41
42
45

MATSUMOTO Daisuke
HAGIWARA Takahiro

KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

Foreword

Rethink of Hydraulics for Sustainable Robotics
HYON Sang Ho*

1. Prolog: Meditation During COVID-19 Pandemic
Two years ago, when the world was first hit by COVID19 infections, I tried to think of the value of robots. I
finally concluded that robots are ultimately a tool for mass
production, rather than machinery that can help people. I
have a university class on Robot Motion Control to teachstudents textbook theories for high-speed and accurate
control of hand motion trajectory tracking. This is essentially robotic theory for mass production. Today, however,
the world is saying "No" to mass production or volume
consumption.
When our socioeconomic activities were substantiallycurbed by the COVID-19 pandemic, people fully realized
how their individual activities should be prioritized or
how many so-called "bullshit jobs" they had. While I wasteaching online via my PC screen at home feeling something was wrong, essential workers throughout the world
were being exposed to risks of the infection as they diligently worked to relentlessly support society.
We may now have grown more or less accustomed tothe pandemic situation. Looking around, we can findroads, waterworks, power grids, and other society supporting infrastructure having seriously deteriorated due toa lack of labor. Infrastructure is something that is manmade. If you say people's health can be maintained byhealth care personnel including doctors and nurses, thenman-made things can be maintained by engineers.
As just an engineer, what could I do for society onearth? What could I do, as an educator, for young people?
One could certainly create novel things to attract people's
attention as in the Expos in the past. Inventors could feelexcited about and satisfied with them. Behind that,
however, people are involved in wasteful volume consumption, which is threatening the globe. It is now necessary to undergo a paradigm shift from robotics that canjust satisfy the mega-corporations' needs for high-volume
production for higher profits to another robotics as a new
methodology for mankind to survive.
Even after two years of agonizing over such issues, I
have not yet reached a solid conclusion. Still, there is achallenge I am now trying to address. It is modular robots.
* Professor at Ritsumeikan University

2. Modular Robot Project
Based on the social and natural environments we are in,needs will rapidly increase for civil engineering and construction, transportation, and facility maintenance operations in basically non-accessible environments, such as inagriculture, forestry and fishery, infrastructure maintenance, and disaster recovery. In response to these various
novel needs, not only high-performance robot equipment
but also total robot solutions that can reduce the operators'
burden and costs are needed.
One of the potential concepts for such solutions ismodular robots. Multiple single-function robots working
independently can be combined with each other to becomea robot assembly that can flexibly perform various tasks.
These modular robots offer many operational benefits,
including structure selection and allocation with the rightrobots in the right place, maneuverability and portability,and easy manufacturing and maintenance. Reconfigurable
robots and self-organized robots already exist in the academic area. These can be defined as robot systems toachieve a specific purpose while adapting their own shape
to indefinite circumstances. Many papers in the past haveshowed examples of concepts or simulations where anumber of objects of similar morphology are combined to
become an assembly forming a specific structure.
However, most of these papers relied on computer graphics (CG) based studies mainly using planning algorithms.
Actual machine-based studies of this kind mainly coveredgroup displacement robots. Attempts to accomplish heavy
duty tasks that are generally assumed to be done by
outdoor robots have seldom been made.
Our challenge is to integrate modular robots withhydraulics. Specifically, we are thinking of maximizing
the robustness and high output specific to hydraulics aswell as the protean power collection and distribution
capability of hydraulic circuits and piping. The former
was introduced in the Technology Introduction article
titled Development of a Hydraulic Module Robot included
in KYB Technical Review No.61 in 2020. The latter
concept was presented at the International Conference on
Robotics and Automation (ICRA) of Institute of Electricaland Electronics Engineers (IEEE) in 2022.
For comparison purposes, let me take conventional―1―Rethink of Hydraulics for Sustainable Robotics

hydraulic machinery. For example, hydraulic excavators
have arms similar in shape to those of industrial manipulators. They can show great activity for disaster recovery
as powerful and reliable robots, although they are seldom
used as autonomous machinery. The front-end part ishighly modularized to accept a variety of attachments. For
hydraulic excavators, hydraulic equipment manufacturers
provide various actuators as discrete components, including cylinders, valves, and pumps. Still, it is difficult tomodularize these actuators because of the design ofhydraulic excavators wherein their drives are located at
the root of the machinery.
Industrial actuators integrated with drive sources represented by electro-hydraulic actuators (EHAs) haverecently become commercially available. Using this typeof actuator will realize robot modules integrated with ahydraulic source, although the power supply challenge
remains. However, such simple integration would inevitably result in robots with too heavy front ends, leading toan overall deterioration in performance. What impedes
modularization is essentially weight. Could it be possible
to realize a modular robot that can be manually carried
and assembled by people and is able to lift loads at least
equivalent to its own weight, although it could not be somodularized that it could easily be assembled by hand likehobby robots? If attachment and detachment of modular
parts can be automated, the robot can also assemble itself
without human intervention.
This research project considers the potential of hydraulics in several areas:A) The use of small pumps will allow robots to deliver
high output with small motors although the motor
speed is low.
B) For light loads, external pumps can be used to moverobots with agility.
C) 
Possible to manufacture shock-resistant, weatherproof robots at low cost.
D) Robot power can be monitored and controlled bymeans of pressure.
E) Pressure boosting and merging will allow multiple
shafts to interchange power.
F) Parts attachment and detachment can be achieved
with hydraulics.
Based on these ideas, research challenges were set up
and a research plan developed.
Certainly, robots that are mechanically merged andassembled are substantially inferior in performance tooptimally-designed integrated robots. Is this always true?
A question to be posed is, based on the operational needs
mentioned at the outset, "what are the conditions that give
hydraulic modular robots advantages to conventional
integrated robots?" Note that conventional robots include
pure electric robots. It is important to specifically verify
several hypotheses.

3. Epilog
Under the big slogan of the paradigm shift from tangible
to intangible goods, people's interest in tangible goods has
diminished. Equipment mechanisms are hidden like a
black box and treated as second-rate things to be consumed in an instant, like something on a smartphone
screen. It is certainly good to get things done easily, but
how many engineers who can understand and interact
with mechanisms of tangible products would survive inJapan if the tendency of people to move away from tangible goods is going to progress in this pace? The samething can be applied to artificial intelligence (AI). Being
indifferent to technology can be considered as a kind ofabandonment of thinking. It is very dangerous to leaveadvanced robot technology to just a few people.
Renovation and similar concepts (including sustainable
design) will increasingly affect how people face nature or
artifacts. Concepts of these kinds always involve inconspicuous and rough-and-ready impressions, rather thanbrave, stereotype cutting-edge images as seen in great
discoveries of novel materials or big inventions regarding
their application. Moreover, they are very hard workrequiring people to be patient and cannot be achieved
without deep understanding of tangible goods and technology. I heard that, under this situation, more and moreyoung people have started to feel something strange aboutmass production and volume consumption. They tend tolove traditional or old things and are trying to put theirown ideas into them to produce additional value. This isdefinitely good news.
To cause renovation to sublimate into science, newinsights and methodologies are needed. Hydraulicmodular robots could be considered as products of renovation of conventional hydraulic machinery. From thenew perspective of modular robots, we can say we aretrying to take lessons from history or hydraulic technology that can be considered well established. While conventional robotics might play the passive role of justresponding to the industrial world's needs (mass production), new robotics should be "technology for all" withwhich people can voluntarily and boldly address difficult
issues in the Anthropocene era. Thinking patiently, wewant to repeatedly make and verify assumptions for as
long as time permits.
Finally, I would like to take this opportunity to thankKYB Corporation for their support for research and education at Ritsumeikan University. While many people areanxious about the sharply worsening issues of global
warming, the COVID-19 pandemic, and food and resource
risks, I hope that all engineers from KYB will continue toproudly support society more and more and work toward
Monozukuri that can save the earth.

―2―

KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

Technology
Introduction

Making Plating Thickness Constant by Simulation
MIZUNO Yuuki, TERADO Ayuko

Introduction

2This chapter describes the major characteristics of electroplating including hard chrome plating. For electroplating, the film thickness is generally proportional to thequantity of electricity (current × time) (Faraday's 1st law).
When applying plating to workpieces, the current islikely to concentrate at the edges of them, resulting inthicker films (Fig. 2). This phenomenon can be prevented
by the use of shorter electrodes. In facilities where workpieces of different lengths are plated, however, just changing the length of the electrode would not be enough. Then,jigs can be installed at the edges of a workpiece to suppress the concentration of the current at the edges, curbing
the increase in plating thickness.

PlatingWork

Surface of plating solution

Electrode

Note 1) M asking jigs used to prevent plating or limit the film
thickness
Note 2) Three to four tries were needed before completion: 2
weeks/try(according to interviews with operators)

Work

Surface of plating solution

Plating

Recent years have seen the promotion of digital technologies including artificial intelligence (AI) and Internetof Things (IoT) in virtually all fields. Even techniques thathave long been conveyed as craftmanship are becoming
subject to standardization with digital technologies.
KYB Corporation frequently applies hard chrome
plating to sliding parts of shock absorber piston rods andother components. This plating requires masking jigs
(hereinafter "jigs") Note 1) because of its characteristics.
Conventional jig design relies on work learned only
through actual experience (so-called knack or intuition) of
operators. It is difficult to achieve constant deposition ofplating (hereinafter "film thickness"). Since jig fabricationand plating prototyping are needed for each try, many
man-hours are spent to discuss and determine the form ofjigs Note 2) (Fig. 1). With this background, KYB has developed a jig design methodology requiring no knack or
intuition by utilizing simulation software. This paper
introduces a case study of our efforts to achieve constantplating thickness of industrial hydraulic equipment products by means of simulation.

Characteristics of Electroplating

Electrode1

Jig

Fig. 2 Illustration of effects of jigs

Designerror

3
Jig fabrication

Form modification

Trial plating
Completion
Fig. 1

Repeated
trial and error

Conventional jig design flow

Preliminary Test on Stepped Work

Before redesigning the jig through simulation, a preliminary test was conducted using a stepped workpiece.
Fig. 3 shows the front view of the preliminary test equipment. The workpiece and electrodes are vertically inserted
into the plating bath. In total four electrodes are installedaround the workpiece. This stepped workpiece consists ofthick and narrow sections: the former has a diameter ofø22 and the latter ø10. All of these sections, regardless ofthe diameter, are 100 mm long. The test conditions areshown in Table 1. As mentioned in the previous chapter,―3―

Making Plating Thickness Constant by Simulation

High

Electrode

Current

Work

The trends of film thickness distribution of sections A,
B and C obtained through simulation almost match thoseobtained through actual measurement. Therefore, the use← density →the edges or corners of the workpiece are likely to havehigher current density which builds thicker films. The test
was carried out to verify whether this phenomenon can be
reproduced in simulation.

Plating bath

Low

Table 1

Plating conditions for preliminary test

Item
Plating bath
Plating solution temperature
Plating area
Current density
Current setting
Plating time

Settings
Sargent bath
50°C
1.7 dm2
40 A/dm2
70 A
30 min.

Analysis results (current density distribution)
Measurement
Analysis

Distance from solution surface [mm]The simulation software used for this research isintended to be used for analysis of current density (A/dm2). Since analysis results cannot be directly comparedwith film thickness measurements, the analysis results (A/dm2) have been converted into the film thickness (μm)
using Equation (hereinafter "Eq.") (1):Film thickness μm = Deposition speed μm/min·A·dm-2 ×
Current density A/dm2 × Plating time min × Current
efficiency
(1)Fig. 5Film thickness

Sketch of preliminary test equipment
Film thickness

Fig. 4
Fig. 3Comparison in section A

Measurement
Analysis

Distance from solution surface [mm]―4―Fig. 6

Film thickness

A contour diagram of the analysis results is shown in
Fig. 4. For convenience, the top section of ø22 is called A,
the middle section of ø10 called B, and the bottom sectionof ø22 called C. The edges of sections A and C as well as
the central part of section B have a higher current density,
while the edges of section B have a lower current density.
Comparison between the analysis results and the measurements are shown in Figs. 5 to 7. For the purpose ofthis paper, the "film thickness" (vertical axis) in the
Figures indicates individual measurements that havebeen divided by the mean value of the film thickness ofthe flat parts (A: 10 mm to 60 mm, B: 130 mm to 170 mm,
C: 230 mm to 270 mm) of the workpiece and then madedimensionless.

Comparison in section B

Measurement
Analysis

Distance from solution surface [mm]Fig. 7Comparison in section C

KAYABA TECHNICAL REVIEW No. 65 OCT. 2022of the simulation model and conditions developed for the
research can be used to obtain a film thickness distribution similar to the actual phenomenon.
4

Making Film Thickness Constant

Since the simulation model was validated through thepreliminary test, its utilization in mass production equipment was tried.
4.1 Target Product
The piston rods for forklift cylinders were selected as
the target product (Fig. 8).
Cylindertime and consumed extra electricity and chemicals.
While the central part of the rod has a constant film
thickness, the edges of the rod have uneven film thicknesses due to the concentrated current and the shielding
effect of the jig. Through comparison with the simulation
results, it was verified that the tendency of the film thickness distribution was successfully reproduced.
4.3 Redesigning the Jig
To make the current density distribution indicated by
the analysis results more uniform, we tried to find an
optimal form of the jig by repeatedly changing and analyzing the aspect ratio, hole diameter and the number ofholes of the jig model (Fig. 10). This redesigning was
carefully conducted because the current density distribution greatly varies with the jig form (Fig. 11). The authors
Analysis software
conditions
setting

Gear pump

Model creation
with CAD
softwareControl valve

Fig. 8Target productCalculation

4.2 Conventional Jig
Fig. 9 shows measurements of plating thickness
obtained with the conventional jig (Photo 1). An electromagnetic plating thickness gauge was used to measure thefilm thickness of workpieces longitudinally along a
straight line. The Figure includes a sketch of the workpiece installed with the jig.
The jig design was based on operators' knack and intuition, resulting in uneven film thicknesses. In particular,
the masked portion had a substantially lower film thickness. To compensate for the film thickness in this portion,
thicker plating was made overall. This led to longer plating

Model modification

Result checking

Jig fabrication

Trial plating

Completion

Fig. 10

Jig design flow using simulation software
Design #3

Design #1

Photo 1

Design #2

Conventional jig

Current density

Film thickness

Measurement
Analysis

Distance from the top edge of plating

Fig. 9Final design

Design #1
Design #2
Design #3
Final design

Distance from the top edge of plating

Comparison between measurement and simulation(conventional jig)

Fig. 11―5―

Analysis results of various jig model versions

Making Plating Thickness Constant by Simulation

had no previous experience of jig form design. After about
two weeks of redesigning work, the "final design" includedin Fig. 11 was obtained through repetitive modification of
the jig model.
As indicated by the workflow in Fig. 10, the simulation
cycle was effectively used to successfully fabricate the jig
and verify the plating with a single try.
4.4 Verifying the Effect
The jig prototype obtained through the jig fabricationand trial plating processes was compared with the conventional jig. For the purpose of this paper, the prototype iscalled the "improved jig" (Photo 2). Fig. 12 shows film
thickness measurements with the conventional andimproved jigs. The film thickness variation {(Maximum
film thickness - Minimum film thickness) / Mean film
thickness} of the conventional jig was 57% of the mean
film thickness. In contrast, the film thickness distributionof the improved jig was as low as 11% of the mean value.

Analysis software
conditions
setting
Optimization software
Model creation
with CAD
softwareCalculation

Result checking

Jig fabrication

Completion

Film thickness

5

Jig design flow using optimization software

5.1 Conditions Setting
For the purpose of redesigning the jig, the five parameters listed in Table 2 were selected for conditions settingin the optimization software. 100 combinations of parameter settings were subjected to calculation by the software
to determine the jig form with the smallest variation infilm thickness. Fig. 14 shows what the parameters indicate
in the actual jig.

Improved jig

Conventional
Improved

Parameter settings for optimization software

Table 2

Distance from the edge of plating

Fig. 12

Automatic model
modification &calculation

Trial plating

Fig. 13

Photo 2Model modification

Comparison of film thickness measurements

Further Efforts for Even Higher Efficiency

The company's traditional jig improvement relied on
operators' knack and intuition and the redesigning required
about six weeks. For the authors' jig improvement throughsimulation, the redesigning time was reduced to two
weeks. However, the model improvement through simulation involved repetitive trial and error and could notcompletely exclude the dependence on operators’ knackand intuition. The reduction of improvement time remains
a big challenge even after the introduction of simulation.
Then, we tried to reduce the redesigning time andeliminate the dependence on knack and intuition by introducing an optimization software product Note 3) to allow themodel modification and calculation processes to be done
automatically (Fig. 13).
Note 3) Software used: Simcenter HEEDS®

―6―

Parameter settings
Outside diameterø47-85 mm
Height5-130 mmHole diameterø1-30 mm
Number of longitudi2-10
nally aligned holes
Number of circum4-20
ferentially aligned
holes

100
combinationsof parametersettings wereanalyzed.

Work

Electrode
Electrode

No. ofcircumferentiallyaligned holes

HeightOD
Work
No. oflongitudinallyaligned holes
Upper surfaceof plating bathFig. 14

Front view of jig

Locations of parameters

Jig

KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

plating has been applied based on the film thickness at theedges, which is lower as shown in Fig. 16. Plating in thisway will provide an excessive film thickness on the flatpart that is away from the edges of the plated work. Then,the improved jig can be used to ensure work has a higher
film thickness at the edges than on the flat part, thereby
enabling the excess in film thickness to be eliminated (seethe shaded zone in Fig. 16). The plating time can also be
reduced by an amount corresponding to the film thickness
reduction, leading to lower processing cost and lower CO2
emissions.

Film thickness

5.2 Film Thickness Measurements
The model obtained through calculation using the optimization software was used to fabricate a jig (Photo 3).
This jig was trial plated and then subjected to measurement of film thickness.
As shown in Fig. 15, the film thickness variations werereduced to about 1/3 (19%) of those of the conventional
jig, although this result was inferior to that of the improved
model (11%) obtained only through the simulation software. Furthermore, the redesigning time was reduced toas little as eight hours, which is about 1/10 of the timespent for the improved jig (i.e., two weeks: equivalent to
80 working hours). Thus, "anyone" can now "easily"
design a jig in a "short time" just by entering the fiveparameters.

Improved Ver.2
Improved
Conventional

Reduceable plating time

Distance from the edge of plating

Film thickness

Photo 3Fig. 16

Improved jig Ver.2

7

Improved Ver.2
Improved
Conventional

Distance from the edge of plating

Fig. 15 Comparison of film thickness measurements #2

6

Future Prospects

Additional expected benefits from this effort include
lower processing costs (for electricity and chemicals) andlower CO2 emissions due to shorter plating time.
Plating should be applied to applicable products toensure that the thinnest part of the plating film meets thefilm thickness requirements. However, conventional

Expected benefits

In Closing

It was verified that the simulation is very effective forachieving constant plating films and higher productivity.
In addition, the utilization of the optimization software
was shown to enable jig redesigning that does not depend
on knack and intuition and a substantial reduction in redesigning time.
The simulation can also be expected to be utilized tofind causes of inappropriate film thickness or even for
discussion of the specifications for new plating lines (suchas throughput). KYB operates a variety of working processes including heat treatment and cutting as well as
plating. It is desirable to effectively apply the simulation
methodology not only to plating but also to various otherworking processes.
Finally, we would like to take this opportunity to sincerely thank all those concerned inside and outside KYB
who have extended cooperation to this development.

Author 
MIZUNO Yuuki

TERADO Ayuko

Joined the company in 2019.
R&D Sect. No.1, Production
Technology R&D Center,
Engineering Div.
Engaged in development of surface
treatment technology

Joined the company in 2012.
R&D Sect. No.1, Production
Technology R&D Center,
Engineering Div.
Engaged in development of surface
treatment technology―7―

Control Technologies for In-Vehicle Electric Actuators

Technology
Explanation

Control Technologies for In-Vehicle Electric Actuators
MATSUMOTO Daisuke, ENOMOTO Daisuke, KENJO Kazunori, FUKUSHI Natsuru

Abstract
KYB develops and manufactures various in-vehicle
actuators including electric power steering (EPS). The
control specifications of the actuator differ depending on
the function, but it is a common issue to achieve a systemthat operates stably and satisfies the required functions
and performance. In addition, when controlling the actuator, the control system may become unstable dependingon the design of the control compensator, so it is neces-1

Introduction

Compared with electric power steering (EPS) for passenger vehicles, EPS for all-terrain and utility task vehicles, particularly for off-road vehicles, is required todeliver more highly responsive steering assist and kickback control performance. To satisfy these performancerequirements, it is a precondition that the EPS hardware(including the motor described later and its driving circuit,gear assembly, etc.) has been properly designed. In addition, it is necessary to maximize the hardware capabilities
by using software (i.e., with a proper control methodology). Specifically, the open-loop gain of the control
system (a gain of the loop transfer function) must be set toa level as large as possible within the frequency ranges inwhich the steering assist and kickback control performance are required. However, care must be exercised insetting the open-loop gain because just using a high openloop gain would reduce the gain and phase margins (hereinafter "stability margin"), resulting in an unstable control
system in some cases. As an approach to ensure a stability
margin while using a high open-loop gain (hereinafter"stabilization"), a phase compensator Note 1) has been used.
For stabilization using this approach, the phase compensator is designed with a focus on the gain and phase
information of the frequency characteristics of the looptransfer function of the control system (called a "nonparametric model"). It is relatively easy to implement aphase compensator, but designers need to adjust design
parameters through trial and error while carefully observing the frequency characteristics. This means that suchdesigners need to have a certain level of experience andsary to design the compensator after grasping the characteristics of the actuator to be controlled.
In this report, we explain the compensator design
method for the steering assist control of EPS for all terrain
vehicles and utility task vehicles and for steering angle
control with an eye toward future application in automatic
steering, as well as the implementation method of thisdesign method. This report also describes the future
outlook.

knack. As described later, the compensator is assumed tobe redesigned in phases during the development stage.
For higher efficiency in development, it is desirable toautomate the compensator development processes, including from design to implementation, to some extent.
However, design tool automation can hardly be achievedby conventional approaches.
Note 1) The compensator in a control system is a computing unit
intended to generate control input to impart desirable
characteristics to the system. A phase compensator isdesigned with a focus on the gain and phase of the looptransfer function of the control system.

On the other hand, robust control theory, typified by the
H∞ control theory, involves approaches that use the transfer function and state equation of the controlled object(called a "parametric model") to design the compensator
through inverse operation from the desirable characteristics (target tracking and disturbance response) of thecontrol system. In these approaches, the controlled object,
the characteristics of the control system, and disturbances
are represented by parametric models and the related
various equations are solved to determine the compensator. This means that design tools can relatively easily be
automated, delivering the benefit that compensators canbe designed more efficiently. These design approaches
may be effective to catch up with the rapid development
specific to the all-terrain and utility task vehicles market.
In general, compensators designed based on robust
control theory tend to be more complicated (with higher
degree) than phase compensators. However, in-vehicle
microprocessors mounted with floating point units (FPUs)
have been generally introduced in recent years to allow―8―

KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

implementation of compensators of relatively high degree.
This report explains how to design steering assist andsteering angle control compensators for EPS based on theparametrization of stabilizing compensators 3), which isone of the basic theories of robust control.
2

EPS Systems

2.1 Components of EPS System
Fig. 1 shows the components of the EPS for all-terrain
and utility task vehicles.
The electromechanical brushless motor shown in the
Figure (hereinafter "the power pack") is a brushless motor
integrated with a controller (hereinafter "the motor") as
the name implies. This component performs computations
for all controls including steering assist control.
The torque angle sensor (TAS) is another component
that detects the torque and angle of the steering wheel
operated by the driver. The steering assist control uses
torque values detected by the TAS as described later. The
steering angle control uses angle values detected by the
TAS to set the origin of the steering angle that is calculated from the motor rotation angle.
The gear assembly has a mechanism by which thetorque generated by the motor is amplified by a worm
reducer and this rotary motion is converted into a linear
motion by a rack and pinion device. This component
transfers the steering torque produced by the driver andthe steering assist torque generated by the motor to thevehicle's wheels as a cornering force.

TAS (Torque Angle Sensor)

communication function to communicate with the vehicle
and other sub systems via a CAN network, and ③ Control
functions including motor vector control, steering assist
control, and steering angle control.
With a focus on the steering assist and steering angle
controls, the next chapter describes how to design compensators for these controls.

Controller

Driving
circuit

Gear
assy

Motor

TAS

Torque signal
Angle signal

Rotation angle
sensorCurrent sensor
Motor rotation angle, current

Fig. 2 Block diagram of EPS system

3

Overview of Compensator Design

3.1 Components of Control System
Fig. 3 shows an overview of the control system (thecontrolled object + compensator) with a focus on thesteering assist control or steering angle control.
The control input to this control system is from motor
current commands. The control output from the system issteering angle or torque values from the TAS (the steering
angle is calculated from the motor rotation angle). The
load torque is attributable to the driver's steering andkickback transferred to the motor via the gear assembly
and the friction torque of the gear assembly.
In the Figure, the area enclosed by the red broken line
represents the controlled object, which is a mixed systemof hardware and software. The former includes the motor,
the driving circuit, the controller, and the gear assembly,
and the latter is for motor vector control and steering
angle computation.
Target value
signal(CAN)

Vehicle speed and othersignals (CAN)

Motorcurrent
commandCompensator
Control
inputElectromechanicalbrushless motor (Power pack)

Controlled
objectLoad torque
TorqueVectorcontrol

Driving
circuit

Motor

Current
sensorRotation
angle
sensor

Gear
assy

TAS

Angle

Current
Control
outputGear assy

Steering
angle SteeringEPS components for all-terrain and utility task
vehicles

2.2 Block Diagram of EPS System
Fig. 2 is a block diagram of the EPS system.
The controller has three major functions; ① A monitoring function to detect any abnormality of the CPU, driving
circuit and sensors, and perform fail-safe processing, ② A

Motor rotation angle

angle
computation

Fig. 3Fig. 1

Steering
kickback

Vehicle speed andother signals (CAN)

Overview of control system

3.2 Compensator Design Policy
Within the controlled object shown in Fig. 3 in the previous section, the hardware including the driving circuit,motor, and gear assembly behaves electrically or mechanically in real time. With these physical phenomena, thehardware constitutes a continuous time system. On theother hand, the software is a discrete time system Note 2)
because vector control and steering angle computation are―9―Control Technologies for In-Vehicle Electric Actuators

performed by digital computers. Therefore, the actual
controlled object is a mixed system of continuous anddiscrete time systems. The control input to and output
from the controlled object are updated or sampled at eachof their own control frequencies. That is, the controlled
object ranging from the control input to the control output
can be represented by a discrete time model Note 3). The
compensator can also be represented by a discrete timemodel because its computation is performed by digitalcomputers.
Note 2) A system whose behavior is defined with discrete time(hereinafter "sampling time").
Note 3) A discrete time model is a difference equation or transfer
function representation of the behavior of the controlled
object under the control of a digital computer at a sampling time or the behavior of a discrete time system.

Conventionally, the set of the controlled object andcompensator has been considered as a continuous timesystem. In this approach, the compensator is designed
according to continuous time and then discretized using,for example, a bilinear expression before implementation.
This approach has the problem that design stability
cannot be ensured in actual systems. One major factor isthat a compensator that has been discretized with a bilinear expression, for instance, cannot necessarily become astabilizing compensator for the discrete time system (i.e.,the stability margin for the discrete time system cannot
be guaranteed) (Challenge ①). Another major factor
relates to modeling error of the controlled object (discrepancy between the model and the actual system). The
system cannot be stable if the designed compensator was
not a stabilizing compensator for the actual system in thefirst place (Challenge ②). To address Challenge ①, it isuseful to represent the controlled object as a discrete timemodel and design the compensator according to the discrete time system. For Challenge ②, it is effective to use
the frequency response method or the method of identification 4) using maximum-length sequence signals todetermine a model for designing the compensator (hereinafter a "compensator design model"). Then, we havedecided to introduce the approach of representing thecontrolled object in a discrete time model and designing
the compensator in a discrete time system. We also identify the system to be controlled upon completion of the
hardware fabrication and design the compensator using
the identified compensator design model. We use δ (delta)
operator 5) as a discrete time operator representing thecontrolled object and compensator model. The δ operator
can be expressed as δ = (z - 1)/Tc (where z is the z operator
and Tc is control frequency). A major advantage of using
the δ operator is that relatively high accuracy can beobtained with compensator computation with a low
number of bits. For more information, see References 4), 5).
3.3 Block Diagram of Control System
The controlled object included in the control system
shown in Fig. 3 can be approximately represented by ablock diagram as shown in Fig. 4:

Zero-orderholdFig. 4

SamplerB lock diagram of controlled object (continuous timesystem)P(s) in Fig. 4 is the continuous time model (transfer
function) of the controlled object. k is an integer not lessthan 0 (zero) used to indicate the sampling time [ts(k) =kTc (k = 0, 1, ...)]. u(k) is the output from the compensator,
namely, control input (motor current command). u(t) isu(k) held every "time" ts(k). y(k) is the control output thatis y(t) sampled every "time" ts(k). Control output y(k) will
be a TAS torque signal for steering assist control or asteering angle for steering angle control. d(t) is the disturbance attributable to the load torque shown in Fig. 3 andthe rotation of the steering wheel operated by the driver.
d0 is a constant. Gd(s) is the transfer function representing
a disturbance generator. Note that u(t) and u(k) are signalsthat are different from y(t) and y(k) signals, but for convenience these are not differentiated by symbols.
The block diagram of Fig. 4 may be represented by adiscrete time system as shown in Fig. 5. P(δ) and Gd (δ)
are transfer functions (discrete time models) obtained byzero-order holding and discretization P(s) and Gd (s) witha sampler, respectively. Note that P(s) and P(δ) are transfer functions that are different from Gd (s) and Gd (δ)
transfer functions, but for convenience these are also notdifferentiated by symbols.

Fig. 5

Block diagram of controlled object (discrete timesystem)Thus, the control system in Fig. 3 can be represented
using the transfer function model P(δ) of the controlled
object and the transfer function model C(δ) of the compensator as shown in Fig. 6. In Fig. 6, r(k) is the target
steering angle signal. r0 is a constant. Gr(δ) is the transfer
function representing the target value signal generator.
This report describes how to design a compensator C(δ)
for the control system in Fig. 6. Note that C(δ) is assumed
to be a two-degree-of-freedom controller as follows:
C(δ) = [Cr(δ) Cy(δ)](1-1)u(k) = Cr(δ)r(k)－Cy(δ)y(k)(1-2)― 10 ―KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

Fig. 6Block diagram of control system

3.4 Compensator Design Flow
Fig. 7 shows the compensator design flow as a V-shaped
process diagram. This section describes what to do in eachof the design processes (the flow to the left in Fig. 7).

Setting design specifications and modeling
controlled object and disturbance
Checking behavior on actual vehicle

Requirement
specification

Reflecting system
identification results andredesigning compensator

Systemevaluation

s

es

pr
oc
on

Unit
evaluation

ati

oc
pr

Agreement
verification
Model
verification

ific

n

Detailed
design

Ve
r

sig

De

es

s

Basic
designActual vehicle
evaluation

Automatic code
generation

Fig. 7

V-shaped process of compensator design

3.4.1 Requirement Specification
The following describes what to do in the Requirement
Specification stage.
(1) Setting design specifications
For steering assist control, an assist map where motor
current commands are mapped against TAS torque signals
is used to set the assist torque. A higher assist torquemeans a larger open-loop gain. A major requirement forthe design specifications is that the required assist torquecan be generated stably (i.e., without issuing harmful
vibration). In other words, the control system will remain
stable even with the maximum assumed open-loop gain.
For steering angle control, the steering angle will follow
the target steering angle signal r(k) in Fig. 6. Major design
specifications include, for example, delay time, rise time,
setting time, overshoot, and steady-state deviation to r(k)that may change stepwise or in ramp rate.
(2) Modeling controlled object and disturbances
Controlled object models can roughly be divided into
two types. One is a high-precision simulation model 6) thatcan estimate in relative detail the behavior of the actual
system (hereinafter "the simulation model"). The other isa simplified model for designing compensators (the aforementioned compensator design model). A compensator
design model can be derived from a differential equationthat has linearized and simplified the controlled object. A

compensator design model can also be derived throughidentification of a system using the simulation model or
actual machine. The identification of systems using an
actual machine will be described later. The simulation
model can be created and implemented mainly by using
tools such as MATLAB®/Simulink® and SimulationX®.
The disturbances that may be applied to the controlled
object include; ① Rotation of the steering wheel operated
by the driver (for steering assist control), ② Load torquedue to kickback, and ③ Friction torque of the gear assembly. For steering assist control, these disturbances can be
represented by a transfer function model with an assumption of steering frequency as described later. For steering
angle control in turn, the disturbances should be represented by a step or ramp function model based on theassumption that, with the driver's hands off the steering
wheel, the steering angle can follow the steering angle
command without steady-state deviation under disturbances ② and ③.
3.4.2 Basic Design
In the basic design stage, a compensator is designed
using the compensator design model and the assumed
disturbance model. The compensator can be expressed bya transfer function model C(δ) in this stage. The simulation model and the designed compensator are used tocarry out simulation and verify the adequateness of thecompensator during this stage. The compensator design
will be described in detail in Chapter 4.
3.4.3 Detailed Design
In the detailed design stage, the compensator designedin the basic design stage is developed into an implementation model to be contained in the controller as software.
This stage should verify that the compensator C(δ) derived
in the basic design stage is equivalent to the implementation model (i.e., identical inputs will produce the same
output).
3.4.4 Automatic Code Generation
Embedded Coder® is used to automatically generate
codes from the implementation model.
4Compensator Design

This chapter describes the details of the basic design ofcompensators for steering assist control and steering angle
control. The compensator design for steering assist control
is different from that for steering angle control in control
output, design specifications, and disturbances. The twocompensators can be applied with the same design
approach.
4.1 Basic Design of Steering Assist Control Compensator
4.1.1 Deriving a Compensator Design Model
An EPS model is shown in Fig. 8:
The EPS shown in Fig. 8 is a single-pinion type. Thismodel can also be applied to double-pinion or column― 11 ―

Control Technologies for In-Vehicle Electric Actuators

Torsion bar

the equations below:
δx(k)＝APδ x(k)＋BPδu(k)(3-1)y(k)＝CPδ x(k)(3-2)
where

Motor

Worm reducer

APδ＝（APz－I2）/Tc , I2: 2 × 2 unit matrix

BPδ＝BPz /Tc, CPδ＝CPz＝CP

APz＝e A T , BPz＝∫T0 e A T dτ BP
P cSpring load

Fig. 8

Rack and pinion

EPS model

EPS. The symbols used in the figure indicate the following:θh : Rotation angle of steering wheel [rad]θp : Rotation angle of pinion [rad]im : Motor current [A], τm: Motor torque [N·m]Kt : Motor torque constant [N·m/A]
KTB : Spring constant of torsion bar [N·m/rad]Rw : Reduction ratio of worm reducer
Ipe : Equivalent inertia moment of pinion shaft [kg·m2]
Cpe : Equivalent viscous resistance coefficient of pinion
shaft [N·m/(rad/s)]
Rp : Specific stroke of rack and pinion [m/rad]Kr : Spring constant of rack load [N·m/rad]The TAS torque signal can be expressed by the equation
below:
τs＝KTB(θh－θp)(2-1)
Assuming that im is equal to u (the actual current completely follows the motor current command) and that all
the parts except the torsion bar are rigid bodies, the rotary
motion of the pinion can be expressed by the differential
equation below:
Ipeθ̈p＋Cpe θ̇ p＝RwKtim＋KTB (θh－θp)－KrRp2θp(2-2)
where
im＝u
From Eqs. (2-1) and (2-2), the following state andoutput equations can be obtained:
x＝A
̇P x＋BPu＋EPθh(2-3)
y＝CPx＋FPθh(2-4)
whereT: State variable, y = -τs: Control outputx＝［θp θ̇p］
u: Control input (motor current command)
⎤

⎡

｜
｜
0
1
2
｜，K ＝K ＋K R
AP＝｜
pe
TB
r p
｜
｜－K /I
/I
－C
pe
pe
pe
pe ⎦
⎣

In the initial development stage where the detailed
design of hardware has not been completed, Eqs. (3-1) to(3-3) should be used as compensator design models todesign compensators. However, these models may need tobe revised when specific hardware specifications are madeavailable or when the hardware fabrication has been completed. With consideration given to these cases, the degreeof the compensator design models (degree of the denominator polynomial dp (δ)) is assumed to be 'n' in the following discussion. Then, the transfer function P(δ) isexpressed by the equation below:n（δ）
n δ n－1＋…＋nP1δ＋nP 0
P（δ）＝ P
＝ n Pn－1 n－1
δ ＋dPn－1δ ＋…＋dP1δ＋dP 0
d（δ）
P
(3-4)
4.1.2 Setting Disturbance Models
This section discusses disturbance models of degree lthat can be expressed by the equations below:
d＝Gd(s)d0(4-1)
n（s）
n sl－1＋…nd 1s＋nd 0
G（s）＝ d＝ l dl－1 l－1ds ＋ddl－1s ＋…dd 1s＋dd 0
d（s）
(4-2)d

The state and output equations of Eq. (4-1) can be
expressed by the equations below:x＝A
̇
d x＋Bd d0(4-3)
d＝Cd x(4-4)
where
⎡
⎤
1
0
…
0 ｜
｜ 0
｜
｜
｜ 0
0
1
…
0 ｜
｜
｜
｜
Ad＝｜
｜
｜
｜ 0
｜
0
0
…
1
｜
｜
｜－d
｜
－d
－d
－d
d0
d1
d2
dl－1⎦
⎣
⎡
｜
｜
｜
｜
｜
｜
｜
⎣

…

⎤

0 ｜
｜，F ＝－KP
TB
KTB /Ipe｜
⎦

n（δ）
P
d（δ）
P

n δ＋nP 0＝ 2 P1
(3-3)
δ ＋dP1δ＋dP 0

…

EP＝

－1
P（δ）＝CPδ（δI2－APδ）
BPδ＝

…

⎤

｜
0
｜，C ＝
BP＝
0］
P ［KTBRw Kt /Ipe ｜⎦P cAPz, BPz and CPz are a system/control matrix where Eq.
(2-3) or (2-4) is discretized by the z operator each. Thesecan be determined using the discretization method "zoh"using the MATLAB® function "c2dm". Eqs. (3-1) and(3-2) are called step invariant models 5) of Eqs. (2-3) and(2-4). When Eqs. (3-1) and (3-2) are selected for the compensator design model, the transfer function P(δ) in Figs.
5 and 6 can be expressed by the equation below:

…
⎤

0｜

In Eqs. (2-3) and (2-4), if θh is 0, the state and output
equations for the discrete time model can be expressed by― 12 ―

Bd＝

｜
｜
｜
｜
｜
｜
⎦

…

⎡
｜
｜
｜
⎣
⎡
｜
｜
｜
⎣

c

0
1

，Cd＝［nd 0 nd 1 nd 2 … ndl－1］

KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

The state and output equations of the discrete time modelof disturbances can be expressed by the equations below:
δx(k)＝Adδ x(k)＋Bdδ d0(4-5)d(k)＝Cdδ x(k)(4-6)
where
Adδ＝
（Adz－Il）/Tc , Il: l × l unit matrix

δ planeStable region

Imaginary
axis

Real axis

Bdδ＝Bdz /Tc , Cdδ＝Cdz

Adz＝e A T , Bdz＝∫T0 e A T dτ Bd
d c

c

d c

Adz, Bdz and Cdz are a system/control matrix where Eq.
(4-3) or (4-4) is discretized by the z operator each. Thesecan be determined using the discretization method "zoh"or "matched" (matched pole-zero model 5)) using the
MATLAB® function "c2dm". Note that the matched polezero model has the same poles as those of the step invariant model.
From Eqs. (4-5) and (4-6), the transfer function Gd(δ) of
the discrete time model of disturbances can be expressedby the equations below:
n（δ）
d
d（δ）
d
ndl－1δ l－1＋…nd1δ＋nd0＝ 1
(4-7)
δ ＋ddl－1δ l－1＋…dd1δ＋dd0

Fig. 9Stable region of δ operator

4.1.4 Deriving a Compensator
For steering assist control, assume that the compensatorCr(δ) in Eqs. (1-1) and (1-2) is Cr(δ) = 0. In this case, thecontrol system can be represented by Fig. 10:

－1
G（δ）
＝Cdδ
（δIl－Adδ）
BPδ＝d

Note that the numerator polynomial of the disturbancemodel nd(δ) will not be used for compensator design.
4.1.3 Coprime Factorization of Compensator
Design Model
To get ready for designing the compensator based on
the parametrization of the stabilizing compensator, thecompensator design model of Eq. (3-4) is expressed by
the coprime factorization below. If the controlled object isa system with multiple inputs/outputs, the model needs tobe expressed in right and left coprime factorizations. This
controlled object is a system with single input/output,
which means that the right coprime factorization is identical to the left coprime factorization. Therefore, this report
simply uses the term "coprime factorization".
P(δ)＝NP(δ)/DP(δ)(5-1)n（δ） nPn－1δ n－1＋…＋nP1δ＋nP0
(5-2)
N（δ）
＝ P
＝ n
P
δ ＋fn－1δ n－1＋…＋f1δ＋f0
（δ）
f
D（δ）
＝
P

d（δ）
δ n＋dPn－1δ n－1＋…＋dP1δ＋dP 0
P＝δ n＋fn－1δ n－1＋…＋f1δ＋f0（δ）
f(5-3)f(δ) is a stable polynomial and any given parameter thatcan be set by the designer. When f(δ) is said to be stable,
this means that its root exists at the center of the complex
plane -1/Tc within the circle of radius 1/Tc (see Fig. 9).
How to set f(δ) will be described later.

Fig. 10Block diagram of steering assist control system

The compensator Cy(δ) based on the parametrization of
the stabilizing compensator can be expressed by the equations below:
Cy(δ)＝NC(δ)/DC(δ)(6-1)
NC(δ)＝XP(δ)＋R(δ)DP(δ)(6-2)
DC(δ)＝YP(δ)－R(δ)NP(δ)(6-3)
X（δ）
＝
P

n（δ）
n δ n－1＋…＋nX 1δ＋nX 0
X＝ n－1Xn－1
ɡ（δ） δ ＋ɡn－2δ n－2＋…＋ɡ1δ＋ɡ0

(6-4)
Y（δ）
＝
P

n（δ）
n δ n－1＋…＋nY 1δ＋nY 0
Y＝ n－1Yn－1
ɡ（δ） δ ＋ɡn－2δ n－2＋…＋ɡ1δ＋ɡ0

(6-5)
g(δ) is a stable polynomial that is any given parameter tobe set by the designer. R(δ) is a stable-proper transfer
function (degree of numerator polynomial is equal to orless than degree of denominator polynomial) that is a freeparameter to be selected by the designer. How to set theseparameters will be described later.
Xp(δ) and Yp(δ) are solutions to Bezout equations.
XP(δ)NP(δ)＋YP(δ)DP(δ)＝１(6-6)
Firstly, Xp(δ) and Yp(δ) should be derived. Multiplying
both sides of Eq. (6-6) by h(δ) = f(δ)g(δ) yields an identical equation below:nX(δ)nP(δ)＋nY(δ)dp(δ)＝h(δ)(6-7)
whereh(δ)＝δ2n－1＋h2n－2δ2n－2＋…＋h1δ＋h0
When np(δ) and dp (δ) do not share a common divisor,nx(δ) and ny(δ) that satisfy Eq. (6-7) will be uniquely
decided. Their coefficient can be determined using theequation below 5):
ΘT＝Ψ TE－1(6-8)― 13 ―

Control Technologies for In-Vehicle Electric Actuators

where

where

ΘT＝［q0 q1 … q2n－2 nR 0 nR 1 … nRl－1］

Θ T＝［nY0 … nYn－1 nX0 … nXn－1］
0
0

dd 1

⎤

0
0

0｜
｜
0｜
…

dd 0

…
…

…

…

…
…

0｜
｜
0｜

dd 2 … ddl－1 1

…

w0

w2

：l ×（2n＋l－1）matrix… w2n－2 …

｜
｜
｜
｜
⎦

⎤

｜
｜
｜
｜
⎦

…

The coefficient of nR (δ) can be determined using theequation below:
ΘT＝Ψ TE－1(7-6)

0

0
0
…

The following identical equation should be set so thatthe numerator polynomial of Eq. (7-3) includes dd (δ):dR(δ)f(δ)nY(δ)－ɡ(δ)nP(δ)nR(δ)＝dd(δ)q(δ)(7-4)
Modifying Eq. (7-4) yields the equation below:
dd(δ)q(δ)＋w(δ)nR(δ)＝γ(δ)(7-5)wherew(δ)＝ɡ(δ)nP(δ)＝δ2n－2＋w2n－3δ2n－3＋…＋w1δ＋w0
γ(δ)＝dR(δ)f(δ)nY(δ)＝δ2n＋l－2＋γ2n＋l－3δ2n＋l－3＋…＋γ1δ＋γ0q(δ)＝q2n－2δ2n－2＋q2n－3δ2n－3＋…＋q1δ＋q0

0

…

（δ）
f
n（δ）
－ɡ
（δ）
n（δ）
n（δ）
d（δ）
Y
P
R
＝ R
(7-3)
（δ）
f
（δ）
ɡ
d（δ）
R

w1 … w2n－20…
w0 … w2n－3 w2n－2 …
…

n（δ）
n（δ） n（δ）
YP－ R（δ） d（δ）
ɡ
（δ）
f
R

E2＝

w0
0

…

(7-2)
where dR (δ) is a stable polynomial. How to set the polynomial will be described later.
Developing Dc(δ) yields the equation below:

⎡
｜
｜
｜
｜
｜
｜
｜
⎣

…

n（δ）
n δ l－1＋nRl－2δ l－2＋…＋nR1δ＋nR0
R＝ Rl－1l－1
δ ＋dRl－2δ l－2＋…＋dR1δ＋dR0
d（δ）
R

D（δ）
＝Y（δ）
－R
（δ）
N（δ）
＝
C
P
P

0

ddl－1

0
1

：（2n－1）×（2n＋l－1）matrix

Next is the process to derive R(δ). In Fig. 10, the control
output y(k) in response to the disturbance d(k) can be
expressed by the equation below:y(k)＝S(δ)d(k)＝DC(δ)DP(δ)Gd(δ)d0(7-1)
Gd(δ) may have unstable poles or a pole that can delay
the attenuation of d(k) regardless of its stability. In orderto minimize fluctuations of y(k) due to the effect of suchpoles as quickly as possible, the zero of Dc(δ) (the root of
the numerator polynomial) must include the poles ofGd(δ). Therefore, it is necessary to select R(δ) so that thenumerator polynomial of Dc(δ) includes the denominator
polynomial dd(δ) of Gd(δ). Since the degree of the disturbance model of Eq. (4-7) is l, the degree of R(δ) is set tol-1. R(δ) is expressed by the equation below:
R（δ）＝

0

1

…

nP2 … nPn－1 0

dd 1 … ddl－1
dd 0 … ddl－2
…

E1＝

d
0

…

⎡
｜ d0
｜
｜
｜
｜
｜
｜
⎣

…

…

…

nP1

｜
｜
｜
｜
｜
｜
｜
｜
｜
｜
｜
｜
⎦

…

…

…

nP0

…

…

…

0

⎡
⎤
｜ E1｜
｜
E＝｜
｜E ｜
⎣ 2⎦

0⎤
｜
｜
0｜

…

…
…

dP1 dP2 … dPn－1 1
0 … dP0
nP1 … nPn－1
0
0 … 0
0
nP0 … nPn－2 nPn－1 0 … 0
0

…

…
0

…

0
n
0

…

E＝

…

…

｜
｜
｜
｜
｜
｜ P0
｜
｜
｜
｜
｜
｜
⎣

0
1

Ψ T＝［γ0 γ1 … γ2n＋l－3 1］…

Ψ T＝［h0 h1 … h2n－2 1］⎡
1｜dP0 dP1 … dPn－1｜
dP0 … dPn－2 dPn－1｜ 00

4.1.5 Example of Basic Design of Compensator(1) Determining the compensator design model
When Ap, Bp, Cp, Ep, and Fp in Eqs. (2-3) and (2-4) are
given their physical parameter values and then discretized,
the transfer function of Eq. (3-3) will be:
P（δ）＝

n（δ）
n δ＋nP 0P＝ 2 P1δ＋dd（δ）
PP 1δ＋dP 0

7.807×10－3（δ＋1.980）＝ 2
(8-1)－2
δ ＋7.964×10 δ＋2.163×10－2
The δ operator and the coefficients of the numerator anddenominator of Eq. (8-1) were made dimensionless with
the inverse of the control period 1/Tc (hereinafter "thecontrol frequency"). In other words, δ in the equation is δ
= Tc δ. All figures appearing in the following examples
indicate dimensionless transfer functions.
The poles and zeros of Eq. (8-1) are all within the stableregion, implying a stable controlled object. Note that thezeros in Eq. (8-1) have been added through discretization.
Next, the coprime factorization of Eq. (8-1) P(δ) =Np(δ) / Dp(δ) is set as follows:n（δ） 7.807×10－3（δ＋1.980）
(8-2)
N（δ）
＝ P
＝
P
2
（δ＋0.2583）
（δ）
f
D（δ）
＝
P

d（δ）
δ2＋7.964×10－2δ＋2.163×10－2
P＝2（δ＋0.2583）（δ）
f

(8-3)
1/f(δ) in Eqs. (8-2) and (8-3) is the matched pole-zeromodel of the following stable transfer function 1/f(s) thathas been made dimensionless with the control frequency
1/Tc:
1/f(s)＝1/(s2＋2ζf ωf s＋ωf2)(8-4)
where 0 < ωf, 0 < ζf
If 1/f(s) is stable, its matched pole-zero model 1/f(δ)isalso stable. To allow the control system to deliver highresponsivity, it is desirable to set ωf to a value as high as
possible. ζ f, which is the attenuation factor of the poles of
the control system, should be set to 1 or more. For convenience, these are set as follows:― 14 ―KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

angularfrequency
ζf＝1 ，ωf＝2 Kpe /Ipe (naturaldecided by the equivalent stiffness and equivalent inertia
moment of the pinion shaft multiplied by 2).
The solutions to Bezout equations Xp(δ) and Yp(δ) canbe expressed in the equations below:n（δ） 8.179δ＋0.2314
X（δ）
＝ X
＝
(8-5)P（δ）
ɡ
δ＋0.2583
(8-6)n（δ） δ＋0.6314
Y（δ）
＝ Y
＝
P
（δ） δ＋0.2583
ɡ

nR1＝10.135
nR0＝1.888
nR1＝3.747
nR0＝0.8549

C（δ）
＝
y

n（s）
n（s）
d
G（s）
＝ d
＝ 2
d
2
（s）
＋2ζ
d
s
(9-1)dd ωd s＋ωd
where ζd = 1. The following settings will be used according to the steering assist torque level:ωd＝0.5ωd＝0.9ωd＝1.5

Kpe /Ipe : Large steering assist torque
Kpe /Ipe : Medium steering assist torque
Kpe /Ipe : Small steering assist torque

C（δ）
＝
y

: Large steering assist torque(10-2)

11.926（δ＋0.205）（δ＋0.1938）（δ＋0.07162）（δ＋0.7172）（δ＋0.2008）2: Small steering assist torque(10-3)

According to the equations above, the poles of Cy (δ)
include the pole dd(δ) of the disturbance model in Eq.
(9-2) for all the torque cases. Fig. 11 shows the poles andzeros of the compensator of Eqs. (10-1) to (10-3) plottedon a complex plane. The figure indicates that all the poles
and zeros are within the stable region. Note that both thevertical and horizontal axes have been made dimensionless with the control frequency 1/Tc.

Imaginary axis × Tc

n（δ）
n（δ）
n（δ）
d
d
＝ 2
＝ d
δ ＋2ζd ωd δ＋ωd2 （δ＋ωd）2d（δ）
d
(9-2)
where ζd = 1. ωd is as follows:ωd = 0.07198: Large steering assist torqueωd = 0.1258: Medium steering assist torqueωd = 0.2008: Small steering assist torquewhere
nR1＝15.640
nR0＝2.429

18.314（δ＋0.1513）（δ ＋0.2392δ＋2.031×10－2）（δ＋0.8172）（δ＋0.1258）2

C（δ）
＝
y

G（δ）
＝
d

n（δ） nR1δ＋nR0(9-3)
R（δ）＝ R＝
δ＋0.2583
d（δ）
R(10-1)

2: Medium steering assist torque

In these settings, the step invariant or matched pole-zeromodel of the transfer function in Eq. (9-1) that has been
made dimensionless with the control frequency 1/Tc canbe expressed by the equation below:(3) Deriving free parameter R(δ)
It is assumed that the pole dR (δ) of the free parameter isthe same as g(δ) of Eqs. (8-5) and (8-6). Substituting Eqs.
(8-2), (8-6), and (9-2) as well as dR (δ) = g(δ) = δ + 0.2583
in Eq. (7-6) yields the following free parameter R(δ):

23.819（δ＋0.121）（δ2＋0.2204δ＋2.358×10－2）（δ＋0.8819）（δ＋0.07198）2: Large steering assist torque

KTB /Ipe is used.

(2) Setting disturbance models
The disturbance model for the continuous time system
is set as follows. The numerator polynomial nd(s) of the
disturbance model is hereinafter omitted because it will
not be used for compensator design.

: Small steering assist torque(4) Frequency characteristics of control system
From the above, substituting Eqs. (8-2), (8-3), (8-5),(8-6), and (9-3) in Eqs. (6-1) to (6-3) yields Cy(δ) as
follows:

1/g(δ) in Eqs. (8-5) and (8-6) is the matched pole-zeromodel of the following stable transfer function 1/g(s) thathas been made dimensionless with the control frequency
1/Tc:
1/ɡ(s)＝1/(s＋ωɡ)(8-7)
where ωɡ＝2

: Medium steering assist torqueStable region (inside the circle)
Zero of controller
Pole of controller

Real axis × Tc

Fig. 11

Poles and zeros of compensator (basic design)

Next, the frequency characteristics of Cy(δ), Cy(δ)P(δ)(loop transfer function), and S(δ) are shown in Fig. 12.
For plotting of the Bode diagrams in Fig. 12, Cy(δ), Cy(δ)P(δ), and S(δ) have been converted into the form of the z
operator and applied with the MATLAB® function"dbode". The horizontal axis of these diagrams has been
made dimensionless with the control frequency 1/Tc.
According to the diagrams, the gain of the compensator orloop transfer function depends on the steering assist
torque level.
This design approach is not intended to design compensators with a focus on the loop transfer function or stability margin. Still, it should be noted that eventually the― 15 ―

Gain [dB]Control Technologies for In-Vehicle Electric Actuators

Large steering assist torque
Medium steering assist torque
Small steering assist torquePhase [deg]Dimensionless frequency f × Tc

Large steering assist torque
Medium steering assist torque
Small steering assist torqueDimensionless frequency f × Tc(a) Frequency characteristics of compensator Cy(δ)

Gain [dB]Gain margin of
10 dB or more
Large steering assist torque
Medium steering assist torque
Small steering assist torquePhase [deg]Dimensionless frequency f × Tc

Large steering assist torque
Medium steering assist torque
Small steering assist torquePhase margin of
40 deg or more

Dimensionless frequency f × Tc

Gain [dB](b) Frequency characteristics of loop transfer function Cy(δ)P(δ)
Large steering assist torque
Medium steering assist torque
Small steering assist torquePhase [deg]Dimensionless frequency f × Tc
Large steering assist torque
Medium steering assist torque
Small steering assist torquedcl(δ)＝｛ f(δ)｝2 ɡ(δ)dR(δ)＝(δ＋0.2583)6(10-4)
That is, f(δ), g(δ) and dR (δ) that were set during design
become the poles of the closed-loop transfer function.
This implies that this design approach is to design a compensator by setting the poles of the closed-loop transfer
function (or poles of the control system).
4.2 B asic Design of Steering Angle Control
Compensator
4.2.1 Deriving a Compensator Design Model
Fig. 13 shows a model of EPS including the steering
wheel. For steering angle control, the steering angle determined from the motor rotation angle must follow thetarget steering angle signal while suppressing vibration
caused by the turn of the steering wheel. Therefore, thecontrolled object is the steering system including therotary motion of the equivalent inertia moment of thesteering wheel shaft. The figure uses symbols to indicate
the following meaning. The other symbols not on the list
below have the same meaning as those used in Fig. 8.
θm : Motor rotation angle [rad] (θm = RPθP)
Equivalent inertia moment of steering wheel
Ih : 
shaft [kg·m2]
Ch : Equivalent viscous resistance coefficient ofsteering wheel shaft [N·m/(rad/s)]
τh : Steering wheel input torque [N·m] (assume τh = 0
with the driver's hands off the wheel)
The control output, namely, the steering angle signal θ̂ p
can be determined using the equation below:θ̂ p＝θm /Rw(11-1)
Assuming again that im is equal to u (the actual current
completely follows the motor current command) and that
all the parts except the torsion bar are rigid bodies, therotary motion of the pinion can be expressed by the differential equation below:
Ipeθ̈p＋Cpe θ̇ p＝RwKtim＋KTB (θh－θp)－KrRp2θp(11-2)
where
im＝u

Steering wheel

Dimensionless frequency f × Tc(c) Frequency characteristics of transfer function S(δ)
Fig. 12

Frequency characteristics of steering assist control
systemgain margin is not less than 10 dB and the phase margin
not less than 40 degrees for all cases.
S(δ), which is called the sensitivity function, is lesslikely to be affected by the parameter variations of thecontrolled object or disturbances with its smaller gain.
The smaller gain means a smaller control output to thesteering wheel rotation, in other words, a larger steering
assist torque. The poles of S(δ) are the poles dcl(δ) of theclosed-loop transfer function of the control system in Fig.
10 and can be expressed by the equation below:― 16 ―

Torsion bar

Motor

Worm reducer

Spring load

Fig. 13

Rack and pinion

Model of EPS including steering wheel

KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

The rotary motion of the wheel can be expressed by theequation below:Ihθ̈h＋Chθ̇ h＝－KTB (θh－θp)(11-3)
From Eqs. (11-1) to (11-3), the following state and output
equations can be obtained:
x＝A
̇P x＋BPu(11-4)
y＝CP x(11-5)
wherex＝［θp θh θ̇ p θ̇ h］T: State variable

ble-proper transfer function (hereinafter a "pre-compensator"). In this case, the control system can be represented
by Fig. 14:y＝θˆp＝θm /Rw＝θp: Control output
⎡
｜
｜
｜
｜
｜
｜
｜
⎣
⎡
｜
｜
｜
｜
｜
｜
｜
⎣

Fig. 14
⎤
｜
｜
｜
｜
｜
｜
｜
h⎦

0
0
1
0
0
0
0
1
AP＝
0
－Kpe /Ipe KTB /Ipe －Cpe /Ipe
KTB /Ih －KTB /Ih
0－Ch /I⎤｜
0｜｜0｜, CP＝
BP＝［1 0 0 0］
Rw Kt /Ipe ｜｜｜0⎦

In Eqs. (11-4) and (11-5), the state and output equations
for the discrete time model can be expressed by the equations below:
δx(k)＝APδ x(k)＋BPδu(k)(11-6)y(k)＝CPδ x(k)(11-7)
where
APδ＝
（APz－I4）/Tc , I4 : 4 × 4 unit matrix
BPδ＝BPz /Tc , CPδ＝CPz＝CP

In the control system shown in Fig. 14, the transfer
function Gry(δ) ranging from the target steering angle
signal r(k) to the control output y (hereinafter "target
tracking characteristics") can be expressed by the equation below:
Gry(δ)＝FC(δ)NP(δ)(13-1)
Then, Gry (δ) is set as follows:
n（δ）
G（δ）
＝ M
ry
d（δ）
M
nMm－1δm－1＋nMm－2 δm－2＋…＋nM 1δ＋nM0＝
δm＋dMm－1δm－1＋…＋dM 1δ＋dM 0
(13-2)where dM (δ) is a stable polynomial.
Next, the deviation er(k) of the output yr(k) of Gry(δ)
from r(k) can be expressed by the equation below:
e（k）＝r（k）－y（k）＝r（k）－G（δ）
（k）
r
r
r
ry

APz＝e A T , BPz＝∫T0 e A T dτ BP
P c

c

d（δ）
－n（δ）
M
M
（k）
r
d（δ）
M
(13-3)d（δ）－n（δ）
M
＝ M
G（δ）
r0
r
d（δ）
M

P c

When Eqs. (11-6) and (11-7) are selected as the compensator design model, the transfer function P(δ) in Figs. 5
and 6 can be expressed by the equation below:
n（δ）
P
d（δ）
P
nP 3δ3＋nP2δ2nP1δ＋nP0
(11-8)＝ 4
δ ＋dP3δ3＋dP2δ2＋dP1δ＋dP0
－1
P（δ）
＝CPδ
（δI4－APδ）
BPδ＝

The setting of disturbance models and coprime factorization of the compensator design model are omitted here
as these are as described in sections 4.1.2 and 4.1.3. The
following describes how to derive a compensator.
4.2.2 Setting a Target Value Signal Model
This section discusses the target value signal model ofdegree l represented by the equation below:n（δ）
n δ l－1＋…nd1δ＋nd0
(12)
G（δ）
＝ r
＝ l dl－1 l－1rδ ＋ddl－1δ ＋…dd1δ＋dd0d（δ）
rNote that the numerator polynomial of the target value
signal model nr(δ) will not be used for compensator
design.
4.2.3 Deriving a Compensator
For steering angle control, assume that the compensatorCr(δ) of Eqs. (1-1) and (1-2) is Cr(δ) = Fc(δ) / Dc(δ) basedon the parametrization 3) of the stabilizing compensator forthe two-degree-of-freedom control system. Fc(δ) is a sta-

Block diagram of steering angle control system

｝
（k）
r ＝
＝
｛ 1－G（δ）
rydM (δ) 's degree m may be any number, but needs to be set
from the following perspectives:①If the compensator design model has an unstablezero, in other words, if np(δ) or dr(δ) has an unstableroot, nM (δ) must include the root.
②In order for the deviation er(k) to converge to zero(0) asymptotically, {dM (δ) - nM (δ)} in Eq. (13-3) musthave the unstable pole of Gr(δ) as its root.
Then, assuming that np(δ) has an unstable root, an identical equation shown below is set so that {dM (δ) - nM (δ)} in
Eq. (13-3) has the pole dr(δ) of Eq. (12) as a divisor:dM(δ)－nP(δ)βM(δ)＝dr(δ)αM(δ)(13-4)
wherenM(δ)＝nP(δ)βM(δ)(13-5)
αM (δ) and βM (δ) are polynomials of degree n-1 and l-1,
respectively. Degree of dM (δ) is m = n + l - 1. Modifying
Eq. (13-4) gives the equation below:nP(δ)βM(δ)＋dr(δ)αM(δ)＝dM(δ)(13-6)
The coefficient of βM (δ) can be determined using theequation below:
ΘT＝Ψ TE－1(13-7)― 17 ―

Control Technologies for In-Vehicle Electric Actuators

where
Θ T＝
［αM0 … αM n－1 βM 0 … βM l－1］
Ψ T＝
［dM0 dM1 … dMn＋l－2 1］
⎡
⎤
｜ E1｜
｜
E＝｜
｜E ｜
⎣ 2⎦

dr1

⎤

0
0

0｜
｜
0｜
…

dr0

…
…

…

…

drl－1

0
1
…

0

1

…

0

…

dr1 … drl－1
dr0 … drl－2
…

E1＝

d
0

…

⎡
｜ r0
｜
｜
｜
｜
｜
｜
⎣

…
…

0｜
｜
0｜

dr2 … drl－1 1：n ×（n＋l）matrix

…

nP0

nP2

… nPn－1 …

（n＋l）matrix
：l ×

⎤

｜
｜
｜
｜
⎦

…

0

0
0
…

0

…

…

nP1 … nPn－10…
nP0 … nPn－2 nPn－1 …

…

E2＝

n
0

…

⎡
｜ P0
｜
｜
｜
｜
｜
｜
⎣

｜
｜
｜
｜
⎦

0

How to set dM(δ) will be described later.
Substituting Eq. (13-2) in Eq. (13-1) and modifying it
gives the equation below:
（δ）
f
n（δ）
M
(13-8)
F（δ）
＝
C
d（δ）
n（δ）
P
M

factor), which is decided by the equivalent inertia momentof the steering wheel shaft and the stiffness of the torsion
bar, appear as an antiresonance point in the zeros of P(δ).
Causing either compensator Cr(δ) or Cy(δ) to have thesezeros as divisors in its poles could prevent the antiresonance point from appearing in the zeros of the transfer
characteristics ranging from the target steering angle
signal r(k) to the control output y(k). In this case, however,
the antiresonance point inevitably appears as a pole of thetransfer characteristics from r(k) to the wheel rotation
angle to be a resonance point. So, if the target steering
angle signal abruptly changes, vibration may occur as thesteering wheel is turned. Then, the compensator should
be so designed that the poles of the compensator cannot
have the zeros of the compensator design model as theirdivisors. This can be achieved by determining the compensator Fc(δ) using Eq. (13-9) and making settings sothat the denominator polynomial f(δ) in Eqs. (5-2) and(5-3), the denominator polynomial g(δ) in Eqs. (6-4) and(6-5), and the denominator polynomial dR (δ) in Eq. (7-2)
cannot have the zeros of the compensator design model as
their divisors.

Substituting the relation of Eq. (13-5) in Eq. (13-8) yields
the equation below:

Poles and zeros corresponding tooriginal continuous time system

Imaginary axis × Tc

（δ）
f
β（δ）
M
(13-9)
F（δ）
＝
C
d（δ）
M

Stable region (inside the circle)
Zero of controlled object model
Pole of controlled object model

Eq. (13-9) can be used to determine a pre-compensator
Fc(δ).
A description of how to derive the compensator Cy(δ) isomitted here as it is the same as for steering assist control.
The next section provides an example of basic design ofthe compensator.
4.2.4 Example of Basic Design of Compensator(1) Determining a compensator design model
When Ap, Bp, Cp, Ep, and Fp in Eqs. (11-4) and (11-5) are
input with their physical parameter values, discretized andmade dimensionless with the control frequency 1/Tc, thetransfer function of Eq. (11-8) is as follows:

Next is to set the coprime factorization P(δ) = Np(δ) /Dp(δ) in Eq. (14-1) as follows:

n（δ）
P（δ）
＝ P
(14-1)
d（δ）
P

n（δ）
N（δ）
＝ P
(14-2)P（δ）
f

Zero added throughdiscretization

Real axis × Tc

Fig. 15

Poles and zeros of compensator design model

d（δ）
D（δ）
＝ P
(14-3)
P
（δ）
f

where
nP(δ)＝3.406×10－5(δ＋1.980)
×(δ2＋8.741×10－3δ＋5.718×10－5)
dP(δ)＝δ(δ＋1.233×10－2)
×(δ2＋7.599×10－2δ＋2.685×10－2)
Fig. 15 shows the poles and zeros of P(δ) in Eq. (14-1)
plotted on a complex plane. With a focus on the numerator of Eq. (14-1), there are three zeros. Of these, a real root
is a zero that has been added through discretization. The
remaining complex roots correspond to the original continuous time system. These complex roots are what makethe resonance point (generally with a low attenuation

1/f(δ) in Eqs. (14-2) and (14-3) are the matched pole-zeromodel of the following stable transfer function 1/f(s) thathas been made dimensionless with the control frequency
1/Tc:
1/f(s)＝1/｛ f1(s)f2(s)｝(14-4)
where― 18 ―

f1(s)＝s2＋2ζf 1ωf 1s＋ωf 12

f2(s)＝s2＋2ζf 2ωf 1s＋ωf 22
0＜ωf 1，0＜ωf 2，0＜ζf 1，0＜ζf2

KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

＝2.3
，ω
where ζf1 ζ=f 1＝ζ
ζf2 =f 22.3
and
ωff11＝ω= ωff22＝0.7= 0.7 Kpe /Ipe .
Reducing ζf1 and ζf2 or raising ωf1 and ωf2 will tend to cause
the controller to have unstable poles. So, these parameters
are set to smaller values than for steering assist control.
The solutions to Bezout equations Xp(δ) and Yp(δ) canbe expressed by the equations below:
n（δ）
X（δ）
＝ X
(14-5)
P
（δ）
ɡ
n（δ）
Y（δ）
＝ Y
(14-6)
P
（δ）
ɡ
where
nX(δ)＝1910.8(δ＋0.4936)
×(δ2＋2.550×10－2δ＋1.781×10－4)
nY(δ)＝(δ＋0.5236)(δ＋0.5953)
×(δ＋1.284×10－3)
ɡ(δ)＝(δ＋2.364×10－2)(δ＋9.930×10－2)
×(δ＋0.3669)
1/g(δ) is the matched pole-zero model of the following
stable transfer function 1/g(s) that has been made dimensionless with the control frequency 1/Tc:
1/ɡ(s)＝1/｛ ɡ1(s)ɡ2(s)｝(14-7)
whereɡ1(s)＝s＋ωɡ1
ɡ2(s)＝s2＋2ζɡ2ωɡ1s＋ωɡ22
where ζɡ2＝2.3 ，ωɡ1＝ωɡ2＝0.7

KTB /Ipe .

(2) Setting target value signal models
To ensure that the control output tracking to the target
steering angle signal, which changes in ramp rate, converges to zero (0) asymptotically, a target value signal
model is set as follows:n（δ） 1
(15)
G（δ）
＝ r
＝ 2
r
d（δ）
δ
r
(3) Setting disturbance models
To ensure that the control output tracking disturbances,which change in ramp rate, converges to zero (0) asymptotically, a disturbance model for the continuous timesystem is set as follows:n（s） 1
(16-1)
G（s）
＝ d
＝ 2
d
d（s）
s
d
A step invariant model or matched pole-zero model of thetransfer function of Eq. (16-1) that has been made into adimensionless transfer function with the control frequency
1/Tc can be expressed by the equation below:n（δ） 1
(16-2)
G
（δ）
＝ d
＝ 2
d
d（δ）
δ
d
(4) Deriving free parameter R(δ)
It is assumed that the pole dR (δ) of the free parameter isdR (δ) = δ + 9.930 × 10-2, which is the same as one of thedivisors of g(δ) in Eqs. (14-5) and (14-6). Substituting
Eqs. (14-2), (14-6) and (15-2) as well as dR (δ) in Eq. (7-6)
gives the following free parameter R(δ):n（δ） 6590δ－9.002
R（δ）
＝ R
＝
(16-3)d（δ）
δ＋9.930×10－2
R(5) Deriving compensator Fc(δ)
The target tracking characteristics are set as follows:n（δ） n（δ）
β（δ）
M(16-4)
G（δ）
＝ M
＝ P
ry
（δ）
d（δ）
d
M
M
where
nM (δ)＝1.601×10－3(δ＋8.925×10－3)
×(δ＋1.980)(δ2＋8.741δ＋5718)
dM (δ)＝(δ＋4.383×10－2)51/dM (δ) in Eq. (16-4) is the matched pole-zero model ofthe following stable transfer function 1/ dM(s) that has
been made dimensionless with the control frequency 1/Tc:
1/dM (s)＝1/｛dM1(s)dM2(s)dM3(s)｝(16-5)
where
dM1(s)＝s＋ωM 1
dM2(s)＝s2＋2ζM 2ωM 1s＋ωM 22
dM3(s)＝s2＋2ζM 3ωM 3s＋ωM 32
0＜ωM 1，0＜ωM 2，0＜ωM 3，0＜ζM 2，0＜ζM 3
ωM1
where ζM2ζ=M2ζ＝ζ
1＝1
and，ω
= ωM2
= ωM3＝0.3×= 0.3 x Kpe /Ipe .
M1＝ω
M2＝ω
M3 =M3βM (δ) in Eq. (16-4) has been determined by substituting
np(δ) of Eq. (14-1), dr(δ) of Eq. (15), and dM (δ) of Eq.
(17-2) in Eq. (13-7).
When f(δ) of Eqs. (14-2) and (14-3) and βM (δ) and dM (δ)
of Eq. (16-4) are substituted in Eq. (13-9), the compensator Fc(δ) can be expressed by the equation below:n（δ）
(16-6)
F（δ）
＝ F
C
d（δ）
F
where
nF(δ)＝46.993(δ＋8.925×10－3)
×(δ＋2.364×10－2)2(δ＋0.3669)2
dF(δ)＝(δ＋4.383×10－2)5(6) Frequency characteristics of control system
From the above, substituting Eqs. (14-2), (14-3), (14-5),(14-6), and (16-3) in Eqs. (6-1) to (6-3) yields Cy(δ) as
follows:
Cy(δ)＝NC(δ)/DC(δ)(17-1)
where
n （δ）
N（δ）
＝ NC
(17-2)
C
d（δ）
C
n （δ）
D（δ）
＝ DC
(17-3)Cd（δ）
CnNC(δ)＝8500.8(δ＋1.381×10－2)
×(δ2＋0.2211×10－2δ＋1.974×10－4)
×(δ2＋0.2360δ＋6.286×10－2)2nDC(δ)＝δ (δ＋1.107)
×(δ2＋0.1766δ＋0.1137)
dC(δ)＝(δ＋0.2364×10－2)2
×(δ＋0.9930×10－2)(δ＋0.3369)2
Next, the frequency characteristics of Cy(δ), Cy(δ)P(δ)(loop transfer function), S(δ), and Gyr(δ) are shown in Fig.
16.

― 19 ―

Control Technologies for In-Vehicle Electric Actuators

ode1 (Euler) and the fixed step size to one (1) allowed
computation of a dimensionless discrete time systemusing the δ operator. Major parameters that were set forthe simulation are shown in Table 1.
The results of the simulation are shown in Fig. 17.
According to Fig. 17, the control output y(k) follows
asymptotically to the target steering angle r(k) thatchanges in ramp rate until the sampling count k is 500.
When a ramp disturbance d(k) is applied at k = 1000, thecontrol output y(k) almost does not change and continues
following the target steering angle r(k). No vibration canbe found with the steering wheel angle θh (k) as well.

Gain [dB]Gain margin of
10 dB or more

Phase [deg]Dimensionless frequency f × Tc

Table 1

Phase margin of

Dimensionless40
frequency
f × Tcdeg or more

Parameter
Target steering angle signal
source r0
Disturbance signal source d0
Disturbance generator
SolverFixed step size(a) Frequency characteristics of Cy(δ), P(δ), and Cy(δ)P(δ)
Bandwidth of Gry(δ)

Gain [dB]60dB/decade

Major parameter settings for simulation
Settings/Description
1/500 (0 at k = 500)
1/500 (applied at k = 1000)
Gd(δ) = P(δ)/(δ)2Fixed step ode1 (Euler)
1 (dimensionless time)

Reponses

Phase [deg]Dimensionless frequency f × Tc

Dimensionless frequency f × Tc(b) Frequency characteristics of transfer functions S(δ) andGry (δ)Fig. 16

Frequency characteristics of steering angle control
systemAs a result of the design, the blue solid line Cy(δ)P(δ) in
diagram (a) shows a gain margin of 10 dB or more and aphase margin of 40 degrees or more. It is generally said
that the desirable gain margin for a servo system is 10 dB
or more and the desirable phase margin is 40 degrees ormore. In the dimensionless frequency range below thefrequency (bandwidth) at which Gry (δ) indicated by thegreen solid line shows a gain of approx. -3 dB in diagram(b), S(δ) indicated by the blue solid line shows low-frequency cutoff characteristics of 60 dB/decade. The control
system is thus expected to deliver robustness against disturbances or fluctuations of the controlled object in the
low-frequency range.
(7) Verifying the basic design
The steering angle control system in Fig. 14 wasmodeled on MATLAB®/Simulink® and subjected to simulation by setting P(δ) of Eq. (14-1), Fc(δ) of Eq. (16-6),
Nc(δ) and Dc(δ) of Eqs. (14-2) and (14-3), and Gr(δ) of Eq.
(15), as well as parameters of the disturbance generator
Gd(δ). Transfer Fcn of the Continuous library was used asa transfer function model. Setting the solver to a fixed step

Sampling count k

Fig. 17

Results of simulation of steering angle control
system4.3 Detailed Design and Implementation ofCompensators
4.3.1 Detailed Design of Compensators
This section describes the detailed design of the compensators. Fig. 18 shows a block diagram of a compensator implementation model. In Fig. 18, the six transfer
functions represented by the aforementioned Transfer Fcn
are collectively called a "function model" and the transfer
function of such a function model implemented in an
appropriate way is called an "implementation model" (theterm "implement" here refers to expressing a transfer
function using state and output equations). For the steering assist control compensator, the pre-compensator in the
Figure is Fc(δ) = 0. In R(δ), its numerator polynomial
parameters depend on the magnitude of the steering assist(assist gain), although a detailed description is omitted
here. The area enclosed by the blue broken line in Fig. 18
indicates a block with state variable estimation and feed-― 20 ―KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

Note 4) An instrument that uses a controlled object model toestimate its state variable and disturbances
Pre-compensator

Stabilizing compensator Cy(δ)

Eq.(13-9)State variable estimation and feedback

Output limiter

Eq.(6-4)

Eq.(7-2)
Eq.(6-5)

Variable according to assist gain(for steering assist control)

Note 5) An acronym of MathWorks® Automotive Advisory
Board. A guideline that specifies protocols for MathWorks products including description rules.

Disturbance estimation and feedback

Block diagram of compensator implementation
model

The following introduces an example of implementation of the pre-compensator Fc(δ). The transfer function of
Eq. (13-9) can be expressed as follows:
FC(δ)＝nF(δ)/dF(δ)＋DF(18-1)
wherenF(δ)＝nFn＋l－2δ n＋l－2＋…nF1δ＋nF0
dF(δ)＝δ n＋l－1＋dFn＋l－2δ n＋l－2＋…dF1δ＋dF0
DF: constant representing a feedthrough term of FC(δ)
A possible realization method for lower computation
error may be balanced realization (calculation using the
MATLAB® function "balreal" for instance). To reduce thecomputation complexity, we decided to select controllable
canonical form (this calculation can also be achieved with
the MATLAB® function "canon").
The controllable canonical form of Eq. (18-1) can be
expressed by the equation below:
δxF(k)＝AFxF(k)＋BFr(k)(18-2)
yF(k)＝CFxF(k)＋DFr(k)(18-3)
where
T
x（k）
＝
［xF1
（k） xF2（k） … xFn＋l－1
（k）
］
F

0
1
…

0
0
0
－dF0 －dF1 －dF2
⎤

…
…

⎤
｜
｜
｜
｜
｜
｜
｜
｜
｜
Fn＋l－2⎦

0
0

…

1
0
…

AF＝

0
0
…

⎡
｜
｜
｜
｜
｜
｜
｜
｜
｜
⎣
⎡
｜
｜
｜
｜
｜
｜
｜
⎣

－d

1

0｜
｜
｜
｜
｜
｜
｜
⎦

…

BF＝

0
1

⎫
｜
｜
｜
（k）＝xFn＋l－2（k－1）
xFn＋l－2｜＋Tc xFn＋l－1
（k－1）
⎬
｜
xFn＋l－1（k）＝xFn＋l－1（k－1）｜⎡n＋l－1
⎤
｜
｜｜
｜
－Tc｜
｛ dFi－1 xFi（k－1）｝＋r（k－1）
｜Σ
｜｜
⎣ i＝1
⎦
⎭
(18-4)
A compensator implementation model is created on
MATLAB®/Simulink® in such a manner that computation
is carried out in the order of Eq. (18-4) and Eq. (18-3). For
higher model readability, the model creation should be
conducted according to the modeling guideline in which
the description rule was established based on MAAB Note
5) 7)
.
xF（k）
＝xF（k－1）＋Tc xF（k－1）
1
1
2

Eq.(5-2)

Eq.(5-3)

Fig. 18

Eq. (18-2) can be developed into the equation below:…

back functions and that enclosed by the red broken line isa block with disturbance estimation and feedback functions. This implies that the parametrization of a stabilizing
compensator can be basically applied with the same
theory as for compensators using the state variable anddisturbance estimation observer Note 4).

，CF＝［nF0 nF1 … nFn＋l－2］

Compensator computation by microprocessors uses the
single precision floating-point format for memory saving.
Therefore, control parameters (variables having a fixedvalue) in Eqs. (18-3) and (18-4) and state variables (whose
value changes with time) are all defined with single precision floating-point variables in the implementation modelstage.
4.3.2 Verifying the Compensator Implementation
Model
The function and implementation models consisting of
the six transfer functions in Fig. 18 are each subject to a
back-to-back test to verify that these models are equivalent to each other.
4.3.3 Implementing Compensators
As described in section 3.3, Embedded Coder® is used
to automatically generate a C code from the implementation model. The generated C code is checked for conformance to the MISRA-C® Note 6) rules using a static analysis
tool. Any nonconforming items are remedied 7). Verification of the implementation results will be described in thenext chapter.
Note 6) Coding standards intended to ensure safe, portable, andreliable software (in C-language)

5

Design Verification

This chapter provides an example of the results of verification of the compensator design for steering assist
control according to the verification process.
5.1 Compensator Unit Evaluation
Software integrated with a designed compensator was
implemented in the power pack. The power pack was thenapplied with sinusoidal signals as motor current commands. From input and output signals of the compensator,
the frequency characteristics of the compensator Cy(δ)
were measured. The results are shown in Fig. 19.
― 21 ―

Control Technologies for In-Vehicle Electric Actuators

Gain [dB]

The measurement results closely match the functionalmodel, verifying that the compensator has been implemented as designed. Note that the results shown in Fig. 19
are for another design different from the basic design
described in 4.1.5 Example of Basic Design of Compensator.

Measurements
Functional model

Phase [deg]Dimensionless frequency f × Tc
Measurements
Functional model

Dimensionless frequency f × Tc

Fig. 19

Example of results of unit evaluation ofcompensator Cy(δ)

5.2 S
 ystem Evaluation and Redesigning of Compensators
The system shown in Fig. 8 was applied with sinusoidal
waves as motor current commands to measure the frequency characteristics of the controlled object. The frequency characteristics of the controlled object are shownin Fig. 20. The figure plots the frequency characteristics ofthe compensator design model of Eq. (8-1) (hereinafterthe "basic design model"), of the measurement results,
and of a model identified from the measurement results.
Gain [dB]

Basic design model
Measurements
Identified model

(19-1)
wherenP(δ)＝5.317×10－3(δ＋0.1864)
×(δ2－0.2701δ＋1.600)
2dP(δ)＝(δ ＋0.5513δ＋8.201×10－2)
×(δ2＋9.755×10－2δ＋2.135×10－2)
All the gains of the basic design model, measurements,
and identified model decrease after around a dimensionless frequency of 0.02 at nearly -40 dB/decade, showing
relatively good agreement with each other. However, thephase of the measurements is much behind the basic
design model after around a dimensionless frequency of
0.03. Possible causes include a response delay of theactual current from the motor current command, thecontrol computation time of the software, frictional torqueand small rattling of the machinery, and deflection of theelements that were assumed to be rigid bodies, whichwere not taken into account in Eq. (8-1).
Since the gain and phase of the measurements are ingood agreement with those of the identified model, thecontrolled object can be approximately expressed in atransfer function of degree 4 as shown in Eq. (19-1).
In fact, the frequency characteristics of the actual controlled object show a larger phase delay than that of thebasic design model. This means that a compensator
designed based on the basic design model may fail to keep
the control system stable. Then, we have redesigned thecompensator using the identified model of Eq. (19-1). The
redesigned compensator can be expressed by the equation
below:nNC（δ）
nDC（δ）
(19-2)where① For large steering assist torque:nNC(δ)＝22.847(δ＋8.494×10－2)
×(δ2＋0.5513δ＋8.201×10－2)
×(δ2＋0.1579δ＋1.889×10－2)
nDC(δ)＝(δ＋0.1864)(δ＋3.666×10－2)2
×(δ2＋1.295δ＋0.7986)

Basic design model
Measurements
Identified model

Dimensionless frequency f × Tc

Fig. 20n（δ）
n δ3＋n δ2＋n δ＋nP 0
P＝ 4 P3 3 P2 2 P1
δ ＋dP 3δ ＋dP 2δ ＋dP 1δ＋dP 0
d（δ）
P

C（δ）
＝
y

Dimensionless frequency f × Tc

Phase [deg]P（δ）＝

Frequency characteristics of controlled object

The identified model was obtained by calculating thefrequency response vector from the measurement datausing the MATLAB® function "fft" and then determinedwith the MATLAB® function "invfreqz". Transfer function parameters determined with "invfreqz" are written in
the z operator form. The obtained parameters were thus
converted into the δ operator form. The identified modelin Fig. 20 can be expressed by the equation below:― 22 ―② For middle steering assist torque:nNC(δ)＝18.246(δ＋0.1022)
×(δ2＋0.5513δ＋8.201×10－2)
×(δ2＋0.1646δ＋1.701×10－2)
nDC(δ)＝(δ＋0.1864)(δ＋6.502×10－2)2
×(δ2＋1.262δ＋0.7211)③ For small steering assist torque:nNC(δ)＝12.111(δ＋0.1336)
×(δ2＋0.1745δ＋1.250×10－2)

KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

Gain [dB]×(δ2＋0.5513δ＋8.201×10－2)
nDC(δ)＝(δ＋0.1864)(δ＋0.1127)2
×(δ2＋1.200δ＋0.6005)
1/f(δ) in Eqs. (5-2) and (5-3) is the matched pole-zeromodel of the following stable transfer function 1/f(s) thathas been made dimensionless with the control frequency
1/Tc:
1/f(s)＝1/｛f1(s)f2(s)｝(19-3)
where
f1(s)＝s2＋2ζf 1ωf 1s＋ωf 12
f2(s)＝s2＋2ζf 2ωf 1s＋ωf 22
0＜ωf 1，0＜ωf 2，0＜ζf 1，0＜ζf 2

Dimensionless frequency f × Tc

Phase [deg]Large steering assist torque
Medium steering assist torque
Small steering assist torqueDimensionless frequency f × Tc(a) Frequency characteristics of compensator Cy(δ)

Gain [dB]，ωwhere ζf1ζ=f 1＝ζ
ζf2 =f 2＝1
1 andωf f11＝ω
= ωff22＝2= 2 Kpe /Ipe . 1/g(δ) in
Eqs. (6-4) and (6-5) is the matched pole-zero model of thefollowing stable transfer function 1/g(s) that has been
made dimensionless with the control frequency 1/Tc:
1/ɡ(s)＝1/｛ɡ1(s)ɡ2(s)｝(19-4)
whereɡ1(s)＝s＋ωɡ1，ɡ2(s)＝s2＋2ζɡ2ωɡ1s＋ωɡ22

Gain margin of
5 dB or more
Large steering assist torque
Medium steering assist torque
Small steering assist torqueDimensionless frequency f × Tc

KTB /Ipe .
Phase [deg]where ζɡ2＝1 ，ωɡ 1＝ωɡ2＝2

Large steering assist torque
Medium steering assist torque
Small steering assist torque

Next, the parameter for the pole 1/dd(δ) of the disturbance model of Eq. (9-1) was set as follows:ωd＝0.9Kpe /Ipe : Medium steering assist torqueωd＝1.5

Kpe /Ipe : Small steering assist torquePhase margin of

Dimensionless frequency
30 degf ×orTcmore(b) Frequency characteristics of loop transfer function Cy(δ)P(δ)

In all these cases, ζd = 1.
Also, it is assumed that the pole of the free parameter R(δ)
in Eq. (9-3) is the matched pole-zero model of 1/g1(s)stated above.
The frequency characteristics of the redesigned Cy(δ),Cy(δ)P(δ) (loop transfer function), and S(δ) are shown in
Fig. 21. As a result, the gain margin is 5 dB or more andthe phase margin is 30 degrees or more in all cases. It has
been verified through system evaluation and actual vehicle
evaluation that a stable control system has been obtainedwith the redesigned compensator, although a detailed
description is omitted here.
5.3 Actual Vehicle Evaluation
In in-house actual vehicle evaluation, a vehicle of an
existing model is used to mainly test stationary steering(steering of a stopped vehicle). The test driver should start
to turn the steering wheel and then turn it back to checkthe effect of the steering assist. The driver should also
check that they feel no vibration via the wheel. The tuning
parameters include the parameters of Eqs. (19-3) and(19-4), the parameters of the pole of the disturbance modelof Eq. (9-1), and the parameters of the poles of Eq. (9-3).
In in-house actual vehicle evaluation, several compensator candidates of different designs should be prepared bymodifying the tuning parameters stated above toward
actual vehicle evaluation at customer sites.

Gain [dB]

Kpe /Ipe : Large steering assist torque

Large steering assist torque
Medium steering assist torque
Small steering assist torqueDimensionless frequency f × Tc

Phase [deg]ωd＝0.5Large steering assist torque
Medium steering assist torque
Small steering assist torque

Large steering assist torque
Medium steering assist torque
Small steering assist torqueDimensionless frequency f × Tc(c) Frequency characteristics of transfer function S(δ)
Fig. 21

Frequency characteristics of redesigned steering
assist control system

In actual vehicle evaluation at customer sites, a driving
test is carried out on a dedicated off-road test course, in
addition to the stationary steering evaluation. During thedriving test, particularly the driver's feeling of steering at
the start of cornering and of kickback during driving
straight ahead or cornering should be checked.

― 23 ―

Control Technologies for In-Vehicle Electric Actuators

6

Future Outlook

The approach explained in this report is just a compensator design method applicable to existing EPS that is alittle bit different from the traditional approach. The
importance of electronically-controlled in-vehicle equipment will rise as in-vehicle equipment automation andautonomous driving is further accelerated. As an in-vehicle equipment manufacturer, KYB needs to develop
various value-added products. In the course of the development, not only electrical and machine element engineers but also control technology engineers should play
two major roles of:①crystallizing and screening product ideas during the
product planning stage to create new products, and;② developing a robust design to minimize uncertainty
throughout the product lifecycle.
For role ①, just think about sensors, for instance. What
are the minimum sensors that can deliver the functions
and control performance required by the product (for cost
reduction)? What physical amounts should be detected
and controlled to satisfy the requirements (for higher
added-value)? An effective means to solve these possible
challenges is to identify controllability and observabilityof the system from the control technology perspective andto utilize the observer theory. For role ②, a parametricmodel involving uncertainty may be identified throughsimulation using a model with product quality (production variations) and secular changes in quality taken into
account or through their testing on an actual machine.
Such a parametric model can be effectively used to designcompensators, ensuring robust stability of the control
system.
Based on the above, we would like to strengthen our
product design and proposal capabilities.
7

Concluding Remarks

Focusing on EPS for all-terrain and utility task vehicles,
this report explains KYB's control technologies for invehicle electric actuators by introducing some numericexamples. The basis of the technologies is a design
approach based on parametrization of stabilizing compensators, which has been developed into a discrete timesystem in the δ operator form. The various equations used
for compensator calculation were converted into software

programs with m-file Note 7). This allows automatic calculation of parameters for the function and implementation
models of compensators just by setting the tuning parameters described in Section 5.3.
Note 7) A text file that describes programs to be executed on
MATLAB®

The control technologies explained in this report can beapplied not only to electric actuators but also to electric
pumps, hydraulic actuators, and other various electronically-controlled components.
Although compensators only make up a small proportion of in-vehicle software-controlled components, they
are an essential technology directly affecting security,
safety, and comfort. We would like to continue contributing to the improvement of quality and added-value of
KYB products with our system analysis and evaluation
techniques, control technologies, and software technologies.
Finally, we would like to take this opportunity to sincerely thank all those concerned who have extended guidance and cooperation to us in implementing and evaluatingthese control technologies.
・MATLAB®, Simulink®, Embedded Coder®, and MathWorks®
are registered trademarks of The MathWorks, Inc.
・SimulationX® is a registered trademark of ESI ITI GmbH.
・MISRA-C® is a registered trademark of The MISRA Consortium Limited.

References
1) MIYAKE, TOMITA: Development of EPS for Non-Passenger
Vehicles, KYB Technical Review No.60, pp 60-63, (2020).
2) 
INAMITSU, HORI: Development of Active Suspension by
KYB, KYB Technical Review No.63, pp 9-14, (2021).
3) MAEDA, SUGIE: System Control Theory for Advanced Control,
Asakura Publishing, (1990).
4) ADACHI: System Identification Theory for Users, The Societyof Instrument and Control Engineers, (1993).
5) 
KANAI, HORI: An Introduction to Digital Control System-Application of Delta Operator-, Maki Shoten, (1992).
6) KITAMURA: Development of Simulation Technology for EPS
System, KYB Technical Review No.59, pp 17-24, (2019).
7) KOBAYASHI: Application of MBD to Development of ECU
Prototype for EPS, KYB Technical Review No.52, pp 49-53,(2016).

― 24 ―KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

Author 
MATSUMOTO Daisuke

ENOMOTO Daisuke

Joined the company in 1995.
Development Sect. No.2, Electronics
Technology Dept., Engineering
Headquarters, Automotive
Components Operations
Special Sect. Manager, BasicTechnology R&D Center,
Engineering Div.
Engaged in analysis of in-vehicle
actuators and development of theircontrols

Joined the company in 2018.
Development Sect. No.2, Electronics
Technology Dept., Engineering
Headquarters, Automotive
Components Operations
Engaged in analysis of in-vehicle
actuators and development of theircontrols

KENJYO Kazunori

FUKUSHI Natsuru

Joined the company in 2015.
Chief Researcher, Electronics
Technology Sect., Basic Technology
R&D Center, Engineering Div.
Engaged in research anddevelopment of control software forin-vehicle actuators

Joined the company in 2017.
Chief Researcher, Electronics
Technology Sect., Basic Technology
R&D Center, Engineering Div.
Engaged in research anddevelopment of control software forin-vehicle actuators― 25 ―

Development of Vane Pump for Medium Passenger Vehicle CVT

Product
Introduction

Development of Vane Pump for Medium Passenger Vehicle CVTHAGIWARA Takahiro, OOTAKI Masashi, KONDO Hirotoshi, SHINDO Shota

1

Introduction

3This report introduces a vane pump for medium passenger vehicle CVT Note 1). This vane pump will bemounted, as a hydraulic power source, to the transmission
mechanism for medium passenger vehicles developed by
JATCO Ltd. as the successor of existing CVT unit thathas already been in mass production and rolled out globally.
Production of this product was started at KYB
Kanayama in October 2020.
Note 1) An acronym for Continuously Variable Transmission.

2

Newly Developed CVT Unit

Compared with the existing type, the new CVT unit thathas just been developed by JATCO Ltd. has the following
features:① Lower fuel consumption due to lower friction② Superior operation feeling③ Lower NVH Note 2)
The new CVT unit has been developed on the assumption that it will mainly be combined with an environmentally friendly downsized turbo engine.
The product is backed up by a global supply chain withproduction sites including Japan, China, and Mexico.

Newly Developed Vane Pump

Partly because it was to be mounted as the successor of
the existing CVT, the new vane pump needed to be rolled
out globally including Japan, China, and Mexico in thesame manner as for the existing vane pump. So, it was
mandatory to achieve a sophisticated design quality
during the development stage.
Based on the existing vane pump, we promoted thedevelopment of a new model with a focus on the discharge
performance and durability being equivalent to or superior to that of the existing model as well as lower friction.
As a trade-off for lower friction with equivalent discharge
performance, a vane pump will inevitably be less durable.
Still, we obtained an optimal design satisfying the specification requirements.
Furthermore, we strove to reduce the pump weight forenvironmental conservation and lower the production costthat was also demanded by end-users.
Photo 2 shows the appearance of the newly developed
vane pump. Table 1 shows the detailed specifications andTable 2 the major improvements.

Note 2) An acronym for Noise, Vibration, and Harshness.

Photo 1 Appearance of new CVT unit
(Extracted from JATCO Ltd.’s website)― 26 ―

Photo 2

Appearance of new vane pump

Table 1

Specifications of new vane pump

Type

Balanced vane pump

Basic discharge

11.3 cm3/rev

Pump revolutions

Up to 7300 rpm

Discharge pressure

Up to 6 MPa

Oil temperature-40°C - 140°C

Production site

Japan, China, Mexico

KAYABA TECHNICAL REVIEW No. 65 OCT. 2022
Table 2

Performance improvements

ments, achieving the lower driving torque as aimed for.
Note 3) PV factor = P (surface pressure) × V (velocity); One of・A notch in the cam ring
Improvements ・Aluminum cover instead of iron cover・Ports of an optimal shape

Excessiveflow

Performance Improvements

Spool

Discharge port

Suction port

Suctionpressure UP

Discharge

SuctionSuction port
Orifice

Discharge
port

Fig. 1 Oil circulation in vane pumpComparison of internal circulation between pumps
Difference ininternal circulation:
About 10%

Flow rate [L/min.]

4.1 Optimally Designed Cam Ring Notch
To ensure that the CVT unit can deliver lower friction
for lower fuel consumption, the driving torque of the vanepump must be reduced.
The driving torque equation for vane pumps can be
expressed as (Basic discharge × Pressure) / 2π. Since there
is no change in service pressure between the existing andnew models, the basic discharge was reduced for lower
driving torque. However, a precondition was that the newmodel must meet the performance specifications equivalent to those of the existing one.
The new vane pump is of a type with an integral flow
control valve (spool). It should be designed to internally
maintain a flow rate that can well cover the required discharge characteristics according to the pump speed.
A vane pump with an internal flow control valve canmake use of the power of any excessive internal circulating flow to enhance the suction capability (Fig. 1).
In designing the new pump, the basic discharge was
reduced, resulting in about 10% lower internal circulating
flow. This led to lower suction capability, making thepump likely to suffer cavitation (Fig. 2).
Cavitation is a phenomenon in which the air dissolvedin the hydraulic fluid forms bubbles. Repetitive formationand collapse of such bubbles wears and damages thepump components. This is because we expected the newvane pump to be unable to satisfy the requirements fordurability testing merely by reducing the basic discharge
while keeping the other specification items unchanged
from the existing ones.
Several countermeasures could be considered. From theviewpoint of cost-effectiveness, we introduced a "notch"
in the suction part of the cam ring that serves as a suction
oil path. The notch expanded the suction oil path to reduce
the pressure loss, raising the suction capability (Fig. 3).
In response to the introduction of the notch, the surfacepressure on the cam ring applied by the sliding vanes
increased, resulting in a higher PV factor Note 3). This
resulted in various durability disadvantages including
abnormal wear of the cam ring.
Then, in order to determine the balance between thenotch depth and the PV factor, in other words, the point at
which performance and durability can go hand in hand,the new vane pump was subjected to a durability test to
identify the critical point. We finally determined the
optimal size of the notch (Fig. 4).
Through these development efforts, the new vane pumpsatisfied both the durability and performance require-Internal circulationof existing pump
Internal circulationof new pump
Discharge ofexisting pump
Internal circulationof existing pump
Discharge of new
pump
Internal circulationof new pump

Pump speed [rpm]Fig. 2― 27 ―

Comparison of internal circulation between pumps

Existing modelFig. 3New model

Comparison of cam ring specifications
PV factor critical line graph

P: Surface pressure [N/mm2]

4

the wear factors

Large Notch

Development
Model
PV factor

NG Area

Small Notch

Current Model
V: Velocity [m/sec]

Fig. 4

PV factor critical line graph

PV factor

OK AreaDevelopment of Vane Pump for Medium Passenger Vehicle CVT

4.2 Aluminum Cover Instead of Iron Cover(Weight and Cost Reduction)
The existing vane pump for medium passenger vehicle
CVT used a core oil path cover made of cast iron (Figs. 5
and 6). The new product has been designed to have an
aluminum diecast cover. With this design, the weight ofthe cover alone has been reduced by 350 g, which is anapproximately 30% reduction in the total weight of thevane pump, contributing to substantial weight reduction,and consequently lower fuel consumption.
Furthermore, the manufacturing method has beenchanged from the cast iron system to an aluminum diecast
system. This has helped improve the productivity andreduce the manufacturing cost.
Along with the introduction of the aluminum diecast
cover, however, the geometry of the oil path inside thecover changed in such a manner that the oil was unlikely
to flow smoothly. We noticed that the new oil path geometry worsened the pump's NVH (Figs. 7 and 8).

4.3 Ports of Optimal ShapeIt was mandatory to improve the pump's NVH in orderto satisfy the requirement that the NVH of the new pump
be equivalent or superior to that of the existing model.
However, the oil path of the new cover, which was a factor
that deteriorated NVH, could not be improved from theviewpoint of manufacturing method. It was impossible todesign an oil path for the diecast cover that is similar tothat of the cast iron cover.

Optimized port shape

Existing (cast iron)

New (aluminum diecast)Time [msec]

Comparison of appearance of cover
Discharge pressure[MPa]Fig. 5

Ports of side plate

Vibration [m/sec2]

Fig. 9Time [msec]

Existing (core oil path)

Fig. 10Comparison of oil path

Pump discharge pressure and vibration before
improvement

Vibration [m/sec2]

Fig. 6

New (diecast oil path)

Fig. 7

Time [msec]

New (diecast oil path)Comparison of flow in oil pathHigh
Pressureloss
Low

Existing (core oil path)
Fig. 8Discharge pressure[MPa]

Existing (core oil path)

Time [msec]

New (diecast oil path)
Fig. 11

Visual comparison of pressure loss in oil path― 28 ―

Pump discharge pressure and vibration after
improvement

KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

Then, we decided to pursue an optimal shape of theports of the side plate for the aluminum cover. With the
optimal port design, the discharge pulsation was reduced
to suppress the vibration, satisfying the NVH requirement(Figs. 9, 10 and 11).

5

Evaluation

This development project was highly rated by JATCO
Ltd. and won the FY2020 JATCO QCDS Best Performance Award.
This prize is awarded only to the one company globally
rated as overall No.1 in development, quality, cost anddelivery. We were only able to win this prize with thecooperation from those concerned not only in Development but also in other departments. We would like to takethis opportunity to deeply thank all those concerned.
As a quality-specific prize, we also won the JATCO
Regional Special Award at the same time.
Furthermore, KIMZ (KYB Industrial Machinery (Zhenjiang)), which launched production in March 2021 after
KYB Kanayama was established, won the QCDS A-rank
Award. KYB has been highly evaluated both at home andabroad.

Photo 36Compared with the existing model, this newly developed product has achieved the following:① About 10% lower pump driving torque② About 30% lighter pump③
Simultaneous achievement of durability and low
driving torque④ Lower noise⑤ Lower cost
The considerations discussed in this development
project are shown in the inclined developed views of theexisting and new products (Fig. 12).

7

In Closing

We sincerely appreciate the cooperation of all thoseengaged in program development from JATCO Ltd. andall other partner companies and all those concerned in
relevant KYB departments.

QCDS Best Performance Award (right), Regional
Special Award (left)

Photo 4

Conclusions

QCDS A-rank Award (China)― 29 ―

Development of Vane Pump for Medium Passenger Vehicle CVT

Existing productCast iron

New product
Aluminum diecast

Optimized port shape
Notch added

Fig. 12

Inclined developed views of existing and new products― 30 ―KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

Author 
HAGIWARA Takahiro

OOTAKI Masashi

Joined the company in 2010.
Pump Engineering Dept., Steering
Business Dept., Automotive
Components Operations
Engaged in design of vane pumps.

Joined the company in 2012.
Pump Engineering Dept., Steering
Business Dept., Automotive
Components Operations
Engaged in design of vane pumps.

KONDO Hirotoshi

SHINDO Shota

Joined the company in 2013.
Gifu Local Office, Basic Technology
R&D Center, Engineering Div.
Engaged in design of vane pumps.

Joined the company in 2014.
Pump Engineering Dept., Steering
Business Dept., Automotive
Components Operations
Engaged in design of vane pumps.

― 31 ―

Essay from Expatriate at HKE

Essay
Essay from Expatriate at HKE
HATTORI Koji

1. Introduction

2. Jingzhou City, Hubei Province

KYB launched a joint-venture project with theHenglong Group of China in August 2017. The project
was implemented under the company's policy to shift thebusiness base of electric power steering (EPS) for
passenger vehicles from Japan to China.
Before that, KYB had surveyed parts suppliers in
China as part of its cost reduction activity for EPS parts.
The Henglong Group was among those with whom KYB
had already gotten in touch. However, a joint-venture
relationship is quite different from a business partnershipin scale and relevance. I remember that I recognized thelaunch of the project as a big milestone.
I am, and was at that time too, in charge of cost planning.
I was involved in the joint-venture project to study thecommercial feasibility of the project from the cost
perspective. Actually, I was quite frustrated about thelimited information we could obtain from the other party
because cost information is very sensitive until bothparties enter into a formal joint-venture contract.
In April 2018, the joint-venture contract was concluded
and Hubei Henglong & KYB Automobile ElectricSteering System Co., Ltd. (hereinafter "HKE") was
formally established. To set up a cost planning organization
for the first time for the Henglong Group, I was assigned
to work for HKE in China, which was my second
expatriation following the first one to the U.S. in 2005. I
moved to China with five colleagues of mine at the end of
November 2018.

HKE is located in Jingzhou City, Hubei Province in
China. Jingzhou is about 200 km inland and west of
Wuhan in the same province, which is considered to be
the origin of COVID-19 that continues to severely affectthe world today. Compared to Japan, Jingzhou City is
located at a latitude south of Tanegashima, which may
give you the impression that Jingzhou is a tropical place.
However, the climate there is very similar to that of Kani
City, Gifu Prefecture in Japan where Gifu North Plant islocated. While in the summer it is so hot and humid in
Jingzhou that the temperature rises to 35°C or more forconsecutive days, it sometimes snows in the winter.
At the end of 2018, in the month after I was sent toJingzhou, several centimeters of snow fell. I heard thatsnow accumulation was quite rare in recent years. Smallchildren were playing in a lively way with the snow in the
courtyard of the apartment where I lived. That was myfirst experience to spend the year-end period in China
and I felt happy to see scenery similar to that in Japan.

Photo 2

Photo 1

Appearance of HKE building

Snow at the end of 2018

Jingzhou City occupies an area of 14,067 square
kilometers. Spreading along the meandering Yangtze
River, the entire city is rich in water with a network of
distributary channels, waterways, and lakes. Many
beaches and parks located along the Yangtze River areoccupied by families and couples enjoying holidays. With
this geographical advantage, Jingzhou City is an
important site of maritime transportation and physical― 32 ―KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

distribution in the middle reaches of the Yangtze River.
Historically, the city is famous for its strategicallyimportant location as seen in the Romance of the Three
Kingdoms. A gigantic statue of Guan Yu (total height of
58 meters), who was a bold military general assigned togovern Jingzhou, had previously existed as a symbol of
the city. Unfortunately, it became evident just before myrepatriation that the statue was an unlawful construction
and it has now already been demolished. (I heard that
there was a plan to relocate the statue, but no relocation
work seems to have been carried out at this moment).

Photo 3Now-lost world’s largest statue of Guan Yu

3. Working in HKE
As mentioned above, my duties during the stay inJingzhou City were to kick off the cost planning operation
for the first time for the Henglong Group and to proliferate
the visualization and standardization of cost issues, inorder to achieve a suitable product cost and EPS businessprofitability. However, it was quite difficult for me to get
the Chinese staff to understand the operation as it was
their first job of this kind. I prepared a cost planning
manual and related documents on the operation inPowerPoint and translated the text into Chinese. After
distributing the documents and holding seminars, I
received my first request from the staff. They asked me to
do a job, saying "we want to buy some curtains for theoffice, please do a cost assessment".
While I encountered various "difficult-to-understand"events like this, I built a friendship with my Chinese

Photo 4

Shore of Yangtze River with many families
enjoying a holiday

colleagues through monthly dinners and birthday parties
within the department. Meanwhile, the project gradually
got on track, enabling us to carry out cost reduction
activities and build a collaborative relationship withrelated departments in a manner similar to how we did inJapan. Then, worrying news came as we approached theend of 2019.

4. Terrible Shock
There were rumors that a new type of pneumonia had
emerged in a seafood market in Wuhan City, which isnear Jingzhou City. This was the later-named COVID-19
as I mentioned above.
The seafood market deals with not only seafood but
also all kinds of foodstuffs. I even heard a Chinese saying
expressing the richness of the food culture that “we eat
everything with four legs except tables and everythingthat flies except airplanes”. It is regular practice to eventreat some wild animals as food, many of which may lookunacceptable to the Japanese. Since COVID-19 was said
to originate in such wild animals, Chinese people aroundme were rather optimistic at the beginning. When I
visited a local supplier, people there said "it is OK because
the seafood market has been closed" or "COVID-19 does
not involve human-to-human transmission". Television
news generally reported similar stories. While I waswondering if things were really so positive, I never everimagined at that time that such a terrible situation would
actually occur.
The first time COVID-19 affected me was during the
Chinese New Year holidays. Based on the lunar calendar,
the Chinese New Year vacation in 2020 began on January
23, which was earlier than most years. During thevacation, I tried to temporarily go back to Japan andfound a dramatic change in circumstances. All flights
scheduled to arrive at Wuhan Airport were reportedly
going to be canceled in the morning of the day I went tothe airport. Among the Japanese expatriates, half were
supposed to fly back to Japan on another flight the next
day for the sake of air ticket arrangement. We were very
anxious whether the flight would take off as scheduled. In
the end, the flight on the next day was the last one toJapan before Wuhan Airport was fully closed. All the
expatriates in HKE successfully returned to Japan safely.
Unfortunately, many expatriates of Japan -based
corporations were left out in Wuhan. The news that they
were eventually transported to Japan by a governmentchartered flight is still fresh in my memory.
Although we managed to come back home safely, we
could not return to China even after the lunar New Yearvacation was over due to the large-scale city lockdown by
the Chinese government. In the end, we continued
working online with China for eight months altogether.
In addition to the time-zone difference of one hour
between Japan and China, which might not be so large,
there is a language barrier. Under these circumstances,― 33 ―

Essay from Expatriate at HKE

doing remote work without face-to-face communication
unfortunately affected the human relationship between
us that had been built with our relentless efforts. This is a
sad memory.
After an eight-month stay in Japan, I was finallypermitted to return to China. Still, the immigration
restriction, which persists even now, was very strict.
Firstly, we were required to take a PCR test at the airport
when we arrived to prove we were negative for COVID-19.
We were quarantined in a hotel room near the airport for
two weeks. We were required to take two further PCR
tests during the quarantine period. Then, we went back to
Jingzhou and took another PCR test. After returning to
the apartment that we lived in, we had to quarantine foranother two weeks. Upon completion of the quarantine,
we had to take yet another PCR test. By the way, I had
had a PCR test before I left Japan to begin with. That was
six PCR tests in one month, which were needed for me toenter China. The Chinese government raised their guard
against foreigners coming in from abroad, while those
who had never taken a PCR test at all were still walking
around in the city as usual. I could not help thinking who
was the more dangerous.

sightseeing venue or amusement spot. Still, the gigantic,
overwhelming structure in the land was so impactful thatit moved me a lot when I saw it with my own eyes. That
was a wonderful experience for me. Because it isrecognized throughout the world, I intentionally visitedthe Great Wall on a day outside the busy period, but thesite was still so crowded that I found an area around a
hilltop along the course of the Wall fully covered bypeople and could not see the architecture.

Photo 6

Photo 5Wuhan Airport where I arrived in September 2020

5. Living in China
I'm afraid I have told a somewhat cheerless story
overall, so I would now like to tell you a little bit happierstory for those who will be future expatriates. The word
"China" may first remind you of historical culture andcuisine. For your information, the Japanese often say that
China has four thousand years of history, but I have heardthat the Chinese prefer to say that China has five thousand
years of history. When you talk about history with
Chinese people, be careful not to say, "four thousand
years of history", which may cause them to doubt thisphrase.
Unfortunately, I had little chance of enjoying travelling
during my assignment in China due to COVID-19. Before
the COVID-19 pandemic, I had the opportunity ofvisiting the Great Wall, which may be the first thing thatcomes to mind for the Japanese when talking about
famous historic buildings in China. As is usual for othersimilar buildings or great natural sites throughout theworld, the Great Wall also has been arranged as a typical

The Great Wall crowded with visitors

Speaking of food, Jingzhou cuisine includes many
spicy dishes partly because of its closeness to Sichuan
Province and Chongqing. People who like spicy food canenjoy many varieties of local delicious cuisine. I actually
got hooked on pork intestine (or "fei chang" in Chinese).
This so-called "hormone" in Japan can be eaten in China
in various ways including as a pot dish and ramen. Friedfei chang with a good amount of hot red pepper wasparticularly marvelous. I loved its spicy taste and texture
that perfectly matched the rather weak Chinese beer of
low alcohol content. I frequently used to go to one goodrestaurant even alone after it had been introduced to me.
With many other family customers in the restaurant, aJapanese who could hardly speak Chinese had taken thetrouble to come there alone to eat typical local food. I― 34 ―

Photo 7

Fried fei chang

KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

wonder if I looked rather strange to the other customers.
Even among the Chinese, some like fei chang but someothers do not because of its unique taste. Those who likeit sometimes asked me to go out to enjoy fei chang
together as we developed a sense of collegiality. That
made me recognize that Chinese culture values eating
more than is the case in Japan.

6. Farewell
Bearing in mind that I would appoint a Chinese
employee to be my successor, I selected and trained local
employees after becoming an expatriate in HKE. Today,
one of my subordinates at the time has taken over myactivities. My colleagues with whom I became goodfriends still keep in touch with me in public and private
life. I consider it a lifelong achievement for me to haveestablished these relationships.
After much joy and hardship, I was directed by thecompany to repatriate in January 2022 after the first termof the HKE joint-venture contract was to finish. I regretted
that there were still many things I had not yet done, but
HKE successfully ended the fiscal year 2021 in the black
for the first time since its foundation, which was amilestone for me before returning home. It was very
emotional for me to be able to say a joyous goodbye to thecolleagues with whom I had earlier struggled.

Photo 8

7. In Closing
Among my Japanese colleagues who were sent to HKE
together in 2018, some are still working hard there even
without a temporary return to Japan under the Chinese
government’s zero-corona policy with no end in sight.
Because of its geography, Jingzhou is an inland center for
peripheral ethnic minorities and seldom accessed by
Japanese, so they are working and living in a very
different environment and having to deal with stress.
They are making efforts to develop profitable products byputting the EPS business on track under this stress.
Hoping that they will be able to proudly return to Japanin the near future, I would like to close this report.
Finally, I would like to express my appreciation to
those who extended support and cooperation to me during
my assignment in HKE and sincerely hope that HKE and
its EPS business will further develop in future.

My colleagues at HKE Finance/Cost Planningwith whom I worked

Author 
HATTORI Koji
Joined the company in 1989.
Expatriate in KYB Asia Pacific Corp.
Ltd.
Took present post after working inSteering Design Dept., expatriate in
the U.S. (Detroit), working in
Product Planning Dept., working in
PS Cost Planning Dept., and as an
expatriate in China (HKE).

― 35 ―

Essay from Expatriate at KMEX

Essay
Essay from Expatriate at KMEXKAWAI Hiroshi

1. Introduction
I was assigned to work for KYB Mexico S.A. de C.V.
(hereinafter "KMEXDF") from May 2015 to April 2022.
KMEXDF is a sales center of commercially available SA(shock absorbers) for the Mexican market as well as forall other Latin American countries (except Brazil).
I have long been involved with Mexico personally as
well. My involvement with the country began withtravelling as a backpacker in my schooldays, followed byanother experience as an expatriate there. Theseexperiences are linked to this assignment at KMEXDF,
further leading to my current position. You never know
where you have a chance or a turning point in your life.
Through my residence in Mexico for seven years, mysoul and body have been completely Mexicanized. I hadvery valuable experiences in my public and private life,
some of which will be introduced in the following:

one of the attractions of the country to be able to experiencesuch a variety of food and culture in this city.
Mexican people are generous, kind, and cheerful. With
the amigo spirit, they are very friendly and welcoming of
foreigners.
I have talked only about the good things about living in
Mexico so far, but I have to point out the issues of traffic
jams and security which gave me such a hard time.
A major cause for concern was traffic jams (Photo 1).
The public transport in Mexico is where many incidentsof pickpocketing or robbery may occur. During my stay inthe city, I basically moved by car. It was a 15-minute walkfrom my home to the office, but in the mornings andevenings it often took nearly one hour to drive there.

2. Living in Mexico
Mexico (United Mexican States) is a huge country ofunited states located between North America and Latin
America. The country has a population of 130 million(almost equivalent to that of Japan) and a total area of 1.96
million square kilometers (five times that of Japan).
Mexico City, where I stayed as an expatriate, is locatedalmost at the center of the country and has a population of
about 21.58 million (1.5 times that of Tokyo) and an areaof 1,479 square kilometers (in contrast only around 70%of that of Tokyo). These figures can easily make you
imagine that Mexico City is a densely populated,
commercially important place.
Mexico City is located on a highland at an altitude ofabout 2,300 meters. In contrast to the typical image that
Mexico is a very hot country, Mexico City has a
comfortable climate with an annual mean temperature of
25°C and low humidity which makes life easy, similar tothe spring or autumn seasons in Japan.
Mexico has the geographical advantage of linking
North America with Latin America and has a very
youthful workforce with an average age of 29. From thesereasons, many foreign-owned companies, including
Japanese ones, have branched out into Mexico, along with
their own cuisine and culture from all over the world. It is

Photo 1

Traffic jam during rush hour

As pointed out by a previous expatriate, it is very easy
to obtain a driver's license in Mexico because there is no
examination system. The traffic is always exceeding thecapacity of the roads. Jams occurring somewhere in thecity will cause gridlock in the entire city partly because
there are numerous complex roads and many one-way
traffic streets.
The maintenance of vehicles depends on their owners,
although they have to pass the national inspection more or
less. On the road, you can always find faulty cars stuckwith their hood open as often seen in a movie. This is oneof the major causes of traffic jams.
Naturally, roadways cannot bear such heavy traffic,
resulting in road surfaces with potholes and deteriorated
pavement here and there. This convinced me that thecountry had a high demand for shock absorber replacement.

― 36 ―KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

I carried out marketing activity while directly experiencing
this situation.
Security is another issue as you know. I had a hard time
initially during my residence there. Until you are familiar
with the local circumstances to some extent, you need todeliberately search for safe places and safe time frames
before being able to go out freely.

2), which is located 400 kilometers northwest of
KMEXDF. I had valuable experiences there including
warehouse arrangement, consideration for physicaldistribution, and completion of initial inventory. It isneedless to say that these experiences drove my
motivation for working in Marketing for the Latin
American market later.

3. Working in Mexico
I was in charge of purchasing for the initial three yearsof my assignment. KMEX sells inventory to the Mexican
market and deals with a commercial flow called drop
shipment (trilateral distribution in which products are
directly delivered from plants to customers and billing is
made by KMEX) for the Latin American market.
While "purchasing" may sound rather easy, ourpurchasing operation actually covered a wide range ofjobs. I was engaged in a variety of jobs, from placing
orders for commercially available SA, following-up thedelivery date with suppliers, ensuring proper inventory
management, and taking measures for improved orderfulfillment, to developing new markets. I initially faced an
uphill battle in accomplishing these jobs for which I had
little prior experience.
I had to estimate demand and determine the amount oforders while striking a balance between inventories andorder fulfilment. To accomplish this job, it is indispensable
to monitor the target markets by collecting informationfrom customers and internal sales personnel and to acquire
information from and work together with plants and otherdepartments.
In fact, many delays in delivery occurred, not only due
to poor demand estimation and other internal factors
attributable to KYB, but also due to the global situationand various other external factors specific to the country.
These included demonstrations by longshoremen's unions
and other labor unions as well as robbery and burglary. Aspurchasing manager, I was often called upon by andreceived complaints from customers about inventory
runout.
Still, in the course of such complaints and advice given
by customers, I was able to listen to voices in the markets
and seriously respond to customer demands. It was a great
achievement for me to have learned a lot of things andbuilt trustworthy relationships with them.
Besides this, there were various events and topics that
affected me during my stay in Mexico. They included the
U.S. government's immigration and trade policies to
Mexico launched upon inauguration of the new U.S.
President in 2016, a big drop in Mexican peso, and
COVID-19 issues. Still, Mexico endured the COVID-19
pandemic without suspending activities of its majorindustries, which allowed KYB to steadily drive sales
promotion.
During the assignment, I also took part in an SA
production start-up project in KMEX Silao Plant (Photo

Photo 2KMEX Silao Plant

After that, I also served as Latin America Sales Manager
between 2018 and 2022. During that period I traveled
across 15 countries in the Central and South American
continent, trying to sell our products to local markets. In
Central and South America, people speak Spanish in all
the countries including Argentina in the south except for
Brazil (and some English-speaking Caribbean countries).
People of various origins including Spain, Africa, andindigenous have different business practices and national
characteristics. I discussed business with local customers
while learning Spanish to gain a lot of experience,
although I actually had difficulty in negotiating with those
diverse people.
A big challenge during marketing was to protect (andexpand) the KYB share in the market from inexpensive
Chinese products that were quickly extending their reach.
Prioritizing commercially available products, I took
various actions.
In fact, inexpensive products were flooding most of theLatin American markets to drive down the market price.
At the time, our sales promotion had already reached aplateau several years earlier. To overcome the situation,
we put made-in-Mexico products in the market atcompetitive prices under the slogan of "local production
for local consumption". We also focused on sales
promotion of the K'lassic brand (low-priced products forolder-model cars).
One thing that was very difficult was that most markets
in Central and South America preferred made-in-Japan,
although it depends on the degree of price difference.
They had prejudice or even "allergy" against products
made in other countries, which posed barriers to sales
promotion of made-in-Mexico products.
As an incentive to overcome the barriers, we invited 14
customers from 10 countries to KMEX Plant for a plant
tour (Photo 3). We tried to make them understand that the
made-in-Mexico products have the same quality as the― 37 ―

Essay from Expatriate at KMEX

made-in-Japan counterparts as both are produced in an
identical total manufacturing system including production
processes, materials used, and quality assurance. We also
continued our sales promotion campaign. However, I was
impatient when these efforts hardly bore any fruit initially.

Photo 3

4. Mexican Food and Liquor
As I said earlier, a full lineup of food from all over theworld is available in Mexico City though not at reasonable
prices. I seldom had a hard time to find a good place to eat.
Mexican cuisine, which is registered in the UNESCO
Lists of Intangible Cultural Heritage, provides a wide
choice of options and is very delicious even to theJapanese.
The staple food in Mexico is basically corn. Tacos(Photo 6) are a typical Mexican food consisting of a cornor wheat-based tortilla topped with a filling of meat, fish,
vegetables, and salsa (sauce). Each region in the country
has its own way of enjoying tacos. Anyway it is common
practice for the Mexicans to finish off a night of drinking
with a taco just like Japanese do with ramen.

KMEX Silao Plant tour (Peruvian customers)

We also held an event called KYB Safety Day for whichan F1 circuit course in Mexico was rented out to invite
customers from 13 countries for testing of various vehicles
for comparison. We patiently continued trying to makecustomers directly feel and understand the KYB quality(Photo 4).
Unexpectedly, the customer demand during fiscal 2021
sharply rose in reaction to the COVID-19 pandemic,
resulting in inventory runout at manufacturers andconfused physical distribution. Customers tended topurchase as much as available of any products regardlessof their origin. We eventually got the sales of made-inMexico products on track.
Sales of the low-priced K'lassic series were launched in2015. Initially, customers hesitated about introducing
them due to their rather streamlined specifications orappearance. We enhanced the product line up mainly for
low-priced models and gradually expanded the marketingarea through sales promotion activities. In fiscal 2021, weeventually expanded the marketing area to the total
KMEX territory.

Photo 5

Taco restaurant

Photo 6

Photo 4KYB Safety Day

Tacos

Mexican liquors are also abundant in type. Corona beer
is very famous in Japan too. Besides that, you can enjoy avariety of tasty beer from light ones to robust craft beer.
When you think of Mexico, the first thing that comes tomind may be tequila. Various types of tequila are sold by
various brands. There are different classes of tequila from"blanco" (white), and "reposado" to "añejo" (ultra-aged)
according to the maturation time, as in "junmai" (purerice), "ginjo" (special brew) and "daiginjo" (very specialbrew) of Japanese sake. It is interesting to try different
classes of tequila for comparison.
― 38 ―KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

Tequila originated in the colonial age in the 16th
century. Tequila was born when a Spanish colonist tried
to make an alcoholic beverage using a local plant named
agave. The village of Tequila exists in the State of Jalisco
in Mexico. Only product produced around the village of
Tequila can be called tequila.

Photo 7

year. The country is abundant in sightseeing spots frompyramids still reflecting the once prosperous ancient Maya
and Aztec civilizations (Photo 9), Cancun, which is aworld-famous beach facing the beautiful turquoise blue
ocean in the Caribbean Gulf (Photo 10), to Acapulco and
Los Cabos on the Pacific coast. All these places are notto-be-missed spots for tourists travelling in Mexico.

Tequila and mescal

Another alcoholic beverage that is a little more special
is mescal. This liquor is produced from the same
ingredients as those of tequila but uses more types ofingredient and more production processes. Bulbs of agave(Photo 8) are buried under the ground and steamed forlong hours to give a smoky flavor, which is similar to thatof very peaty Scotch whisky.
The production processes of both tequila and mescal
have been traditionally passed down over several hundredsof years. You can spend precious time recalling the history
and tradition cultivated in each distiller.

Photo 9Pyramid of the Moon viewed from the top of
Pyramid of the Sun

To visit these tourist spots from Mexico City which islocated inland, you have to take a flight. Still, any of thesespots are easily accessible with just a two hour or sodomestic flight. I often travelled to Cancun and fully
enjoyed fishing and marine sports there.

Photo 10 Cancun

Photo 8

Agave - Raw material of tequila and mescal

5. World Heritage and Sightseeing in Mexico
One of the joys for expatriates is travelling in the
country and its adjacent areas. In Mexico, the tourism
industry is the third biggest source of foreign earnings. It'sno exaggeration to say that tourism is an engine for the
Mexican economy.
That is why the Mexican government continued
accepting foreign tourists through borders kept open
without tightening immigration control even during the
COVID-19 pandemic in 2020.
Moreover, Mexico is positioned as an entry gate toLatin America and is teeming with tourists throughout the

Another popular tourist amusement in Mexico is winery
tours (Photo 11). Wine making is carried out in 14 statesof Mexico. The largest producers are wineries in
Guadalupe located in Baja California Peninsula. Thesewineries collectively produce 17 million bottles of wine
every year, which is 60% of the domestic production.
Speaking of wine in the American continent, Chile andArgentina are famous producers. In fact, Mexico has thelongest history of wine making throughout the continent.
The country has continued wine making for over 400
years since the technique was introduced from Spain in
the 16th century.
Mexico is warm and dry in climate with a substantial
difference in temperature between day and night. This
climate is the best for grapes to grow. Consequently, the― 39 ―

Essay from Expatriate at KMEX

country produces many varieties of wine including
Cabernet Sauvignon, Merlot, and Shiraz. So, a variety of
tasty, high-cost performance wines are available in the
country.

Baja California Peninsula, which is located south ofCalifornia State in the U.S., is a very popular tourist place
along with Cancun.
In this slender peninsula, sandwiched between the
Pacific Ocean to the west and the Gulf of California to theeast, cultivation of tuna and other marine products is
actively conducted. You can eat fatty tuna, fresh sea
urchin, abalone, and other premium marine products withgreat relish.

6. In Closing
I finished my seven-year assignment in Mexico thanks
to warm-hearted support from my supervisors, otherexpatriates, local staff, and my family. I would like to takethis opportunity to express my appreciation and say thanks
to all these people. I believe that my experience andpersonal contacts accumulated during the assignment will
give me much sustenance and confidence to carry out myfuture work. I greatly appreciate that I was given thisvaluable opportunity.
Photo 11WineryGuadalupe has a famous wine road where a number ofwineries stand side by side. Tourists can visit thesewineries to join a winery tour to taste wine and learn theirwine making processes.
In addition, there are a lot of restaurants that serve
dishes of locally-produced cheese and local specialties.
You can join a tour to visit three or more such restaurants,
spending a happy holiday.

Compañeros, gracias a sus amables apoyos que me hanbrindados durante 7 años, pude cumplir el reto que tenia
en Mexico exitosamente.
Era mi gran orgullo por haber trabajado con ustedes yesta experiencia sera mi gran confianza para seguir
trabajar en KYB ahora en adelante.
Muchas gracias!
Saludos,

Author 
KAWAI Hiroshi
Joined the company in 2013.
Commercial Product Sales Sect.
No.1, Global Marketing Promotion
Dept., Marketing Div.
Took present post after working in
Product Planning Sect. ofCommercial Product Headquarters,
working in Commercial Product
Sales Div., and as expatriate at KYB
Mexico DF branch.

― 40 ―KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

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Hard Chrome Plating
Refer to “Making Plating Thickness Constant by Simulation” (page 3)

MOCHIZUKI Yoshitaka
R&D Sect. No.1, Production Technology R&D Center, Engineering Div.

What is Plating?

DC supply

Plating is a technique to provide the target material withadditional surface properties that the material does nothave itself. Plating is conducted to impart one or more of
the following three major properties:① Corrosion resistance plating
To prevent corrosion of the material(Example) Galvanizing: Galvanized sheet roof
② Decorative plating
To improve the appearance(Example) D ecorative chromium plating:Automotive emblems③ Functional plating
To impart wear resistance, electrical properties, heat
resistance, or other properties(Example) Hard chrome plating: Sliding parts

2

What is Hard Chrome Plating?

The main constituent of hard chrome plating ischromium trioxide (CrO3). The plating uses a bath
containing a minute amount of sulfuric acid as catalyst.
As shown in Fig. 1, an object to be plated (work) is put inthe plating bath as the cathode while a lead alloy electrodeis used as the anode. When they are energized, chrome
metal is deposited on the work.
The plating film (chrome metal) obtained in this way is
generally applied to sliding parts of machinery, molding
dies, rolls for papermaking, and other various components
and shows the following characteristics:
・Rust-proof, metallic luster in normal environments
・Hard coating (800 to 1,000 HV - about three times
harder than iron)・A low coefficient of dynamic friction

Work

－

Cr

Cr6+

Cr

Cr6+

Cr

＋

Cr3+
Cr6+
Cr6+

Cr3+

Cr

Cr6+

Lead electrode

1

Cr3+

Fig. 1 Chrome plating system

3

Applications of Hard Chrome Platingin KYBKYB applies hard chrome plating to piston rods of shock
absorbers for four-wheel vehicles (Photo 1) and hydrauliccylinders mainly for the purpose of improving corrosion
resistance, wear resistance, or sliding characteristics.

― 41 ―<Shock absorber for
four-wheel vehicles>
Piston rod(chrome plated)

Photo 1 Chrome plated productCompensators in Control Systems

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Compensators in Control Systems
Refer to “Control Technologies for In-Vehicle Electric Actuators” (page 8)

MATSUMOTO Daisuke
Development Sect. No.2, Electronics Technology Dept., Engineering Headquarters,
Automotive Components Operations

1

For the control system in Fig. 1, the velocity v of thevehicle can be expressed by the equation below:

What is a Compensator?

v＝1.1 Role of Compensators
The compensator Note 1) in a control system refers to acomponent that generates manipulated variables (control
input) to attain a desirable response (control output) fromthe system.

As time elapses (s→0), the vehicle velocity v can be
expressed by the equation below:
C（0）P（0）P（0）
v－d
1＋C（0）P（0） r 1＋C（0）P（0）
1
(2)
1
C（0）
＝
v r－
d
1
1
＋1
＋1
C
（0）P
（0）
C
（0）P（0）v＝Note 1) This document uses the term “compensator”, not theterm “controller” which may sometimes be used.

As an example, a case is considered in which avehicle is applied with a driving force u (control input)
and controlled so that its velocity v (control output) is
maintained at a fixed target velocity vr (setting value)(Fig. 1). The vehicle is affected by disturbances d such as
aerodynamic drag, friction against the road surface, andforces caused by gravity on slopes. It is assumed here that
disturbances d are almost constant.

Fig. 1 Vehicle velocity control

Then, a control system is configured as shown in Fig. 2:

Fig. 2

Vehicle velocity control system (1)where
P(s): Transfer function of controlled object (transfer
function from the force applied to the vehicle
u-d to the velocity v)
C(s): Transfer function of compensators: Laplace operator (or differential operator)

C（s）P（s）
P（s）
(1)
vr－
d
1＋C（s）P（s）
1＋C（s）P（s）

When the compensator C(s) is designed so that C(0) is
sufficiently large, 1/C(0) in Eq. (2) is almost zero (0).
The vehicle velocity v is almost v = v r accordingly.
Designing the compensator C(s) in this way will achieve
one of the control objectives, that is, “to keep the velocity
close to the target value”. Behind the control objectives
lie a wide range of needs including cost-effectiveness,safety, and comfort. The role to be played by thecompensator in order to satisfy these needs will be
described in Chapter 3.
1.2 Types of Compensators and Example ofControl System Characteristics
Typical compensators include proportional, differential,
integral, phase lead, and phase lag compensators. A
detailed description of these compensators is omittedhere.
To achieve one of the control objectives “to keep thevelocity close to the target value” stated in the previous
section, a proportional and integral compensator will be
sufficient, provided that the transfer function of thecontrolled object can be expressed by the equation
below:
1
P（s）＝
(3)
Ms
where M indicates the weight [kg] of the vehicle. Eq. (4)represents an ideal vehicle that is applied with a control― 42 ―KAYABA TECHNICAL REVIEW No. 65 OCT. 2022

input u without delay. The transfer function of the
proportional and integral compensator can be expressedby the equation below:
K
K s＋KI
C（s）＝KP＋ I ＝ P(4)sswhere K P and K I are proportional and integral gains,respectively. When Eqs. (3) and (4) are substituted in Eq.
(1), the vehicle velocity v can be expressed by theequation below:
C
（s）P
（s）
P
（s）
v－
d
1＋C
（s）P
（s） r 1＋C
（s）P
（s）
KP
K
1
s＋ I
s
M
M
M
＝
v－
d
K
K r
K
K
(5)
s2＋ P s＋ I
s2＋ P s＋ I
M
M
M
M
1
s
2ζωn s＋ωn2
M
＝ 2
v－
d
s ＋2ζωn s＋ωn2 r s2＋2ζωn s＋ωn2
v＝

where

ωn＝ KI /M ，ζ＝KP 1 /（KIM）/ 2
Setting KP and KI to achieve 0 < ωn and 0 < ζ will makethe control system stable. The equation also implies that,as time elapses (s → 0), v = vr will hold.
1.3 How to Configure Compensators
There are two types of compensator configuration:
analog and digital. An analog compensator uses resistors,
capacitors, operational amplifiers, and other elements.
The example shown in the previous section assumes
control with an analog compensator. The transfer
function of an analog compensator is represented using
the Laplace operator s (or differential operator). A digitalcompensator is configured using a logic circuit or digitalcomputer. Digital compensators have the advantage thatcomplex compensators can be configured using software,
thereby enabling the user to easily modify parametersettings. Today, many control systems for in-vehicle
actuators use digital compensators because theperformance of microprocessors has been improved. The
transfer function of a digital compensator is represented
using the z and δ operators.

2

a model of the controlled object and the desirable
characteristics of the control system, instead of “first
selecting the type of the compensator”, such as
proportional or integral as introduced in section 1.2,
before designing. In other words, the designer can find acompensator satisfying the desirable characteristics ofthe control system even if the controlled object is quite
complex. Still, a more-or-less accurate model of thecontrolled object (a mathematical model such as transfer
function) will be needed. In some cases, the achievablecharacteristics of the control system may be limited
depending on the characteristics of the controlled object.
For your information, the proportional and integral
compensator stated in section 1.2 can also be derived
from the parametrization of a stabilizing compensator.

3

Two-degree-of-freedom Control
SystemThe control system described in Chapter 1 may haveother control objectives than just “to keep the velocity
close to the target value”, attributable to various demands
including “[1] to reduce the fuel (or electricity for electricvehicles) consumption during acceleration (costeffectiveness)”, “[2] to reduce the shock felt bypassengers during acceleration or deceleration (ridecomfort)”, and “[3] to minimize speed variations during
driving on slopes (safety)”. Demands [1] and [2] mainly
relate to target tracking and [3] relates to disturbance
response. With a focus on Eq. (1) in section 1.1, target
tracking (the first term on the right-hand side) anddisturbance response (the second term on the right-handside) are both decided by the compensator C(s). Thismeans that, in some cases, demands [1] & [2] anddemand [3] can hardly all be satisfied at the same time.
Then, another control system should be considered asshown in Fig. 3:

Fig. 3 Vehicle velocity control system (2)Parametrization of Stabilizing
Compensators

Parametrization of stabilizing compensators was
proposed by Youla and others during the 1970s 1). Thismay be called “Youla parametrization”. Studies on robust
control theory became active toward the 1990s and many
books explaining how to apply Youla parametrization toactual control scenes 2) were published. A stabilizing
compensator design with parametrization should
represent “how the compensator should be” derived from

The velocity v of the vehicle with the control system inFig. 3 can be expressed by the equation below:
F（s）C
（s）P
（s）
P（s）
(6)
v＝
v－
d
1＋C（s）P（s） r 1＋C（s）P（s）
With an additional compensator F(s), target tracking(the first term on the right-hand side) and disturbance
response (the second term on the right-hand side) can be
set separately. That is, two-degree-of-freedom design is
now available. In this sense, the control system in Fig. 3
is called a two-degree-of-freedom control system.

― 43 ―

Compensators in Control Systems2) MAEDA, SUGIE: System Control Theory for Advanced Control,

References
1) D.C. Youla, Hamid A. Jabr, J.J. Bongiorno Jr: Modern WienerHopf Design of Optimal Controllers - Part II: The Multivariable
Case, IEEE Trans. Auto Control, AC-21, No. 3, pp. 319-338,(1976).

― 44 ―

Asakura Publishing, (1990).

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PV Values of Vane Pumps
Refer to “Development of Vane Pump for Medium Passenger Vehicle CVT” (page 26)

HAGIWARA Takahiro
Pump Engineering Dept., Steering Business Dept., Automotive Components Operations

1

What is the PV Value?

The PV value (or PV factor) is one of the wear factors ina sliding scene and can be calculated from the pressure (P)applied to the contact surfaces of the sliding parts and thesliding velocity (V).
The surface pressure P can be determined by dividing thepressing force N by the contact area A.

2

PV Value of Vane Pumps

2.1 Operating Principle of Vane Pumps
First of all, the following describes the pumping mechanismof vane pumps to suck or discharge the hydraulic oil:
①The engine outputs a driving force to rotate the rotor of thepump via the shaft.
②As the rotor rotates, vanes inserted in the slots pop up radially with the centrifugal force and the pump’s internal pressure increase on the back of the vanes.
③The pop-up vanes slide along the curved internal surface(oval shape) of the cam ring.
④The pump sucks or discharges the oil as the oil chamber
formed by the cam ring, rotor and vanes increases or decreases in volume.
These parts and their operation are shown in Fig. 1.

2.2 PV Value of Vane Pumps
As the rotor rotates, the pop-up vanes are pressed against
the cam ring by the centrifugal force and the pump’s internalpressure increase on the back of the vanes. This applies thesurface pressure P to the contact surfaces. The vanes slide along
the cam ring surface at a sliding velocity V as the rotor rotates.
A lower PV value implies higher wear resistance and ahigher PV value brings about lower wear resistance. The PVvalue at which the cam ring wears out is called the PV limit.
Photo 1 shows a cam ring that was subjected to a durability testwith a PV value exceeding the PV limit and eventually wornout. Photo 2 shows a cam ring that was subjected to a durability
test with a PV value lower than the PV limit.
To improve the wear resistance of a vane pump, the PV value
should be kept at a low level. To do so, the surface pressure P
must be reduced by increasing the contact area A, decreasing
the pressing force N, or lowering the sliding velocity V.
Wear resistance is affected not only by the PV value but
also by material, surface roughness, and hardness of the parts
coming into contact with each other, lubrication of the hydraulicoil, and other factors. It is necessary to design a vane pumpwith considerations given to the balance among these factors.

Abnormally worn partCam ring

Shaft

Photo 1

Abnormally worn cam ring with PV value exceeding
the limit

Photo 2

Cam ring with PV value lower than the limit after
durability test

Vane

Rotor

Vane

Fig. 1

Cross section of vane pump

― 45 ―

Editors Script
I have long been involved in research and development. For me, KYB Technical Review is a stage from which to advertise theresults of engineering and product development efforts to the external world. Article auditors can leave the resulting technologies
here as a record to be handed down to posterity. As an engineer, I am honored to be one of the contributors to the Review. Since
it is difficult to publish sensitive information about, for example, products under development or knowhow related to productionengineering, the Review might not provide readers with sufficient information at this moment. For compiling articles in the future,
we need to fully consider what information readers may find useful. Then, we would like to introduce technologies and productsthat are commonly known internally but might be novel to readers.
(SAITO)I definitely think it is difficult to explain something to others that is unknown to them. Words that are used among one group ofpeople in a casual way often cannot be understood by another group of people. Basically, others do not listen to your words from aspeaker’s position. I always find the text in the articles of KYB Technical Review easy to understand. I really respect contributors
to the Review who respond to me amiably when I visit their place to urge them to finish their script even when they are busy.
Thanks to them, I, as an editorial member, have been able to help continue publishing this issue. If possible, I wanted to buy thema glass of beer and say, "you did it", but that was difficult under the current situation. I seriously hope that various controls related
to COVID-19 will be lifted soon.
(SASAKI)I have been involved in editing KYB Technical Review for the first time after a change of editors. I had once contributed to the
Review but had never joined the editorial team. Now I am able to understand how the editors are working hard behind the scenes
on a publication that I had been reading without noticing them. The Mie district that I am in charge of has not yet come up witha new research and development achievement, so I have had little chance of helping our engineers contribute to the Review. I
am now part of the editorial team of the Review, which is one of the media to publish research and development being steadily
carried out at other sites. As an editorial member, I will do my best to support contributors and other editors in any way I can.
(YONEKAWA)

Editorial members◎ ITO Takashi
KABASAWA Ryoichi
HAYASE Tomonori
SUO Shiro
AMANO GenkiOTA Yasuhiro
MIYATANI Osamu
SASAKI Kazuhiro
NOGUCHI Yoichi
SAITO Keiji

Basic Technology R&D Center,
Engineering Div.
Basic Technology R&D Center,
Engineering Div.
Basic Technology R&D Center,
Engineering Div.
Intellectual Property Dept., Engineering
Div.
Corporate Planning Dept., Corporate
Planning Div.
Engineering Headquarters, AC
Operations
Engineering Headquarters, AC
Operations
Engineering Headquarters, AC
Operations
Production Engineering Dept., PS
Business Operations, AC Operations
Sagami Hydraulics Engineering Dept.,
HC Operations

UMEDA Yoshinori
YONEKAWA Norihide
YAMAGATA Hideki
KAWASHIMA Shigeru
OKUMURA Kazuyuki
KAWANO Yoshihiko
KOBAYASHI Hirotaka○ KOBATA Hiroshi○ OBAYASHI Yoshihiro

Engineering Headquarters, HC
Operations
Mie Engineering Dept., HC Operations
Engineering Dept., Aircraft
Components Div.
Engineering Dept., Kumagaya Plant,
Special Purpose Vehicles Div.
Design Sect., No.3, KYB Motorcycle
Suspensions (KMS)
Development Dept., Engineering Div.,
Takako Industries, Inc.
Design Dept., KYB-YS Corporation
Engineering Planning Dept.,
Engineering Div.
Engineering Planning Dept.,
Engineering Div.

◎ Editorial Chief○ Editorial Secretariat
HC Operations: Hydraulic Components Operations
AC Operations: Automotive Components Operations

Notification regarding website release
KAYABA TECHNICAL REVIEW No.65[All rights reserved] [NFS]

Published on October 1, 2022
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