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This is the author’s version of a work that was submitted/accepted for pub-lication in the following source:
Neath, M.J., Swain, A.K., Madawala, U.K., Thrimawithana, D.J., & Vi-lathgamuwa, D.M.(2012)Controller synthesis of a bidirectional inductive power interface for electricvehicles. InProceedings of IEEE Third International Conference on Sustainable En-ergy Technologies (ICSET), IEEE, Soltee Crowne Plaza, Kathmandu, pp.60-65.
This file was downloaded from: https://eprints.qut.edu.au/74755/
c© Copyright 2012 IEEE
Notice: Changes introduced as a result of publishing processes such ascopy-editing and formatting may not be reflected in this document. For adefinitive version of this work, please refer to the published source:
https://doi.org/10.1109/ICSET.2012.6357376
Abstract—Bidirectional Inductive Power Transfer (IPT) systems
are preferred for Vehicle-to-Grid (V2G) applications. Typically,
bidirectional IPT systems are high order resonant circuits, and
therefore, the control of bidirectional IPT systems has always been
a difficulty. To date several different controllers have been
reported, but these have been designed using steady-state models,
which invariably, are incapable of providing an accurate insight
into the dynamic behaviour of the system. A dynamic state-space
model of a bidirectional IPT system has been reported. However,
to date this model has not been used to optimise the design of
controllers. Therefore, this paper proposes an optimised
controller based on the dynamic model. To verify the operation of
the proposed controller simulated results of the optimised
controller and simulated results of another controller are
compared. Results indicate that the proposed controller is capable
of accurately and stably controlling the power flow in a
bidirectional IPT system.
I. INTRODUCTION
Inductive Power Transfer (IPT) systems are now recognised
as efficient and effective methods for transferring power
wirelessly. IPT systems are widely used in a number of
different areas ranging from low power biomedical implants to
high power material handling systems [1–5]. IPT technology
has gained popularity in these areas due to the high efficiencies
possible, typically 85 – 90 %, and its ability to operate in hostile
environments, being unaffected by dirt and moisture [6]. Due
to these benefits, the current focus of much of the research on
IPT technology is on developing IPT systems that can be used
to wirelessly charge Electric Vehicles (EVs) [3], [7]. More
recently, several bidirectional IPT systems have been proposed
and developed for applications in which power needs to be
transferred wirelessly in either direction, such as a wireless
Vehicle-to-Grid (V2G) systems [8–10].
The power handling capability of IPT systems is typically
improved through either series or parallel compensation. As a
consequence, these systems become high order resonant
networks, which are complex in nature and thus, difficult to
design and analyse. Especially, when considering the high
operating frequencies of IPT systems, which typically are in the
rage of 10 – 50 kHz [11–14]. Numerous unidirectional IPT
systems have been designed and analysed using relatively
simple steady-state models [9], [15], [16]. However, steady-
state models are incapable of providing an accurate insight into
the dynamic behaviour of the system and, as such, cannot be
regarded as a tool that facilitates proper controller synthesis,
without which the control of the system cannot be optimised.
Furthermore, the control of unidirectional IPT systems is
inherently simpler than the control of bidirectional IPT systems.
However, a dynamic model of a bidirectional IPT system has
been described, but to date this model has only been used in the
design of relatively simple controllers without much
consideration for the overall optimisation of the system [17].
To address this need, this paper proposes a decentralised
Proportional Integral Derivative (PID) controller that controls
the power flow in a bidirectional IPT system. The controller is
designed such that the closed loop transfer function of the
system and the controller match a reference transfer function.
The reference transfer function is obtained by determining the
required rise time, settling time and percentage overshoot.
Once the reference transfer function has been found, the steady-
state model is used to determine the transfer function of the
controller, thus giving the desired closed loop response. To
verify the performance of the controller, the response of the
optimised controller was compared to the response of a
controller designed using the Ziegler-Nichols tuning method.
Finally, the overall response and the applicability of the
controller is discussed.
This paper is organised as follows. Section III, briefly
describes the operation of a bidirectional IPT system. The
design of the optimised controller is presented in Section IV,
along with a brief description of the dynamic model. In Section
V, the response of the system is analysed and compared with
the response obtained from another controller and finally
Section VI presents the conclusions.
II. BIDIRECTIONAL IPT SYSTEMS
A typical bidirectional IPT system is shown in Fig. 1, which
M. J. Neath*, A. K. Swain*, U. K. Madawala*, D. J. Thrimawithana* and D. M. Vilathgamuwa+
*The Department of Electrical and Computer Engineering, The University of Auckland, New Zealand +Division of Power Engineering, School of Electrical & Electronic Engineering, Nanyang Technological University
Email: [email protected], [email protected], [email protected], [email protected] and
Controller Synthesis of a Bidirectional
Inductive Power Interface for Electric Vehicles
comprises a primary and a pick-up converter, resonant network
and controller. In a wireless V2G system, such as the one
described in [10], the primary converter is connected to a dc bus
fed from the grid by an active rectifier, which is schematically
represented as a dc source, to either supply or absorb power
from the pick-up. The output of the pick-up side converter is
connected to the EVs batteries, which again is schematically
represented as a dc supply, to either absorb or deliver power.
As analogous with unidirectional IPT systems, the primary
power converter is controlled to produce a constant high
frequency sinusoidal current in the track winding . A
pick-up coil is placed in the magnetic field produced by the
primary track current, and by using virtually identical
electronics as on the primary side of the system the pick-up can
deliver or source power to/from the primary converter.
When power is flowing in the forward direction, from the
primary to the pick-up, the primary converter operates as an
inverter and the pick-up operates as a controlled rectifier.
Conversely, in the reverse direction, the pick-up converter
operates as an inverter and the primary converter operates as a
controlled rectifier. Details on controlling the direction and
amount of power flow are given below.
Assume that the primary side converter of the bidirectional
IPT system, shown in Fig. 1, produces a reference sinusoidal
voltage at an angular frequency of , and the track
current, is held constant by the primary controller.
At steady state, the voltage induced in the pick-up coil
due to the track current can be given by
(1)
where M represents the magnetic coupling between the
primary and the pick-up coil inductances.
The pick-up may be operated either as a source or a sink by
the controller and, despite the mode of operation, the voltage
reflected back on to the track can be expressed by
(2)
If the inductor-capacitor-inductor (LCL) circuits on both the
primary and pick-up sides are tuned to the angular frequency ω,
and and then
(3)
Under these conditions, it can be shown that the input
current of the pick-up can be given by
(4)
Solving for using (4) and (1)
(5)
If the equivalent ac voltage of the voltage applied to the
input of the pick-up side resonant network is given by ,
then the output power of the pick-up can be given by
M
Pick-upcontroller
switching signals
Lsi
Lst
vsr Cst~
isi ist
Isin
vstvsi Vsin
switching signals
Lpi
Lpt
vprCpt ~
ipi ipt
Ipin
vptvpiVpin
Primarycontroller
Primary Pick-up
Sp1+
Sp1-
Sp2+
Sp2-
Ss2+
Ss2- Ss1-
Ss1+
Fig. 1 A typical bidirectional IPT system
| |
| | ( )
(6)
It is evident from (6) that the maximum power transfer takes
place when the phase angle θ is ± 90 degrees. A leading phase
angle constitutes power transfer from the pick-up to the
primary, while a lagging phase angle enables power transfer
from the primary to the pick-up. Thus, for any given primary
and pick-up voltages, both the amount and direction of power
flow between the primary and pick-up can be regulated by
controlling both the magnitude and relative phase angle of the
voltages generated by the converters [9].
A. Controller
A simplified diagram showing the operation of the pick-up
side controller is shown in Fig. 2. The input voltage and current
from the pick-up side converter are sampled and converted into
digital signals by the ADC. These signals are multiplied in the
micro-controller to give the power output of the converter. The
error between the output power and the reference power is
calculated, and this error is fed into a controller, typically a PI
or PID. The reference power level is set by the user through a
communication protocol. The output of the controller , is
used to adjust the duty cycle of the pick-up converter. The duty
cycle of the converter varies between ± 90 degrees, where – 90
degrees corresponds to the maximum power in the forward
direction and conversely, + 90 degrees corresponds to the
maximum power in the reverse direction. The output of the
controller is divided in half and each leg of the converter is
shifted by half of the duty cycle period. The left hand leg Ss1+ is
delayed/shifted to the right by αs/2, and the right hand leg Ss1+ is
advanced/shifted to the left, by αs/2. Each leg of the inverter
needs to be shifted like this to ensure that the fundamental
frequency of the voltage has a constant phase angle when
compared with .
Timer Count up
Mode synchronized
with primary
ControllerADC
Vsin
isin
Psin
Compare
Toggle
on match
Power
Reference
Communication
Protocol
Out Ss1+
Out Ss2+
To pick-up
converter
Pick-up
Output V
and I
User
input
αs
1/2Compare
Toggle
on match
αs/2+
+
+
-
Compare
value
Phase shifter
αs/2
Fig. 2 Simplified pick-up control strategy for a bidirectional IPT system
III. CONTROLLER DESIGN
A dynamic state-space model of a bidirectional IPT system
was derived and experimentally verified [17]. The model can
be expressed in the state-space form as
(7)
(8)
where A is the system matrix, B is the input matrix, C is the
output matrix, x is the state matrix, y is the output vector and u
is the input vector.
The inputs to the Multi-Input Multi-Output (MIMO) state-
space system model are the output voltages of the primary
converter, and pick-up converter, . The outputs of the
model are the primary track current, and the pick-up input
current, . Therefore the input and output vectors can be given by
[ ]
(9)
[ ] (10)
The Relative Gain Array (RGA) is a heuristic method to
predict the degree of coupling or interaction between the inputs
and outputs in a MIMO system [18]. The RGA matrix of the
bidirectional IPT system was calculated at 20 kHz and is given
by
[
] (11)
The RGA elements λ11 and λ22 at 20 kHz are close to 1. This
indicates that there exists a strong interaction between and
and between and . Therefore, the input current to the
pick-up side converter, can easily be controlled by . Similarly, the output should be controlled or paired with the
input . Since the other RGA elements λ12 and λ21 are
negative, this implies that the inputs and should not be
paired or controlled with and respectively. From the
RGA analysis it can be observed that a controller can be
designed using a decentralised approach to achieve the desired
performance. Further details about interpreting the RGA
elements can be found in [18].
A. Ziegler-Nichols PI Tuning Method
Initially, a PI controller was designed using the Ziegler-
Nichols method, which requires knowledge of the ultimate gain
and ultimate frequency of the system [19]. From the Bode plot
of the input and the output the gain and ultimate
period can be determined. From these values and the
Ziegler-Nichols tuning rules, the proportional gain and the
integral time can be calculated by
(12)
For the bidirectional IPT system considered here the values
of the gain parameters become and .
However, this gives unsatisfactory results, as the rules proposed
by Ziegler-Nichols only give a rough estimate of the controller
gains. The proportional gain was therefore decreased by 1.5
times to give and .
B. Optimised PID Controller Design
Results from the Ziegler-Nichols tuned controller indicate
that the controller is not optimally designed, as there are large
overshoots and oscillations around the desired output power.
Therefore, a more analytical method of determining the
controller gains needs to be used to improve the response of the
system.
The optimised controller is designed by matching the closed
loop response of the system and controller with a reference
transfer function. This reference transfer function can be
determined from the desired response of the system. A PID
controller was selected to control the power in the bidirectional
IPT system and the transfer function of a PID controller can be
given by
( ) [
] (13)
where kp is the proportional gain, Ti is the integral time and
Td is the derivative time.
The closed loop transfer function can be determined by
( ) ( ) ( )
(14)
where Gc(s) is the transfer function of the system relating the
pick-up’s input voltage to the input pick-up current, which can
be determined analytically from the dynamic state-space model.
An analytical method was chosen to determine the PID gains
based on the response of the system from the dynamic state-
space model. The PID tuning method has a target phase margin
of 60 degrees and automatically determines the PID gains to
ensure the best performance between response time and
stability margins. In designing the controller for a bidirectional
IPT system, the robustness is important as overshoots and
oscillations can cause instability in both sides of the IPT
system. This can be seen in the results for the Ziegler-Nichols
tuned PI controller. For the controller proposed in this paper a
response time of 700 μs was chosen and this gives the following
PID parameters kp = 0.0182, Ti = 27.17 μs and Td = 1.352 μs.
Results of the Ziegler-Nichols tuned PI controller and optimised
PID controller are given in section V.
IV. RESULTS
In order to determine the performance of the optimised
controller, the step response of the optimised controller was
compared with the step response of the original Ziegler-Nichols
PI controller. The two controllers were compared using
simulated results from PLECS a simulation package for
MATLAB. The parameters of both the simulated systems are
given in Table I. In each control technique, the phase shift
between and was set to 90 degrees and the duty cycle
was adjusted to control the power flowing between the two
sides of the system.
Fig. 3 shows the operating waveforms of the bidirectional
IPT system using the non-optimised PI controller, with a step
change in the reference output power occurring at 0 μs. At this
time the reference power level is changed from 0 to 1.5 kW in
the forward direction (from primary to pick-up). The primary
converter is controlled to produce a constant output waveform,
which produces a nearly constant sinusoidal current in the
track . The output of the pick-up side converter is
controlled to produce a varying duty cycle waveform that in
turn regulates the power flowing from the primary to the pick-
up. As evident from the controller output, and the output
power, there are significant oscillations and overshoots, and
these correspond to the oscillations seen in the pick-up’s input
current and primary track current. Oscillations in the primary
converter are not ideal for IPT systems especially when
multiple pick-ups are connected to the primary, and any change
in the primary will affect all the pick-ups.
Fig. 3 Primary track current, pick-up input current, pick-up controller output
and output power of the pick-up converter. With a + 1.5 kW step change in
output power results from the non-optimised controller.
The step response of the system with the same conditions as
in Fig. 3 is shown in Fig. 4; however, in Fig. 4 the system is
controlled using the optimised controller. Again, the primary
converter produces a constant sinusoidal track current and the
pick-up’s input voltage is controlled to regulate the power flow.
In this case, it is evident that only very small oscillations in the
power flow exist. This is further shown in the track current and
pick-up side input current being much steadier, without the
large spikes and oscillations.
Fig. 4 Primary track current, pick-up input current, pick-up controller output
and output power of the pick-up converter. With a + 1.5 kW step change in
output power results from the optimised controller.
Fig. 5 Primary track current, pick-up input current, pick-up controller output
and output power of the pick-up converter. With a - 1.5 kW step change in
output power results from the non-optimised controller.
In a bidirectional IPT system, the response of the system to
power flow in the reverse direction (from pick-up to primary) is
also important. Fig. 5 and 6 show the response of the system to
a step response from zero to 1.5 kW in the reverse direction,
with the non-optimised and optimised controller respectively.
From the plots, it can be seen that the non-optimised controller
produces large overshoots and oscillations when compared to
the optimised controller. It is also evident that the system
behaves differently in the forward and reverse directions;
therefore, any controller optimisation needs to consider the
operation in both the forward and reverse directions.
Fig. 6 Primary track current, pick-up input current, pick-up controller output
and output power of the pick-up converter. With a - 1.5 kW step change in
output power results from the optimised controller.
The output power and controller duty cycle are shown in Fig.
7, for 4 different power levels +2 kW, +1 kW, –1 kW and – 2
kW, from the non-optimised controller. As can be seen there
are large overshoots and oscillations in the power flow.
Especially with the power reference set to +2 kW, where the
system after 5 ms starts to become unstable. Conversely, Fig. 8
shows the operation of the optimised controller at the same
power levels as in Fig. 7. As can be seen there are no large
overshoots or oscillations and that the system does not become
unstable. It is also evident from both of the plots that the
bidirectional IPT system behaves differently depending on the
directional and magnitude of power transferred.
Fig. 7 Pick-up output power and controller output for various power
references results obtained from the non-optimised controller
Fig. 8 Pick-up output power and controller output for various power
references results obtained from the optimised controller
TABLE I
Parameters of the Prototype Bidirectional IPT System
Parameter Value
V. CONCLUSIONS
A control has been designed, which enables the power flow
in a bidirectional IPT system to be optimally controlled. A
dynamic state-space model of a bidirectional IPT system has
previously been developed and analysed. From this analysis,
the RGA matrix of the system could be determined. The RGA
matrix indicates that a decentralised controller can be used to
control the power flow. Therefore, a decentralised PID
controller was designed and optimised using the dynamic state-
space model. Simulated results of the controller’s operation are
compared with simulated results of a PI controller designed
using the Ziegler-Nichols tuning method. Results indicate that
the optimised controller preforms better with much lower
overshoots and oscillations when compared with the Ziegler-
Nichols controller, in both the forward and reverse directions.
Thus, the optimised PID controller is a much more suitable
controller for a wireless V2G IPT system when compared to the
Ziegler-Nichols PI controller.
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