Download Dissipativity-based adaptive and robust control of UPS

334
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 2, APRIL 2001
Dissipativity-Based Adaptive and
Robust Control of UPS
Paolo Mattavelli, Associate Member, IEEE, Gerardo Escobar, Member, IEEE, and
Aleksandar M. Stanković, Member, IEEE
Abstract—In this paper, we investigate the output voltage control for a three-phase uninterruptible power supply (UPS) using
controllers based on ideas of dissipativity. To provide balanced
sinusoidal output voltages, even in the presence of nonlinear and
unbalanced loads, we first derive a dissipativity-based controller
using a frequency-domain representation of system dynamics.
Adaptive refinements have been added to the controller to cope
with parametric uncertainties. Second, based on the first adaptive
controller, we propose a controller which turns out to have the
proportional-plus-integral-type structure on rotating-frame
variables, but with a special design of gain matrices. A sufficient
condition in terms of the design parameters is presented for this
controller that guarantees stability of the desired equilibrium and
robustness against parameter uncertainties. Finally, simulation
and experimental results on a three-phase prototype show effectiveness and advantages of the proposed approach.
Index Terms—Adaptive control, dissipative systems, nonlinear
systems, power supplies, uninterruptible power systems.
I. INTRODUCTION
T
HE most important performance specifications for uninterruptible power supply (UPS) systems include voltage
regulation, total harmonic distortion (THD), output impedance,
transient response, and operation with nonlinear and distorted
loads. If we add to all these requirements the fact that UPS systems, usually affected by parameter uncertainties, are expected
to operate under unbalanced conditions, then the problem
of designing an appropriate control strategy that fulfills all
these goals is clearly challenging. The growing importance
of UPS systems has motivated a flourishing development
of different control schemes found in the literature [1], [2],
[4]–[9], [13]–[15]. Some controllers rely on a single voltage
loop using proportional-plus-integral (PI), deadbeat [5], or
sliding-mode controllers as compensators (see [11], [8], and
[14] for a brief survey on conventional control techniques for a
UPS), others propose a nested connection of output voltage and
inductor current control loops, usually two PIs or possibly a PI
plus a high-gain controller like a sliding-mode controller [2],
Manuscript received June 15, 2000; revised November 15, 2000. Abstract
published on the Internet December 18, 2000.
P. Mattavelli is with the Department of Electrical Engineering, University of
Padova, 35131 Padova, Italy (e-mail: [email protected]).
G. Escobar is with the Department of Electrical and Computer Engineering,
Northeastern University, Boston, MA 02115 USA, on leave from the Engineering Faculty, National University of Mexico, Mexico City, Mexico (e-mail:
[email protected]).
A. M. Stanković is with the Department of Electrical and Computer
Engineering, Northeastern University, Boston, MA 02115 USA (e-mail:
[email protected]).
Publisher Item Identifier S 0278-0046(01)02632-6.
[9]. Although these techniques are able to ensure good transient
response, the distortion on the output voltage due to nonlinear
loads is typically not compensated completely.
To partially overcome these limitations, other nonconventional approaches have emerged, like repetitive control which
has the capability to compensate for periodic disturbances [7],
[4], [15]. To complete the design and to ensure acceptable
transient response, this technique has still to be combined or
embedded with another control design approach (e.g., model
reference adaptive control or pole placement), thus yielding
controllers that are complicated for implementation, even in
the single-phase case.
To provide an alternative solution for the reduction of unbalance and distortion in UPS applications, this paper proposes
a family of controllers designed following the dissipativity approach using rotating-frame quantities, which we also refer to as
dynamic phasors. The frequency-domain framework offers the
advantage that control loops involve dc quantities and, thus, the
bandwidth requirements on the controllers are less demanding.
Using dissipativity ideas, we first derive an adaptive controller
that guarantees stability of the whole system under parameter
uncertainties. The controller realizes a partial inversion of the
system, and adds the required damping. The resulting system
contains a disturbance term due to the uncertainty on the system
parameters that is tackled via adaptation. Due to the complexity
of this controller, its implementation may be quite involved.
Nevertheless, it is shown that, after some simplifications, this
controller is downward compatible with the PI control with rotating-frame variables.
Motivated by the form of the first controller, a second
controller that preserves the same structure is proposed. In
the second case, we fix the parameter estimates to certain
values, thus avoiding the adaptation. The resulting controller
is much easier to implement because it turns out to be a linear
control with constant coefficients (LTI). This, in turn, can be
translated into a controller defined in terms of the fixed frame
variables according to [16]. The closed-loop system with this
second controller, denoted here as the robust controller, turns
out to be LTI. Thus, stability tests may be performed with
traditional tools. We have preferred to use here an extension of
the Routh–Hurwitz criterion [3] to simplify the proof, and to
obtain more transparent analytical conditions.
For implementation both our controllers require measurements of inductor currents; however, in the case of second
controller, the inductor currents are used just to increase the
natural damping of the system. Indeed, inductor current sensing
could be avoided at the expense of a transient performance
0278–0046/01$10.00 © 2001 IEEE
MATTAVELLI et al.: DISSIPATIVITY-BASED ADAPTIVE AND ROBUST CONTROL OF UPS
Fig. 1. UPS inverter system.
deterioration. Moreover, the value of the dc-source voltage
(if not measured) might be substituted by a good constant
approximation without affecting the stability conclusions.
Finally, the proposed control scheme has been implemented
using a fixed-point single-chip digital signal processor (DSP)
(ADMC401 by Analog Devices). Both simulation and experimental results for the proposed robust controller are presented,
and compared with those of the conventional multiloop PI,
displaying the advantages of our solution.
II. SYSTEM CONFIGURATION AND PROBLEM FORMULATION
The basic setup for a three-phase UPS application discussed
in this paper is shown in Fig. 1. The system dynamics is described by the following model:
335
varying,
is the set of harmonic indexes
a skew symmetric matrix
under consideration, and
.
of the form
The design objective is to track a balanced voltage
coordinates is expressed as
reference which in
, a purely sinusoidal vector signal,
i.e., containing only fundamental component, in spite of the
presence of harmonic disturbances. The control objective
thus implicitly includes both problems, reference tracking in
the fundamental harmonic and disturbance attenuation of the
output voltage response to higher harmonics mainly introduced
by the load current.
In the developments that follow, we will use both the complex
number and the matrix ; the former is used when dealing
with complex variables, specially useful in the analysis, while
the second is used when these complex variables are explicitly
split in real and imaginary quantities, mainly used in the control
design.
A. Dynamic Phasor Model
We find it very convenient to convert the model expressed
in time-domain signals into a frequency-domain representation,
which is often denoted as dynamic phasor description [12]. Fol; then
lowing the standard notation, we introduce
. Then, a
the square of equals its complex conjugate
time-domain waveform can be written as
(4)
(1)
(2)
the vector
where is the vector of currents in the inductors,
of voltages in the capacitors, and is the switching control
vector, which for the purposes of control design is considered
as a continuous vector, i.e., we consider only its average value.
For this reason, we do not explicitly write the star-point voltage
as the average voltage applied by
in (1) since we consider
the inverter respect to the load star point. Vectors , , and
are three phase quantities of the form
.
The inductance , the capacitance , the parasitic resistance ,
and (possibly) the source voltage are all assumed unknown
constants, or slowly varying, except for possible step changes
following structural changes in the system. The load current
is an unbalanced periodic signal which contains higher
harmonics of the fundamental frequency represented by , that
coordinates1 ( ) as
is, we can represent in
and we denote the square transformation matrix with . It can
is unitary, as
, where
debe checked that
notes complex conjugate transpose (Hermitian). As commonly
encountered in transforms, scaling factors other than
are possible in the definition of matrix , but they require adjustments in the inverse transform. The coefficients in (4) are
(5)
, negative
Equation (5) defines dynamical positive
symmetric components at frequency
and zero-sequence
as
,
,
(3)
,
are the th harmonic coefficients
where vectors
for the positive and negative sequence representation of the current load which are considered unknown constants, or slowly
1We refer to here as coordinates the ones obtained from the application
of a simple
P X , with
p Park’s (or 3 to 2) transformation of the form x
P (2= 3)[
], that is, x
are the coordinates referred to a
fixed frame.
=
=
where
ation:
(6)
is defined at time by the following averaging oper-
(7)
336
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 2, APRIL 2001
We found it more convenient to work with real vectors in the
place of complex numbers for the purpose of control design.
Thus, in our derivations, we split all signals into real and imaginary parts, and consider them as real vectors.
Using (6) to system (1) and (2), we obtain a set of dynamic
phasor models (each phasor being represented as a real vector)
in the references), and keeping in mind that the final control for
and sequences will be the addition of all different controllers
for each in the respective and sequences.
Let us write the system (8) and (9) in incremental terms as
(11)
(8)
(12)
(9)
is a block diagonal matrix of skew
where
. Recall that every vector
,
symmetric matrices
, and
has four components, for instance,
, with
stems for the
real and imaginary parts, respectively.
We are considering the case where there is no connection to
a fourth conductor; thus, no zero-sequence (homopolar) symmetric components appear in the model. If a four-conductor
topology is considered, either by splitting the dc-link capacitor
or by considering a four-leg inverter [1], similar results can be
obtained following the design ideas proposed here.
The models are parameterized by the harmonic index
. Using these models as a basis for design, a
different control component is designed, independently for
each harmonic. The total control action is then obtained as a
sum over the set of significant harmonics. Note also that the
transformation shown above includes, roughly speaking, a
, so the corresponding model is denoted as
rotation by
a dq–PN model, with the inherent advantages of dealing with
variables converging toward constant references.
and
, and we have used
where
and
(10) in (12) and defined
.
In the case of known parameters, the following controller stabilizes the system in the desired equilibrium point:
where
and
are design parameters
.
and
In the case of uncertain parameters, we propose the following
adaptive controller which is motivated from the structure of the
controller above
(13)
stems for the parameter estimate.
where
The closed-loop system becomes
(14)
B. Control Objective in Terms of Phasor (dq–PN) Variables
After the above transformation, the reference2 for the output
becomes
for
capacitor voltage
and
for
.
The equilibrium point of the overall system (8) and (9) by
is given by
forcing
and we have defined
where
We will consider the following adaptive laws:
.
(15)
(16)
(10)
Note that, in order to perform the voltage regulation, the inductor current must provide the harmonic content of the load
current.
and
are design parameters.
where
and
. These adaptive laws make
Notice that
negative semidefinite the time derivative of the energy storage
function defined as
III. CONTROLLER DESIGN
A. Adaptive Strategy
to reduce
In what follows, we will omit the subscripts
the notational clutter. Moreover, we will split the dynamics in
positive and negative sequence and we will consider only one of
them for design. This is possible because both dynamics have
identical structure/parameters and both are completely decoupled. Thus, we will obtain only one controller indexed by a given
and valid for either and (with the only difference evidenced
2Here, and in what follows, ( 1 ) will be used to denote references and ( 1 )
for the equilibria.
where represents the module of a vector, thus,
.
. Then, invoking stanAs a first conclusion, we have that
dard LaSalle’s theorem arguments [10] we can prove stability
and convergence of the estimates. For this, the term
in (14) is very important, as it prevents
from having an equilibrium other than zero which prevents (15) from growing indefinitely. Notice that, in the controller above, an estimator for
, needed in (13) and
, has been automatically obtained.
MATTAVELLI et al.: DISSIPATIVITY-BASED ADAPTIVE AND ROBUST CONTROL OF UPS
B. Simplifications of the Adaptive Controller
Notice that the control signal (13) unfortunately depends on
parameter ; this parameter may be also updated with an adaptive law, but convergence in this case is not guaranteed and,
moreover, the complexity of the control is increased considerably. Instead, we will show, using a plausible approximation,
that the uncertainty in this parameter can be absorbed by the integral action introduced by the adaptation of .
is estimated in (15) very slowly compared
Assume that
with the dynamics of ; then, in (13) and (16), we can consider
as almost constant. The controller (13) plus (15) and
(16) can be approximated then by
337
The closed-loop system with the controller above yields the
following LTI dynamics:
where matrix
is given by
(17)
and the equilibrium point is
(18)
(19)
where we have defined
which is considered a constant matrix;
, with
;
a
the nominal value of .
constant vector and
We observe that the constant can be absorbed by the control
coefficients, and the effect of the uncertainty on this parameter
(reduced to a simple constant offset) is absorbed by the integral
on the right-hand side of (17)
term. Indeed, the term
can also be absorbed, but we prefer to keep it in order to reduce
the control effort in the integral term. Hence, as a conclusion,
to implement the controller (13), we can replace with an a
priori known value .
C. Robust Controller
The adaptive controller (13), (15), and (16) can be significantly simplified if estimation of ( and ) in (16) is avoided.
For this, assume that an upper bound on and a lower bound
and , such that
on are known, i.e., there exist
and
. Thus, instead of using the estimate ( and )
in (13), we propose to use some predefined values for them,
and . Note that
and are considered to be design parameters, and not necessarily estimates of and , respectively. As
before, a discussion will be presented to show the robustness of
the controller with respect to uncertainties in . Thus, according
to (13), we propose
Moreover, a sufficient condition to guarantee asymptotic stability of the equilibrium point can be stated as follows
(21)
and
should be chosen. To prove this
which tells us how
statement, we need to compute the characteristic polynomial of
the linear system above. The system order has to be reduced
to make this symbolic calculation tractable, so we interpret the
and we
matrix as analog of the complex number
consider all design matrices as scalars. The resulting polynomial
has complex coefficients, so the generalized Routh–Hurwitz algorithm [3] is needed to show that all the roots belong to the
open left-half plane of the complex plane.
is large enough, this condition is reduced
Notice that if
. We also observe from this analysis that gain
to
helps to relax condition (21).
D. Simplifications of the Robust Controller
Similarly to the previous discussion in Section III-B, we can
show that the parameter in the control (20) can be absorbed
by the coefficients. In this case, we can write the control (20) as
follows:
(22)
where
is still computed as in (15). Indeed, using (15), this
controller can be expressed as
(20)
is the nominal value of ,
where
and
.
defined
Condition (21) in this case is transformed to
and we have
which (with the new notation) coincides with the previous condition. Hence, control (22) can be used instead of (20) pre-
338
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 2, APRIL 2001
serving the same properties, with the clear advantage that now
we are incorporating robustness with respect to parameter3 .
E. Implementation Discussion
As far as the control implementation is concerned, it is worth
noting that the resulting control is expressed in terms of phasor
variables with, roughly speaking, the moving average on rotating variables [see (5)]. To avoid the possible estimation of
such moving average, whose dynamics should be included in
the stability analysis, we have transformed all proportional contributions to – – coordinates and applied the remaining integral parts on the rotating-frame variables (without any moving
average) relying on the low-pass filter properties of the applied
integrators. This is possible since the resulting controller is still
linear. Of course, the controller does not guarantee tracking of
nonselected harmonics, but it does guarantee the overall stability
strongly simplifying analysis and implementation of the proposed solution. Moreover, all integral rotating-frame terms have
been simplified into equivalent stationary frame transfer functions, as suggested by [16]. The controller, recalling the
notation, then takes the following form:
Fig. 2.
Block diagram of the proposed controller.
Finally, by expressing the dynamical part of the controller in
the form of a transfer function, we get
(24)
(23)
where
and
as suggested by [16]. Notice that we have assumed that parameters
and
are chosen so that term
has
. The
the same value for every th harmonic, as well as
in second sum of (23) comes
minus sign of term
from the fact that
.
The implementation can be further simplified by proposing
the following transformations which avoid the use of rotations:
where is the complex variable. Fig. 2 presents the block diagram of the reduced controller (24).
As far as the DSP implementation is concerned, we recall that
our solution requires the sensing of output voltages and inductor
currents, so that the requirement in term of hardware peripheral
devices is exactly the same as in conventional multiloop scheme.
Instead, as shown in Fig. 2, the computing power requirement is
greater, since two second-order filters are needed for each compensated harmonic, one for the component and one for the
component. However, such signal processing requirement is not
a limitation on actual motion control DSP, even for the compensation of a large number of harmonics. Our nonoptimized implementation of such filters, for example, requires around 2.5
s for each harmonic component.
IV. SIMULATION RESULTS
This yields the following expression for the controller:
3It
is clear that if measurement of the voltage in the source represented by
E is available, then performance of the aforementioned controllers would be
improved—for example, disturbances other than infrequent step changes may
be rejected.
The system of Fig. 1 has been simulated using the following
mH,
,
F,
V,
parameters:
kHz, while the nominal load
and switching frequency
and
Hz. The proposed control
is 5 kVA at 220 V
strategy has been implemented for the compensation of the fundamental components, as well as some harmonic components.
Focusing on the compensation of diode or thyristor rectifiers,
possibly under unbalanced conditions, the 3rd, 5th, 7th, 9th and
11th harmonic components have been selected. Control param,
mH,
eters have been chosen as follows:
,
50.9, 5.45, 6.08, 6.88, 7.75, 8.67 , where
for the fundamental component,
for the 3rd harmonic component, and so on, and the same for
0.092, 0.166, 0.165, 0.164, 0.163, 0.161 . With this
choice, our primary focus in based on fast dynamic response for
MATTAVELLI et al.: DISSIPATIVITY-BASED ADAPTIVE AND ROBUST CONTROL OF UPS
Fig. 3. Three-phase rectifier load. (a) Proposed controller. (b) Conventional controller. [Top: load voltage v
i
and load current i (dotted line).]
339
and its reference (dotted line); bottom: filter current
Fig. 4. Proposed controller. (a) Turn-off of a resistive load. (b) Turn-on of a resistive load. [Top: load voltage v
current i .]
the fundamental components and slower transient response for
the harmonics components. Indeed, this choice seems to reduce
overshoot under step-load changes at the expense of slower control of harmonic components, which, however, very well suits
the typical slow variation on load harmonic components.
The performance of the proposed control with three-phase
diode rectifier loads is reported in Fig. 3(a). It is worth noting
that the output voltage is very close to the sinusoidal reference
(dotted line) and the inverter is able to supply all selected harmonic currents required by the distorting load, as shown in the
bottom part of Fig. 3(a). Indeed, the output voltage distortion has
been strongly improved and we have verified that all selected
frequencies are 40 dB below the fundamental component. For
comparison, we implemented a conventional multiloop control
and its reference (dotted line); bottom: load
scheme, where an outer PI voltage regulator (both for the and
components) sets the reference currents for an inner PI current
regulators. The bandwidth of the current loop has been set to 1
kHz with a phase margin of 60 and the voltage loop bandwidth
to 250 Hz and the same phase margin. The results obtainable
with a conventional approach, under the same load conditions,
are reported in Fig. 3(b). Note that the output voltage distortion
is quite high and the harmonic compensation is quite poor, even
if the rating of the output capacitors is quite high (3 kVA) compared to the nominal load power. Indeed, the reduction of the
output filter rating would increase the output voltage distortion
only for the conventional solutions, but would not significantly
affect our controller performance. Moreover, it is worth noting
that the small output voltage distortion of Fig. 3(a) has been ob-
340
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 2, APRIL 2001
Fig. 5. Unbalanced test. (a) Proposed controller. (b) Conventional controller. [Output voltages, their references (dotted line). and output current for (from top to
bottom) phase a, b, and c, respectively.]
0 0
Fig. 6. Three-phase rectifier load with the proposed solution. (a) From top to bottom: output voltage phase a b c (100 V/div) and phase c output current
(10 A/div). (b) From top to bottom: output voltage reference, output voltage in coordinate, and the corresponding error (40 V/div).
tained in spite of an increase of harmonic components absorbed
by the rectifier load. Indeed, diode rectifier load with capacitive filter on the dc side changes the input current waveforms
in function of supply impedance, which we are able to strongly
decrease at the selected frequencies by control action.
In order to verify the control under dynamic conditions, step
load changes with linear resistive loads are investigated and the
results reported in Fig. 4(a) and (b). Note that, in both cases, the
transient behavior is excellent and we have verified that overshoot and undershoot are very close to those obtained with the
conventional multiloop control scheme.
We have also verified the performance of our control in the
presence of unbalanced conditions, for instance, those caused by
a single-phase diode rectifier. Fig. 5(a) shows the ability of the
proposed approach to compensate also for whatever load conditions and highlight the potentiality of our approach compared to
the responses in conventional solutions presented in Fig. 5(b).
V. EXPERIMENTAL RESULTS
The system of Fig. 1 has been experimentally tested using
a reduced-scale prototype with the following parameters:
MATTAVELLI et al.: DISSIPATIVITY-BASED ADAPTIVE AND ROBUST CONTROL OF UPS
341
0 0
Fig. 7. Three-phase rectifier load with PI control. (a) From top to bottom: output voltage phase a b c (100 V/div) and phase c output current (10 A/div).
(b) From top to bottom: output voltage reference, output voltage in coordinate, and the corresponding error (40 V/div).
mH,
F,
V, switching frequency
kHz, output voltage frequency
Hz, and
selected frequencies: 1st, 3rd, 5th, 7th, and 9th. Following
the proposed design guidelines, control parameters have
,
mH,
been chosen as follows:
,
, where
for the fundamental component,
for the 3rd
harmonic component, and so on, and the same for
. The proposed control strategy
has been implemented by means of the 16-bit fixed-point
DSP-based controller ADMC401 by Analog Devices. This
DSP unit represents a powerful tool for digital control implementation of high-performance motion control applications
due to the fast arithmetic unit (26MIPS) and several embedded
peripherals, such as a high-resolution pulsewidth modulation
(PWM) modulator, flash 12-bit A/D converters, which allow
conversions up to eight channels in less than 2 ms, event capture
channels [17]. It is worth it to point out that the time required to
implement the control of each frequency (both for the and
components) is around 2.5 s using a nonoptimized assembly
code. This allows the control of a large number of harmonic
components.
The results of the proposed control with three-phase diode
rectifier loads are reported in Fig. 6(a) and (b), while the results
obtained with conventional PI control are reported in Fig. 7(a)
and (b). Note that the quality of the output voltage has been
strongly improved respect to the PI control, since the dominant
harmonics (i.e., the 5th and the 7th components) have been well
compensated by the proposed strategy. Moreover, comparing
Figs. 6(b) and 7(b), it is worth noting that also the fundamental
component on the output voltage error has been strongly reduced. The improvement in terms of THD reduction are also
evident from Fig. 8, which reports output voltage spectrum of
Figs. 6(a) and 7(a). Again, note that the distortion at the selected
Fig. 8. Normalized output voltage spectrum.
frequencies has been strongly reduced by control action. The
compensation is indeed not complete since a small residual distortion at the selected frequencies is still present. This phenomenon is mainly due the quantization and rounding errors in the
fixed-point DSP implementation.
As a final test for unbalanced conditions, we have applied
a single-phase rectifier load to a phase-to-phase voltage. The
results, reported in Fig. 9(a) and (b), are indeed much better
than those obtained with the conventional multiloop scheme
[see Fig. 10(a) and (b)], highlighting the advantages of the proposed solution.
VI. CONCLUSIONS
This paper has investigated a dissipativity-based control for
UPS systems. The proposed solution is intended to compensate
for harmonics due to unknown nonlinear loads, which can also
be of an unbalanced nature. The control task is to deliver balanced sinusoidal signals even in the presence of uncertainties
in the system and load parameters. Vital for our development
342
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 2, APRIL 2001
0 0
Fig. 9. Unbalance test (single-phase rectifier) with the proposed solution. (a) From top to bottom: output voltage phase a b c (100 V/div) and phase c output
current (10 A/div). (b)From top to bottom: output voltage reference, output voltage in coordinate, and the corresponding error (40 V/div).
0 0
Fig. 10. Unbalance test (single-phase rectifier) with PI control. (a) From top to bottom: output voltage phase a b c (100 V/div) and phase c output current
(10 A/div). (b) From top to bottom: output voltage reference, output voltage in coordinate, and the corresponding error (40 V/div).
is the use of a frequency-domain description of the system dynamics, denoted as phasor dynamics. Thus, proceeding in a similar fashion as in other frequency-domain techniques (such as
repetitive control suggested in the UPS literature), we proceed
to compensate only for a selected group of harmonics. The first
proposed controller follows the ideas of dissipativity-based control where adaptation is added to estimate the system parameters, resulting in a somewhat complicated nonlinear controller.
The controller is written in terms of the rotating-frame vari-
ables, which makes its implementation more challenging. Based
on the structure of the first nonlinear controller, we proposed a
second controller where part of the adaptation is avoided. This
results in a linear controller of the PI form, but with appropriate matrices of coefficients that allow us to establish global
stability of the aggregate system, even in the presence of uncertainties in system and load parameters. Moreover, due to
the linear nature of this controller, its implementation becomes
much easier. Finally, simulation results and experimental results
MATTAVELLI et al.: DISSIPATIVITY-BASED ADAPTIVE AND ROBUST CONTROL OF UPS
on a three-phase prototype using a single-chip fixed-point DSP
by Analog Device (ADMC401) were presented, illustrating the
effectiveness and advantages of the proposed solution.
REFERENCES
[1] S. M. Ali and M. P. Kazmierkowski, “Pwm voltage and current control
of four-Leg vsi,” in Proc. IEEE IECON’98, Aachen, Germany, 1998, pp.
196–201.
[2] T. L. Chern, J. Chang, C. H. Chen, and H. T. Su, “Microprocessor-based
modified discrete integral variable-structure control for ups,” IEEE
Trans. Ind. Electron., vol. 46, pp. 340–348, Apr. 1999.
[3] F. R. Gantmacher, Matrix Theory Vol. II. New York: Mir, 1960.
[4] H. A. Gründling, E. G. Carati, and J. R. Pifheiro, “Analysis and implementation of a modified robust model reference adaptive control with
repetitive controller for ups application,” in Proc. IEEE IECON’98,
Aachen, Germany, 1998, pp. 391–395.
[5] T. Haneyoshi, A. Kawamura, and R. G. Hoft, “Waveform compensation
of PWM inverter with cyclic fluctuating loads,” IEEE Trans. Ind. Applicat., vol. 24, pp. 582–589, July/Aug. 1988.
[6] T. Ito and S. Kawauchi, “Microprocessor-based robust digital control
for UPS with three-phase PWM inverter,” IEEE Trans. Power Electron.,
vol. 10, pp. 196–203, Mar. 1995.
[7] U. B. Jensen, P. N. Enjeti, and F. Blaabjerg, “A new space vector based
control method for ups systems powering nonlinear and unbalanced
loads,” in Proc. IEEE APEC, New Orleans, LA, 2000, pp. 895–901.
[8] H. L. Jou and J. C. Wu, “A new parallel processing ups with the performance of harmonic suppression and reactive power compensation,” in
Proc. IEEE PESC’94, 1994, pp. 1443–1450.
[9] S. L. Jung and Y. Y. Tzou, “Discrete feedforward sliding mode control
of a PWM inverter for sinusoidal output waveform synthesis,” in Proc.
IEEE PESC’94, 1994, pp. 552–559.
[10] H. K. Khalil, Nonlinear Systems, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 1996.
[11] C. D. Manning, “Control of UPS inverters,” in Proc. IEE Colloq., 1994,
pp. 3/1–3/5.
[12] A. M. Stankovic, S. R. Sanders, and T. Aydin, “Analysis of unbalanced
AC machines with dynamic phasors,” in Proc. Naval Symp. Electric
Drives, 1998, pp. 219–226.
[13] A. Von Jouanne, P. N. Enjeti, and D. J. Lucas, “DSP control of highpower UPS systems feeding nonlinear loads,” IEEE Trans. Ind. Electron., vol. 43, pp. 121–125, Feb. 1996.
[14] M. J. Tyan, W. E. Brumsickle, and R. D. Lorenz, “Control topology
options for single-phase UPS inverters,” IEEE Trans. Ind. Applicat., vol.
33, pp. 493–500, Mar./Apr. 1997.
[15] Y. Y. Tzou, R. S. Ou, S. L. Jung, and M. Y. Chang, “High-performance
programmable ac power source with low harmonic distortion using dspbased repetitive control technique,” IEEE Trans. Power Electron., vol.
12, pp. 715–725, July 1997.
[16] D. N. Zmood, D. G. Holmes, and G. Bode, “Frequency domain analysis
of three phase linear current regulators,” in Conf. Rec. IEEE-IAS Annu.
Meeting, Phoenix, AZ, 1999, pp. 818–825.
[17] “Single-Chip, DSP-Based High Performance Motor Controller,” Analog
Devices, Norwood, MA, ADMC401 Data Sheet, Rev. 0.
343
Paolo Mattavelli (S’95–A’96) received the Dr.
degree with honors and the Ph.D. degree, both
in electrical engineering, from the University of
Padova, Padova, Italy, in 1992 and 1995, respectively.
He has been a Researcher at the University of
Padova since 1995.
Dr. Mattavelli is a member of the IEEE Power
Engineering, IEEE Power Electronics, and IEEE
Industry Applications Societies and the Italian
Association of Electrical and Electronic Engineers.
Gerardo Escobar (M’00) received the B.Sc.
degree in electromechanics engineering (specialty
in electronics) and the M.Sc. degree in electrical
engineering (specialty in automatic control) from
the Engineering Faculty, National University of
Mexico (UNAM), Mexico City, Mexico, and the
Ph.D. degree from the University of Paris XI, Paris,
France, in 1991, 1995, and 1999, respectively.
He was a Technical Assistant in the Automatic
Control Laboratory, Graduate School of Engineering, UNAM, from May 1990 to April 1991.
From August 1991 to August 1995, he was an Assistant Professor in the Control
Deparment, Engineering Faculty, UNAM. He is currently a Visiting Researcher
at Northeastern University, Boston, MA. His main research interests include
nonlinear control design, passivity-based control, hybrid systems control,
switching power converters, electrical drives, and active filters.
Aleksandar M. Stanković (S’88–M’91) received
the Dipl.Ing. and M.S. degrees from the University
of Belgrade, Belgrade, Yugoslavia, and the Ph.D.
degree from Massachusetts Institute of Technology,
Cambridge, in 1982, 1986, and 1993, respectively,
all in electrical engineering.
Since 1993, he has been with the Department of
Electrical and Computer Engineering, Northeastern
University, Boston, MA, where he is currently
an Associate Professor. His research interests are
modeling, analysis, estimation, and control of energy
processing systems.
Dr. Stanković is a member of IEEE Power Engineering, IEEE Power Electronics, IEEE Control Systems, IEEE Circuits and Systems, IEEE Industry Applications, and IEEE Industrial Electronics Societies. He serves as an Associate
Editor of the IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY.