IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 5, MAY 2010
1073
A Design Approach For Digital Controllers Using
Reconfigurable Network-Based Measurements
Rong Liu, Antonello Monti, Senior Member, IEEE, Ferdinanda Ponci, Senior Member, IEEE, and Anton H. C. Smith
Abstract—In this paper, the authors propose and analyze
a network-based control architecture for power-electronicsbuilding-block-based converters. The objective of the proposed approach is to distribute the control system to guarantee maximum
flexibility in the control of power distribution. In the proposed
control system, controller and controlled devices are connected
through the network, which affects the measurement and control
signals mostly due to delays. The main goal of this work is to
outline a design methodology for controllers operating with measurements coming from a network. The approach proposed here
assesses the robustness of the control system in the presence of delay and aims to design an optimal controller for robustness against
network delays. This methodology is based on uncertainty analysis
and assumes that the delays are the main element of uncertainty
in the system. The theoretical foundations of this approach are
discussed, together with the simulation and implementation of a
physical laboratory prototype.
Index Terms—Induction machines, networks, power systems
measurements, robustness, uncertainty.
I. I NTRODUCTION
R
ECENTY, the power electronics building block (PEBB)
concept has widely been accepted, and commercial PEBB
devices have been implemented in many applications and fields.
A very important application is given by the interface converters
used in power distribution systems. One example of such power
distribution system is the future All Electrical Ship [1].
To dynamically manage such power system, a flexible, reliable, and integrated control system needs to be built. In ship
power system applications, it is extremely critical to design the
control system in such a way as to ensure safe operating modes
both under normal or emergency conditions (e.g., partially
damaged system). To achieve this goal, the PEBBs play an
important role by offering a high degree of flexibility in the
management of the power flows.
In this paper, the authors propose and analyze a networkbased control architecture for PEBB devices. The objective of
this approach to PEBB control is to create a distributed control
system that is capable of guaranteeing maximum flexibility in
Manuscript received June 30, 2009; revised August 14, 2009. Current version
published April 7, 2010. This work was supported by the U.S. Office of Naval
Research under Grant N00014-07-1-0603. The Associate Editor coordinating
the review process for this paper was Dr. Subhas Mukhopadhyay.
R. Liu and A. H. C. Smith are with the Department of Electrical Engineering,
University of South Carolina, Columbia, SC 29208 USA.
A. Monti and F. Ponci are with the Institute for Automation of
Complex Power Systems, E.ON Energy Research Center, RWTH Aachen
University, Aachen, NRW 52062, Germany (e-mail: antonello.monti@eonerc.
rwth-aachen.de; fponci@eonerc.rwth-aachen.de).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIM.2010.2040906
the control of a power distribution system. In particular, the
networked controllers are seen as distributed control resources
that can be allocated, at any given time, for the control of
a specific piece of hardware (PEBB converters in particular)
and for specific functionalities (e.g., feeding loads, charging
energy storages, and correcting power quality). In this architecture, controller and controlled device communicate through
the network, which affects the measurement and control signals
mostly with stochastic delays.
The coordination and reconfiguration of controller deployment are done through an agent-based system at system level.
Such intelligent system is able to reconfigure the control architecture assigning controllers and functionalities to the PEBBs,
depending on the overall mission of the system and on the
specific occurrence. The analysis of the agent system is not
the focus of this work, but the underlying approach has been
presented in [2]. The main goal of the work discussed here is
to outline a design methodology for controllers operating with
measurements remotely taken and transmitted over the network.
An approach is proposed to assess the robustness of the control
system in the presence of delays and to design for robustness to
network delay. This approach is based on uncertainty analysis,
assuming that delays are the main element of uncertainty in
the system. The theoretical foundations of this approach are
discussed, together with the simulation and implementation of
a physical laboratory prototype.
Preliminary results of this study have been presented in
[3]. In this paper, the work is extended, providing a design
methodology and experimental validation. In particular, the
field-oriented control on an induction machine is adopted as
a case study to demonstrate the proposed design procedure.
The speed-loop control is realized by a network-based optimal
proportional–integral (PI) controller. The design is performed
by treating the delays as main uncertainties. Polynomial Chaos
Theory (PCT) is adopted as theoretical basis for design of the
optimal controller and the assessment of its robustness.
II. N ETWORK -BASED C ONTROL
The idea of performing closed-loop control through the
network is not new [3]. Nonetheless, applications in the power
electronics domain are still limited. An overview of the topic is
provided in [4]. Predictive controllers are often used to address
the issue of network delay; in particular, [5] focuses on the case
of delay on the feedback line, [6] on the case of forward line
delay, and [7] on the case where the delay is directly assessed.
Huang and Nguang [8] proposed a solution of the stabilization problem for state-feedback uncertain networked control
0018-9456/$26.00 © 2010 IEEE
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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 5, MAY 2010
Fig. 1. Proposed architecture for network-based control.
systems with random communication time delays. An approach
with neural network delay compensator and fuzzy PID controller is presented in [9], together with experimental results. An
implementation specifically for power electronics applications
is presented in [10] for stepping motors, although in an open
loop.
The motivations for a reconfigurable network solution for
the control of power electronics systems have been provided
in [11], where the architecture schematically shown in Fig. 1 is
introduced and discussed. The main goal is to achieve a higher
system reconfigurability leveraging on the feature that each
controller can be allocated to any of the hardware devices at any
time. This advantage is partially counterbalanced by the loss of
bandwidth capability due to delays introduced by the network
in the feedback measurement from the device to the controller
and in the control signal from the controller to the device. The
decision on the controllers’ deployment and the control strategy
for mission consistency is taken at the upper level by a multiagent system.
The main challenges of designing the network-based controller addressed here are stability and robustness under the
following effects due to the network:
1) random delay in the feedback loop carrying the measurement from the field device to the controller;
2) random delay in the forward loop taking the control signal
from the controller to the field device;
3) variations in the rate of execution of the controller that
may be not constant over time but may be affected by the
delay action.
In literature, the majority of research focuses on the design
of PI controllers, optimized for this new scenario. The typical
solution adopted for this type of controllers are gain scheduling
[12], [13]. A discussion on the issues related to multirate
operation can be found in [14].
In this paper, the authors propose to model the effect of
network delay as uncertainty by adopting a PC expansion of the
model of the system [15], [16]. A preliminary application of this
modeling approach to the control of power electronics systems
is presented in [17], whereas a more advanced control approach
is discussed in [18]. Here, the PC approach is extended to
different control structures, and the mathematical conditions for
robust stability are discussed.
Fig. 2.
Example of network-based control.
The proposed procedure can easily be implemented with
standard mathematical tools such as Matlab and Maple, thus
making the process applicable to real systems with reasonable
effort.
III. M ATHEMATICAL F ORMULATION OF THE P ROBLEM
AND D ESIGN P ROCEDURE
The linear system under analysis is summarized in block
diagram form in Fig. 2.
The system in Fig. 2 can be modeled with a set of state
equations. If we consider the network delay as an uncertain
parameter with known probability density function (pdf), the
model becomes a stochastic process. A truncated PC expansion
can be applied to all the state equations, thus resulting in a
deterministic model with an extended set of states. These new
states are the coefficients of the truncated PC expansion of the
original state variables. This transformation process can easily
be automated with the help of Maple scripts [19]. Once the
PC model is synthesized, the control design can be performed
by solving a constrained optimization problem, where two
conditions hold.
1) The cost function is designed to significantly penalize the
uncertainty of the state variables, which, in mathematical terms, implies penalizing the coefficients of the PC
expansion of the state variables representing other values
than expected.
2) Constraints are added to enforce the control solution to be
compliant with a specific control architecture (e.g., state
space feedback or PI).
Different optimization functions can be adopted to perform
the design. In the following, an example of application is
proposed where an integral square error (ISE) optimal [20]
method is adopted to design a PI controller.
The solution of the minimization problem yields the parameters of the controller, whose architecture is implicitly defined as
the state equations of the closed loop.
IV. S TABILITY A NALYSIS
Once the optimization problem is solved and the controller is
fully defined, it is then important to verify that the resulting control system is stable for any possible value of delay, within the
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LIU et al.: A DESIGN APPROACH FOR DIGITAL CONTROLLERS USING RECONFIGURABLE NETWORK-BASED MEASUREMENTS
Fig. 3.
Block diagram of the system.
Fig. 4.
Probability distribution of one-way network delay.
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Fig. 5. Flowchart of PC expansion.
TABLE I
PARAMETERS U SED FOR THE A NALYTICAL T EST (ROBUSTLY S TABLE )
range that is assumed in the design. The design objective is, in
fact, to achieve a robust controller without the online adaptation
of the parameters. This approach is similar to other methods for
robust control design synthesis, as in [19]. The uniqueness of
this approach, however, lies with the accounting of the whole
pdf of the uncertain delay parameter. This approach is expected
to yield a less conservative design with a computable risk factor
associated to it.
The analysis of robustness is based on the analysis of convergence of the PC series expansion of the states. If the series
actually converges, then the moments of the pdf of the state
variables are finite. This is a necessary condition to guarantee the stability according to a bounded-input–bounded-output
(BIBO) stability definition.
The proof of convergence can be obtained from the asymptotic convergence of the error of the expected value of the state
variables, depending on the order of truncation. In other words,
the exponential convergence to zero of the error of the expected
value obtained from successive incrementally higher orders
of truncation guarantees that the pdfs of the state variables
converge to the correct one and that the moments are finite.
More formally, the procedure for robust stability verification
can be described as in the following. Let us consider a linear
Fig. 6. Mean speed calculated using PCT for different PCT orders.
system in the form:
ẋ = Ax + Bu.
(1)
Notice that matrix A in this case contains parameters of the
system, as well as the delays.
Let us suppose that the system is affected by parametric
uncertainty; in particular, the delay parameter is uncertain. This
implies that a set of elements of matrix A is uncertain, with
known pdf. As a consequence, the generic coefficient aij of
matrix A can be expressed in terms of PC expansion [15], [16],
i.e., as a function of a vector of random variables ξ
aij =
P
akij Φk (ξ).
(2)
k=0
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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 5, MAY 2010
Fig. 7. Sytem is robustly stable, with variance = 0.0024 s. (a) Error norm. (b) Log of error norm.
Let us also suppose that all these system uncertainties are
defined over a closed and limited range. For example, we could
assume that all the parameters have a uniform distribution,
a Gaussian distribution, or other distributions. In any case,
the analysis is limited to a finite subset of the support of the
distribution with a predefined coverage factor.
For what concerns the definition of stability, the BIBO
definition is adopted, implying that a stable system responds
to a bounded input signal with a bounded output signal. If
the system is stable for every possible value of the uncertain
parameters, the whole set of possible transient responses is
composed of bounded functions. In addition, if the system is
stable and the transients are bounded, then all the moments of
the pdf of a generic variable of the system are also bounded.
Therefore, it can be stated that the PC expansion of the solution
exponentially converges to the exact solution [16].
Let us now consider the expansion of system (1) with a PC
expansion truncated at an order equal to k and consider the
application of a bounded input for the duration of a generic
interval 0–t. The coefficients of the expansion and, in particular, the zeroth-order coefficients of all the state variables are
functions of time, and their 2-norm can be computed. Let us
call x0k the zeroth-order coefficient of state variable x when
the polynomial expansion is truncated to order k. The 2-norm
is defined as
t
x0k =
2
x20k (τ ) dτ.
(3)
0
The value of the zeroth-order coefficient also depends on
order k of the expansion. Thus, there is a difference between
the expected value at orders k and k + 1 of the expansion, and
this represents the error due to the truncation of the expansion
at order k due to a one-order difference.
Naming xi0k , which is the zeroth-order coefficient of the ith
state variable expanded to order k, we can then introduce the
norm of the state of the system X0k 2 in the form
X0k 2 =
n
xi0k 2 .
(4)
1=1
This value is the sum of the squares of all the norms of the
state variables of the system.
TABLE II
PARAMETERS U SED FOR THE A NALYTICAL T EST
(N OT ROBUSTLY S TABLE )
Fig. 8. Mean speed calculated using PCT for different PCT orders, with
max delay = 0.190 s.
If the system is stable, the norm X0k converges to its
correct value. As a result, the following condition holds:
2 lim X0k 2 − X0(k+1) = 0.
(5)
k→∞
The same should occur for all the coefficients and, for
example, for the first-order term
2 lim X1k 2 − X1(k+1) = 0.
(6)
k→∞
As a result, for a system expanded to the first order, if (5)
and (6) hold, the necessary condition for robust stability can be
inferred.
V. E XPERIMENTAL ACTIVITY
Let us now apply the approach to the control system of
an induction machine. The control method of choice for the
induction machine is field-oriented control [21], and its currentloop control runs locally (PEBB’s site) without the effect of
network delay. The speed-loop control runs on a remote PC, and
the values it exchanges with the controlled system are affected
by network delays. The control structure is shown in Fig. 3.
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LIU et al.: A DESIGN APPROACH FOR DIGITAL CONTROLLERS USING RECONFIGURABLE NETWORK-BASED MEASUREMENTS
Fig. 9.
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System is not robustly stable, with variance = 0.0028 s. (a) Error of norm. (b) Log of error norm.
In this section, the stochastic characteristic of the network delay is studied first. Second, a PC expansion model considering
the two uncertainties is obtained. Third, an optimal PI controller
is designed to minimize the error between reference and the
system’s output. Fourth, stability analysis based the proposed
method is verified. Fifth, the simulation result in Simulink is
presented. Finally, the experiment results are presented. The
same designed PI controller remotely and locally runs, and their
control performances are compared.
Following this design procedure, one can design a networkbased controller for other devices, such as voltage-loop control
of dc–dc converters, as far as the required control bandwidth
falls in limited range. This design procedure also provides an
analytical way to design a robust controller for the systems with
multi-uncertainties.
A. Delay Study
To get proper PC expansion model, the stochastic characteristic of network delay is studied first. Two PCs (A and B) use a
Transmission Control Protocol (TCP)/Internet Protocol socket
to set up the communication. For every test loop, a message
called M is sent out by B to A, whereas A returns the same M
back to B immediately after receiving it. When B gets M back,
it records the time delay in the loop. Basically, A functions as
an echo server. The time costs for each way (from A to B and
from B to A) are assumed to be equal. The cable length between
the two PC is 20 ft, and a switch is used to bridge the PCs
together. The delay measured in this test includes the transmission delay on cable and switch and the time cost for software
execution. Test results amounting to 4900 are recorded, and
the mean value and variance of one-way delays are 0.0078
and 0.000822 s. The maximum and minimum delays are 0.03
and 0.0011 s, respectively. The probability distribution of
4900 tests, in Fig. 4, can be approximated with a Gaussian
distribution with limited support.
The parameters used for the PC expansion are reported
in Table I. For the two network delays, we report the mean
value (coefficient 0) and the variance of the uncertainty
(coefficient 1).
B. PC Expansion
Following the results of the previous analysis, both delays
are represented with an uncertain parameter having Gaussian
distribution. The PC form of the system is obtained, starting
from a fourth-order representation with two uncertain parameters. The state-space matrices (A, B, C, and D) of the fourthorder model are first obtained: starting from these matrices, the
first-order PC expansion matrices (Apct , Bpct , Cpct , and Dpct )
are evaluated. The dimension of Apct results is 12 × 12. The
flowchart of the PC expansion procedure is shown in Fig. 5.
The complete Maple script cannot be reported in this paper for
lack of space, but it can be obtained by request to the authors of
this paper.
C. Optimal Control Design
In this experiment, an ISE optimal [20] method is adopted
to design an optimal PI controller. The control target is to
minimize the error between the reference r(t) and the system
output y (Fig. 3).
In (7), y comes from the PC first-order expansion model in
(8). In (8), Gpct stands for the closed-loop transfer function of
the PC first-order expansion model
∞
|y(t) − r(t)|2 dt
ISEmin = min
0
= min
1
2π
∞
∞
|Y (jω) − R(jω)|2 dω
−∞
|y(t) − r(t)|2 dt
ISEmin = min
(7)
0
Gpct = Cpct (sI − Apct )Bpct + Dpct
Y (s) = Gpct · R(s)
Gpct = Cpct (sI − Apct )Bpct + Dpct
.amp(8)
Y (s) = Gpct · R(s)
The Kp and Ki , which minimize (7), are 0.34 and 0.01,
respectively. ISEmin is 0.1553.
D. Stability Analysis
The parameters used for the simulation test are reported in
Table I, with the Kp and Ki obtained in previous section. Under
these conditions, the system’s step response is shown in Fig. 6.
The error norm and the log of the error norm series, as shown
in Fig. 7, quickly converge toward zero, thus indicating that the
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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 5, MAY 2010
Fig. 10. Whole system schematic in Simulink.
Fig. 11. Control schematic.
system is robust stable. In this case, the PC expansion of the
whole model is up to the fourth order (Table II).
Increasing the uncertainty’s variance up to 2.8 ms2 , the system becomes unstable, and the zeroth order does not converge.
In this situation, the PCT expansion model does not converge,
and then, the modes of the pdf of the variables are unbounded.
Therefore, as expected, the error series no longer converges, as
shown in Figs. 8 and 9. In both cases, the PC expansion of the
whole model is up to the fourth order.
E. Simulation in Matlab
The system is first tested in the Simulink environment. In
this simulation, the induction motor, power supply, and PEBB
are represented by the corresponding models in Simulink’s
Simpower System toolbox, and the nonlinear characteristics
of these components are included. The scheme of the whole
system is shown in Fig. 10. Fig. 11 shows the control scheme,
including current-loop control, speed-loop control, and network
delays. The simulation of the step response is shown in Fig. 12.
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LIU et al.: A DESIGN APPROACH FOR DIGITAL CONTROLLERS USING RECONFIGURABLE NETWORK-BASED MEASUREMENTS
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Fig. 14. Experiment setup.
Fig. 12. Step response.
Fig. 15. Step response of motor speed when ref = 30 rad/s and 40 rad/s (scale
factors of the Y - and X-axis: 10 rad/s/V and 2 s/scale).
Fig. 13. Experiment structure with the network delays involved.
F. Experimental Verification
The network-based control system has been built and implemented in our laboratory with customized PEBB platforms.
The experiment structure and setup are shown in Figs. 13
and 14. The PEBB is controlled by a dSpace [22] platform
model CP1104. A Virtual Test Bed (VTB) [23] schematic,
which is called the VTB server and runs on a local PC, is
capable of exchanging data with the CP1104 through Matlab
workspace at runtime. The PI controller for the speed loop runs
in another schematic called VTB client at remote PC. These
two schematics communicate with each other through the TCP
protocol. The communication with the PCs is achieved through
an Ethernet network, allowing for the insertion of this device in
the PC-based network of controllers.
Fig. 15 shows the motor’s speed step response when the
speed reference is 30 and 40 rad/s in sequence. The steady
state of the motor speed is shown in Fig. 16. To show the
effects introduced by the network delay, a local control test
without network communications involved is implemented, and
experiment results are shown in Figs. 17 and 18.
From the two test results, we can see that the control bandwidth reduction introduced by the network implementation is
Fig. 16. Steady-state status of motor speed in remote control mode (scale
factors of the Y - and X-axis: 10 rad/s/V and 2 s/scale).
not evident. From the steady-state results, it is clear that the
main effect introduced by network delays in feedback and
forward loop is a small but contained oscillation. As expected,
while the delays inserted are in the range adopted for the design,
the system is designed to be robust and performs a stable
behavior.
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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 5, MAY 2010
Fig. 17. Experiment result when the PI controller runs in Dspace locally
without network delays involved (scale factors of Y - and X-axis: 10 rad/s/V
and 2 s/scale).
Fig. 18. Steady-state status of motor speed (scale factors of Y - and X-axis:
10 rad/s/V and 2 s/scale).
VI. C ONCLUSION
This paper has proposed a network-based control architecture for PEBB devices. A critical aspect in such a system is
the management of a measurement affected by stochastic delay.
The authors have outlined a design methodology for controllers
operating with this type of measurements. In particular, an
approach based on uncertainty analysis was proposed. The
theoretical foundations of this approach have been discussed,
together with the implementation and results of a physical
laboratory prototype. Following this design procedure, one can
design a network-based controller for other devices. This design
procedure also provides an analytical way to design a robust
controller for the systems with multi-uncertainties.
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Rong Liu received the B.E. degree in electrical
engineering from Southwest Jiaotong University,
Chengdu, China, in 1997 and the M.E. degree in
electrical engineering, in 2006, from the University
of South Carolina, Columbia, where she is currently working toward the Ph.D. degree in electrical engineering with the Department of Electrical
Engineering.
Her research interests are electrical drive control
design, power electronics, and power systems.
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LIU et al.: A DESIGN APPROACH FOR DIGITAL CONTROLLERS USING RECONFIGURABLE NETWORK-BASED MEASUREMENTS
Antonello Monti (M’94–SM’02) received the M.S.
and Ph.D. degrees in electrical engineering from
Politecnico di Milano, Milano, Italy, in 1989 and
1994, respectively.
From 1990 to 1994, he was with the research
laboratory of Ansaldo Industria of Milan, where he
was responsible for the design of the digital control
of a large power cycloconverter drive. In 1995, he
joined the Department of Electrical Engineering, Politecnico di Milano, as an Assistant Professor. From
2000 to 2008, he was an Associate Professor and
then a Full Professor with the Department of Electrical Engineering, University
of South Carolina, Columbia. He is currently the Director of the Institute
for Automation of Complex Power Systems, E.ON Energy Research Center,
RWTH Aachen University, Aachen, Germany.
1081
Anton H. C. Smith received the B.S. degree in electrical engineering and the M.E., and Ph.D. degrees
from the University of South Carolina, Columbia, in
2002, 2004, and 2008, respectively.
He is currently a Research Assistant Professor
with the Department of Electrical Engineering, University of South Carolina. His research interests are
embedded control and robotics.
Ferdinanda Ponci (SM’08) received the M.S. and
Ph.D. degrees in electrical engineering from Politecnico di Milano, Milano, Italy, in 1998 and 2002,
respectively.
In 2003, she joined the Department of Electrical Engineering, University of South Carolina,
Columbia, as an Assistant Professor with the Power
and Energy Research Group, and was promoted to
Associate Professor in December 2008. She is currently with the Institute for Automation of Complex Power Systems, E.ON Research Center, RWTH
Aachen University, Aachen, Germany. Her research interests include methods
for uncertainty representation and propagation, and multiagent systems for
control and monitoring of power electronics systems.
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