Damping Controller Integrated into Output Current
Control Loop and Design for Multiple Servo Drive
Systems Connected to Common DC-Bus Line
Katsuki Miura
Dept. of Electrical, Electronics, andInformation Engineering
Nagaoka University of Technology
Niigata, Japank_miura@stn.nagaokaut.ac.jp

Hiroki Watanabe
Dept. of Electrical, Electronics, andInformation Engineering
Nagaoka University of Technology
Niigata, Japanhwatanabe@vos.nagaokaut.ac.jp

Takeshi Kiribuchi
OMRON Corporation
Kyoto, Japantakeshi.kiribuchi@omron.com

Hiroyuki Tokusaki
OMRON Corporation
Kyoto, Japanhiroyuki.tokusaki@omron.com

Abstract— This paper proposes a damping control tostabilize multiple servo drive systems connected to a common
DC-bus line. The DC-bus servo drive system has a systeminstability problem due to interference between a constant
power load and bus impedance. The damping controller
integrated into the output current control loop evaluates theinfluence of the damping controller on the current responsecompared with the second-order standard form. The
parameters of the damping controller for the multiple units aredesigned by the impedance method. The experimental results
mention that the output current response almost agrees withthat of the simulation within a 1% error. Furthermore, thestable operation range with the proposed damping control is
expanded by 28% of the motor-rated power.
Keywords— DC-Bus System, Servo Drive, Damping Control,
Impedance-based Stability Analysis

I. INTRODUCTION
In recent years, servo drive systems have been used widelyin industrial applications. It is generally required to achieve
high control performance, low noise, and high power
density[1-5]. The control panel, including servo drivers andservo motors, are connected to three-phase AC lines in theconventional configuration of the servo drive systems.
However, the conventional configuration has a problem,
which is a radiated noise from the AC lines due to the inverter
switching. Thus, the countermeasure for the radiation noise isneeded in order to prevent interference from other equipment.
However, the countermeasure, shielding cables, and layout of
power and signal lines lead to increase costs.
In order to solve this problem, the DC-bus servo drive
system, which connects the servo drivers to a common DCbus line, has been proposed [6]. This configuration reduces theradiated noise due to the shorter length of the AC power line
and the system loss due to no rectifier stage in each servo
driver. Moreover, the DC-bus servo drive systems prevent
complicated wiring and reduce the costs of noise suppression
since the number of long power lines is reduced.
However, the DC-bus servo drive systems have theproblem of system instability due to the interference between
the line impedance of the DC-bus and the negative impedance
characteristics of the constant power load [7-8]. This problem

Jun-ichi Itoh
Dept. of Electrical, Electronics, andInformation Engineering
Nagaoka University of Technology
Niigata, Japan
itoh@vos.nagaokaut.ac.jp

leads to a system trip due to oscillation in the bus current andvoltage when the system is unstable. Therefore, damping
control is needed for the DC-bus servo drive system in orderto prevent system instability. The damping control method forthe DC-bus system and cascaded DC-DC converter have been
proposed [9-15]. In these papers, the parameters of thedamping controllers are designed based on the impedance
method, which analysis the system stability from eachsubsystem impedance [16]. The impedance method is suitable
for the system analysis method for multiple units systems.
However, the damping controller influences the output current
control performance, such as significant overshoot, due tozeros in the damping controller.
Ref. [17] has proposed the damping controller integrated
into the output current controller for a matrix converter. This
damping control method evaluates the influence of thedamping controller quantitatively from the closed-looptransfer function of the output current controller bycomparison with the second-order standard form. Thus, thismethod is suitable for the DC-bus servo drive system, whichis required high torque control accuracy. However, theparameter design method in Ref. [17], that by the linear modelof the whole system, has a problem with the extensibility ofmultiple units system because the linear model is complex due
to interference among each unit.
This paper proposes a damping controller integrated into
the q-axis current control loop and parameters design method
for the multiple DC-bus servo drive systems. The proposed
damping controller is inserted into the feedback path of the qaxis current control loop. The current control performance isevaluated by comparison with the standard second-order form.
In addition, the proposed parameter design method is based on
the impedance method, which analyzes the system stability
from the impedance of each subsystem. The originality of thispaper is that the damping controller parameters are designed
based on the impedance method expanded the multiple units
system.
The paper is organized as follows: firstly, the DC-bus
servo drive system and its damping controller are described.
Secondly, the system stability is analyzed by the impedance
method. Thirdly, the proposed design flow for the damping
parameters is described. Finally, the proposed design method

INV

Unit
#1

Lbus Rbus
Vdc

ibus

vbus

Unit
#2

M

Cb1

M

INV

iv

M

Cb2

+

0

Common Bus

PI(s)

-

・・・

・・・
・・・

CbN

iq*

M

-

PI(s)

Fig. 1. The DC-bus servo drive system. Each servo unit is connected to acommon DC-bus line. The DC-bus line has a large impedance due to its long
length.

is evaluated by the experiment and discussed in terms of the
impact of the influence of the controller delay.

PWM

3f

6

Gate

vq*

+

wre(Lmid+Ke)

iq

3

dq

+

id
iq

iw

vd*

-

wreLmiq

+

2

3f
dq

+

id

INV
Unit
#N

qre

iu

qre

Fig. 2. The configuration of each servo driver. The controller of each
unit is based on Field Oriented Control (FOC). Zero-d-axis-current
control and decoupling control are also applied.

iq*

+

-

Controller
PI(s)

vq

Motor
G(s)

iq

T(s)

II. SYSTEM CONFIGURATION OF DC-BUS SERVO DRIVESYSTEM
A. System configuration
Fig. 1 shows the system configuration of the DC-bus servo
drive system. Each unit is connected to a common DC-bus line.
In this system, the servo driver is placed near the motor. In Fig.
1, Lbus is the bus inductance, Rbus is the bus resistance, and Cbk(k = 1, 2, ... N) is the DC-link capacitor of each servo driver.
Note that the DC-bus line has a large impedance due to its long
length. In this paper, the system with two servo units isanalyzed.
B. Controller configuration of each servo driverFig. 2 shows the main circuit and controller configurationof each servo unit without the damping controller. The output
current controller is based on Field Oriented Control (FOC)for the servo motor. In Fig. 2, qre is the rotor position detectedby the encoder, PI(s) is the Proportional-Integration regulator
for the output current control, wre is the rotor angular speed,
Lm is the inductance of the motor, and Ke is the back-EMF
constant of the motor. Zero-d-axis-current(id=0) control anddecoupling control for canceling cross term of permanent
magnet(PM) motor. The gate pulses for each output voltage ofthe inverter are generated by pulse width modulation(PWM).
The transfer function of the PI controller for current
control is expressed as

æ
1 ö
(1),
PI ( s) = K p ç1 +÷è sTi øwhere Kp is the proportional gain, and Ti is the integral time.
The parameters of the PI controller are designed to cancel
zeros
asìï K p = wc Lm(2),íïîTi = Lm / Rawhere Ra is the armature resistance, and wc is the bandwidthof the current controller.

Fig. 3. The simplified control block diagram of each servo unit without
the damping controller. The zero-d-axis-current(id=0) control and thedecoupling control are implemented for the PM motor.

iq*

F(s)

+

PI(s)

-

vq

G(s)

iq

+

-

H(s)

Fig. 4. The control block diagram with the damping controller
integrated into the output current control loop. The first-order delay F(s)is inserted into the current command in order to cancel the zeros of thedamping controller.

Fig. 3 shows the simplified q-axis control block diagram
under id=0 control of each servo driver without the damping
controller. In Fig. 3, the transfer function of the PM motor G(s)is expressed as

G( s) =

1
Ra + sLm(3).

The open-loop transfer function T(s) is given by

T ( s) = PI ( s)G( s) =

wc

(4).
s
The open-loop transfer function is the same as the integral
form.
C. The damping controller integrated into the output
current control loop
Fig. 4 shows the control block diagram of each unit withthe proposed damping controller integrated into the output
current control loop. The damping controller H(s) is inserted
into the feedback path of the q-axis current control loop. The
damping controller H(s) is expressed as

(5),1 + sThpf
where Kdamp is the damping gain, and Thpf is the time constantof the high pass filter. In addition, the first-order delay F(s) isinserted into the q-axis current command in order to cancel thezero of the damping controller and prevent a large overshoot.
The first-order delay F(s) is expressed as

F (s) =

1
1 + sThpf(6).

The loop gain of the current controller with the damping
controller Tdamp(s) is given by (7).

Tdamp ( s ) = PI ( s)G ( s) {1 - H ( s)} =wc sThpf (1 - K damp )s
1 + sThpf(7)
The transfer function of the feedback path {1-H(s)} is thesame form as a phase delay compensator.

Gain [dB]sThpf

w/o damping
withdamping

Reducing gain

Phase [deg.]H ( s ) = K damp

Frequency [Hz]Fig. 5 The bode diagram of the current control loop gain with andwithout the damping controller. The damping controller reduces the loop
gain at the high-frequency range.

Lbus
Vs’

Rbus

Cb1 +Cb2=Call

Fig. 5 shows the bode diagram of the current control loop
gain T(s) and Tdamp(s). The loop gain with the damping
controller is reduced at a high-frequency range. The damping
controller stabilizes the system by decreasing the loop gain.
The closed-loop transfer function of the current controller
with the damping controller Gclose(s) is derived as

wc / Thpf

Gclose ( s) =s2 +1 + Thpf wc (1 - K damp )
Thpf

s+

wc

(8).

Thpf

Equation (8) is the same form as a second-order standard form.
The second-order standard form is expressed as

wn 2
(9),
s 2 + 2zwn s + wn 2
where z is the damping factor, and wn is the natural angularfrequency. The damping factor z and the natural angularfrequency wn of the current controller with the damping
GSOSF ( s ) =controller are derived by comparison between (8) and (9) asz =1 + Thpf wc (1 - K damp )2Thpf wc / Thpf

wn =

wc
Thpf

(10),

(11).

Equation (11) means that the bandwidth of the current
controller with the damping control is determined by wc andThpf. The system stability is improved with increasing Thpf
since z is increased, while the current response is degraded.
Thus, Thpf needs to be designed as small as possible in order toprevent the current response degradation.
III. STABILITY ANALYSISThe stability of the system shown in Fig. 1 is analyzed
based on the impedance method, which is proposed by
Middlebrook [16]. In the impedance method, the wholesystem is divided into source and load sides, and the systemstability is determined by the Nyquist plot of the minor loop

Zo(s)Yin_all(s)=Yin1 (s)+Yin2(s)Fig. 6. The equivalent impedance model of the DC-bus servo drive
system. The servo drivers are expressed as the input admittance. Thismodel consists of the LC filter and the combined admittance.

gain, which is the product of the output impedance of thesource side and the input admittance of the load side.
A. The impedance of each subsystem
Fig. 6 shows the equivalent impedance model of the DCbus servo drive system. In Fig. 6, the servo drivers and motorsof each unit are expressed as the input admittance Yin1(s) andYin2(s). The equivalent impedance model consists of the LC
filter and the combined admittance Yin_all(s). Here, the output
impedance of the LC filter Zo(s) is expressed asZo ( s) =sLbus + Rbuss Lbus Cbus + sCbus Rbus + 1
2

(12).

The input admittance of each servo unit is derived by the
extra element theorem [6][16]. The input admittance of aconstant power load YCPL(s) is expressed as

YCPL (s) =1
T ( s)
1
1+
Z N ( s) 1 + T ( s) Z D ( s) 1 + T ( s)(13),where ZN(s) is the input impedance of the constant power loadwith ideal feedback, and ZD(s) is the input impedance without
feedback. The input impedance of the servo driver with ideal
feedback ZN(s) is expressed asV
V 2
Vb,0 2(14),
Z N ( s) = - b,0 = - b,0 = Ib,0Pout
( I q,0 Ra + wre Ke ) I q,0
where Vb,0 is the steady value of the DC-link voltage, Ib,0 is thesteady value of the DC-link current, Pout is the output powerof the servo driver, and Iq,0 is the steady value of the q-axis
current. Note that ZN(s) is a negative impedance depending on
the motor output power.
The input impedance of the servo driver without feedback
ZD(s) is expressed aswhere a is the conversion ratio from the DC-link voltage tothe q-axis voltage.

Gain [dB]

2

æ
ö
Vb ,0
Z D ( s ) = 2 ( Ra + sLm ) = ç÷÷ ( Ra + sLm )çaè Ra I q ,0 + wre K w ø(15),
1

Fig. 7 shows the bode diagram of the input admittanceYin(s). The input admittance of the servo driver changes
depending on its operation points, such as the torque (q-axis
current) and the motor speed. The phase in the lower
frequency range is near 180 deg when the motor outputs thetorque. This means that the servo driver has negative
resistance characteristics.
B. The stability analysis
The stability of the system shown in Fig. 6 is analyzed by
the Nyquist plot of the minor loop gain, which is the productof the Zo(s) and Yin_all(s). The minor loop gain of the system
TMLG(s) is expressed as (17).

TNLG ( s) = Z o ( s)Yin _ all ( s) = Z o ( s)Yin1 ( s) + Z o ( s)Yin 2 ( s)(17)
The minor loop gain of the whole system is expressed as thesum of the minor loop gains of each unit. The minor loop gainsof each unit are expressed as TMLG1(s) and TMLG2(s).
Fig. 8 shows the bode diagram of the minor loop gain of
the whole system TMLG(s) and each unit TMLG1(s) and TMLG2(s).
The gain and phase are changed sharply at the resonant
frequency fres of the LC filter. The phase crossover frequency
fo of each minor loop gain is almost the same near the resonant
frequency. The minor loop gain of the whole system at thephase crossover frequency TMLG(fo) is expressed under thecondition that the phase crossover frequency of each unit is
the same as
TMLG ( f o ) = Re {TMLG ( f o )}= Re {TMLG1 ( f o )} + Re {TMLG 2 ( f o )}(18)

! Im {TMLG ( f o )} = Im {TMLG1 ( f o )} = Im {TMLG 2 ( f o )} = 0

Fig. 9 shows the Nyquist plot of the minor loop gains of
the whole system TMLG(s) and each unit TMLG1(s) and TMLG2(s).
The gain margin of a system corresponds to the reciprocal of
the real part of minor loop gain at the phase crossover
frequency. The relationship between the gain margins and theminor loop gains is expressed as
Re {TMLG ( f o )} = -GM all
Re {TMLG1 ( f o )} = -GM 1

(19),
(20),

(21),
Re {TMLG 2 ( f o )} = -GM 2
where GMall is the gain margin of the whole system in dB, and
GM1 and GM2 are the gain margins of each unit in dB. Thus,

Frequency [Hz]Fig. 7. The input admittance of the servo driver. The input admittancechanges depending on the operation point of the servo motor.

TMLG2(s)TMLG(s)TMLG1(s)Phase cross180 degfofresFrequency [Hz]Fig. 8. The bode diagram of the minor loop gain of the whole system andeach unit. The phase crossover frequency of each minor loop gain isalmost the same near the resonant frequency of the LC filter.

TMLG(s)TMLG2(s)TMLG1(s)Imaginaly part(16)

Iq,0 = 3.5 A
wre = 1570 rad/s

Gain [dB]2Phase [deg.]

I q ,0 ( Ra I q ,0 + wre Ke ) T ( s)( Ra I q,0 + wre Ke ) 1
Yin ( s) = +2Vb,0
1 + T (s) Vb,0 2 ( Ra + sLm ) 1 + T (s )Iq,0 = 0 A
wre = 1570 rad/s

Phase [deg.]

The input admittance of the servo driver Yin(s) is derived
by substituting (13)-(15) as (16).

Iq,0 = 3.5 A
wre = 523 rad/s

-GM2
-GM1
-GMallReal partFig. 9. The Nyquist plot of the minor loop gains of the whole system andeach unit. The gain margin is the reciprocal of the real part of the minor
loop gain at the phase crossover frequency.

The relationship between the gain margin of the whole systemand each unit is given by (22).

GM all = GM1 + GM 2

(22)

As shown in (22), the gain margin of the whole system isexpressed as the sum of the gain margins of each unit in the
DC-bus servo drive system.
IV. PROPOSED PARAMETER DESIGN METHODThis section proposes the parameters of the damping
controller design method for multiple DC-bus servo drive
systems based on the relationship of the gain margins.
A. Design flow
Fig. 10 shows the proposed parameters design flow for
multiple DC-bus servo drive systems. The proposed flow
consists of three steps. At first, the minimum gain margin of
the whole system GMall is set. Second, the minimum gain
margin of each unit GMk is set based on GMall. Finally, theparameters of the damping controller of each unit are tuned sothat the unit ensures the desired gain margin GMk over the all
operating range of the motor. As shown in (22), the wholesystem ensures the minimum gain margin GMall when all units
ensure GMk.

Start

step 1・・・

Setting the minumum gain margin of
the whole system GMall

step 2・・・

Setting the minumum gain margin ofeach unit GMk

step 3・・・

Adjustment the damping
parameters of each unit
Finish(a) The flow chart for the design of the Dc-bus servo drive system

Start
Kp, TiSet Thpf to 1/wc

Fig. 10(b) shows the subroutine for tuning the damping
parameters of each unit. At first, the time constant of HPF is
set to 1/wc because the natural angular frequency wn is thesame as wc when Thpf is equal to 1/wc. Second, the damping
gain Kdamp is calculated by (23), which is derived by (10).

K damp =1 + Thpf wc
Thpf wc- 2z

1
Thpf wc

Calculation of Kdamp
Satisfying
GMk ?

B. The parameters design
Table 1 shows the parameters of the system. The same twounits are connected to a common DC-bus line. In this paper,
the parameters are designed in order to be stable within therange of rated torque and speed. In general, the gain margin of
the whole system GMall is set to less than 0dB. In this paper,
GMall is set to 0 dB in order to check the validity of the designfrom the waveform. In addition, the gain margin of each unit
GMk is set to 6 dB, which is twice of GMall, because the twosame units are connected to the DC-bus line.
Fig. 11 shows the relationship between the motor speed andthe gain margin of one unit when the q-axis current is rated
current of 3.5 A. As a result of the design, the time constantThpf is set to 0.765 msec, and The damping gain Kdamp is set tobe 0.648 when z is 0.707. The natural angular frequency of thecurrent controller with the damping wn, which is calculated by(11), is 4053 rad/s. The gain margin of the unit with thedamping controller has a bottom with increasing the motor
speed at 1340 r/min.
Fig. 12 shows the gain margin of the whole system
calculated by (22), and the true value, which is calculated by
the transfer function of the whole system based on (17). In Fig.
12, Unit #1 is driven at the operation point where the gain
margin of Unit #1 is minimum, and the motor speed of Unit
#2 is changed. The gain margin of calculated by (22) and thetrue value is agreed in the range from low speed to the speed
at which the gain margin is bottom. However, the proposed
analysis based on (22) underestimates the whole system’s
stability in the high-speed range. The error occurs because thephase crossover frequency of Unit #2 is shifted to the lower

No
Yes

Finish(23)

If the system does not satisfy GMk, Thpf is changed, andKdamp is calculated again. If the system satisfies GMk, thedesign of the damping parameters is finished.

Changing of Thpf(b) The subroutine for adjustment of the damping parameter of each unit
Fig. 10. The proposed design flow for the damping controller of the DCbus servo drive system. The gain margin of the whole system is satisfied
when each unit satisfies the minimum gain margin GMk.
Table 1

Lbus
Rbus
Cb1, Cb2
Vdc

wc
Kp
Ti
fsw
fsamp
Td

The parameters of the DC-bus servo drive system.

Circuit
Wiring indutance of DC Bus
Wiring resistance of DC Bus
Inverter input capasitanceDC bus voltage
Controller
The bandwidth of current controller
Proportional gain
Integration time
Switching frequency
Sampling frequency
Dead time
Drive Side Motor (Unit #1, #2)
R88M-1M40030T (Omron)

11 mH
2.2 W
6.8 µF
280 V
4000p rad/s
42.7
2.43 ms
20 kHz
20 kHz2 µs

frequency side due to the influence of the positive term of the
input admittance Yin(s).
Fig. 13 shows the bus current waveform when both units
are driven at the operation point where the gain margin is
minimum. Note that the simulation model includes the ideal
controller, which is not considered the delays. The continuous
oscillation occurs because the whole system becomes thestable limit. This result shows that the proposed design
method is valid for the design of the DC-bus servo drive
system.

15
10

(GMk)
6 dB

5

Iq,0 = 3.5 A

with damping ctrl.
Thpf = 0.765 ms

Gain margin [dB]Gain margin [dB]201340 r/min

5

w/o damping ctrl.
0

0

500

1000

1500

2000

2500

3000

B. The damping effectFig. 15 shows the bus current waveform with the proposed
damping controller. The oscillation occurs in the period
without the damping controller because the system becomes
unstable. The oscillation is suppressed when the damping
controller is tuned on. Thus, the proposed damping controller
suppresses the oscillation of the DC-bus current effectively.
Fig. 16 shows the stable operation area when two motors
are driven in the experiment, the analysis, and the simulation.
Unit #1 motor is driven at 3000 r/min, and Unit #2 is driven at
1500 r/min. Note that the simulation model includes thecontroller with the PWM delay. The stable limit output of one
unit is changed depending on another unit’s output. The stable
operation area in the experiment is expanded by 28% of the
motor-rated power by the damping controller. However, thestable operation area in the experimental is reduced by 40% of
the motor-rated power compared to the analysis. The result of
the simulation is reduced error with the experimental. Thus,
this result shows that the delays in the controller influence thesystem’s stability.
C. Discussion
This section discusses the impact of the PWM delay on thesystem’s stability. Fig. 17 shows the block diagram of each
unit with the damping controller and PWM delay. The delay
time of the controller with PWM is 1.5 times the sampling
period.
Fig. 18 shows the input admittance of the servo unit withthe damping controller with and without delay. The gain is
increased near the natural frequency fn by the PWM delay.

Proposal(Eq. 22)

1
0
0

500

1000

1500

2000

2500

3000

Unit #2 motor speed [r/min]Fig. 12. The relationship between the Unit #2 motor speed and the gain
margin of the whole system. The operation point of Unit #1 is constantat the point that the gain margin is minimum. The error occurs in thehigh-speed range because the phase crossover frequency of Unit #2 isshifted to the lower frequency.

Unit #1 and #2 : 1340 r/min, Iq,0 = 3.5 A

3Bus current [A]A. The current response
Fig. 14 shows the step response of the q-axis current by
the standard second-order form, the experimental, and thesimulation. Note that the simulation model includes thecontroller with the PWM delay and the discretization. The
overshoot in simulation and experiment is larger than that of
the standard second-order form due to the influence of thePWM delay and the resonant of the LC filter. The overshootvalue and the peak arrival time in the experiment agree withthat of the simulation result within 1%.

True value (Eq. 17)

22

1
0.1 sec

10 ms

0Fig. 13. The bus current waveform in the simulation. Both units are
driven at the operation point where the gain margin is minimum. The
continuous oscillation occurs because the whole system is a stable limit.

q-axis current [A]V. EXPERIMENTAL RESULTS AND DISCUSSION
This section evaluates the validity of the proposedparameters design method in the experiment. The parametersin the experiment are based on Table 1. The motor speed iscontrolled by the load-side motor.

2 dB

3

Motor speed [r/min]Fig. 11. The relationship between the motor speed and the gain marginof each unit. With the damping controller, the unit satisfies GMk within
the rated current and speed.

Unit #1 : 1340 r/min, Iq,0 = 3.5 A
Unit #2 : Iq,0 = 3.5 A

432

Motor speed : 2000 r/min
Current command
Experiment
Sim.
Standard second-order form

1
0
-1

0

1

2

3

Time [ms]Fig. 14. The step response of the q-axis current by the standard secondorder form, the experimental, and the simulation. The overshoot value
and the peak arrival time in the experiment agree with that of thesimulation result within 1%.

Bus Current ibus 1A/div

20ms/div

0A
Damping controlleroffDamping controller
onFig. 15. The DC-bus current waveform when the damping controller isturned on. The oscillation due to the system instability is suppressed
effectively.

Sim. with delay
Analysis

output power [W]Unit #2 Stable limit Ouptput[W]limit
Unit Power#2 stable

600
600

400
400

iq*

Exp.
(w/ damp.)

F(s)

200
200

00

200
200

-1.5T
- PI(s) e

samp s-Exp.
(w/o damp.)

00

+

400
400

600
600

iq

+

H(s)

800
800

Unit
stable limit
limit output
power[W] [W]
Unit#1#1Stable
Ouptput
Power

Fig. 16. The operation area when two motors are driven. Unit #1 isdriven at 3000 r/min, and unit #2 is driven at 1500 r/min. The stable
operation area with the damping controller is expanded by 28% of the
motor-rated power.

Fig. 17. The block diagram of each unit with the damping controller
and PWM delay. The delay is 1.5 times the sampling period.

Iq,0 = 3.5 A
1340 r/min

with delay

with delay
w/o delay

Imaginary partw/o delay

Phase [deg.]

Gain [dB]G(s)GM: 6 dB

GM: 4.6 dB

fres

fn

Frequency [Hz]fn= wn/2p

Fig. 18. The input admittance of the servo driver with the damping
controller. The gain of the input admittance with the delay is increased
near the natural frequency. The phase with the delay is reduced over thenatural frequency.

This factor leads to the system stability being reduced. On theother hand, the phase of the model with delay is changed fromthe model without the delay over the natural frequency.
Fig. 19 shows the minor loop gains of one unit with andwithout the PWM delay. The gain margin of the model withthe delay is reduced by the model without delay with 1.4 dB
because the gain of the input admittance near the resonant
frequency of the LC filter is increased. As shown in Fig. 18
and 19, the delay of the controller influences the systemstability when the resonant frequency of the LC filter is nearor over the natural frequency. The input admittanceconsidered the controller delay is needed to design the DC-bus
servo drive system in order to consider the impact of delays.

VI. CONCLUSIONSThis paper proposed the damping control and its parameters
design method for multiple servo drive units connected to acommon DC-bus line. The damping controller was integrated
into the q-axis current controller and evaluated the influenceon the current response by compared with the second-orderstandard form. In addition, the parameters design method forthe system with multiple units was proposed. The proposed
design method was based on the impedance method andensured the desired gain margin. The proposed method wasevaluated by the analysis and the experiment. The experiment

Real partFig. 19. The Nyquist plot of the minor loop gains of each system.
The gain margin of the model with controller delay is reduced by 1.4
dB.

results showed that the stable operation area is expanded by
28% of the motor-rated power by the damping controller. This
paper also discussed the impact of the controller delay on thesystem’s stability.
In the future, the controller achieving both high current
response and damping performance will be considered.

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