602 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 45, NO. 4, AUGUST 1998
A Novel Switch-Mode DC-to-AC Inverter
with Nonlinear Robust Control
Zaohong Yang, Student Member, IEEE, and Paresh C. Sen, Fellow, IEEE
Abstract A switch-mode dc-to-ac inverter based on a dc-to- Compared to the bridge-type inverter, the inverter using
dc converter topology using a novel nonlinear robust control to
a dc-to-dc converter configuration has several advantages.
generate a sinusoidal output waveform is presented. The control
Only one switch operates at high frequency and, as a result,
scheme is based on simultaneous feedback of the output voltage
switching losses will be significantly less. The conduction
and feedforward of the input voltage and inductor voltage. As a
loss will be slightly higher because of one extra switch
result, the output voltage remains dynamically unchanged when
there are large disturbances in input voltage or load current.
compared to the bridge configuration. The overall losses will
The nature of the control law is explained. Computer simulation
be less, thereby increasing efficiency. In addition, the output
results show the robustness and fast dynamical response of
filtering capacitors in the dc-to-dc converters can be a dc-type
the control system. The experimental results are presented to
capacitor, e.g., an electrolytic capacitor which is smaller and
verify the analysis and demonstrate the feasibility of the control
strategy. less expensive than the ac-type capacitor for the same capacity
required in the bridge configuration. However, the inverters
Index Terms Control techniques, dc ac power conversion,
using bridge configuration must use an ac-type capacitor as
dynamic response, pulsewidth modulated inverters.
a filter. More important is that, with a dc-to-dc converter
topology, the advanced control techniques, such as current-
I. INTRODUCTION
mode control, digital data sampling control, and sliding-mode
WITCH-MODE dc-to-ac inverters have been used in var- control, etc., developed from the investigations of dc-to-dc
ious types of applications, such as uninterruptible power
S converters can be directly applied to the dc-to-ac switch-
supplies, communication ring generators, aerospace power
mode inverter. Therefore, a good dynamic performance can
systems, and variable-speed ac machine drives. The loads in
be achieved.
the aforementioned applications are either critical or sensitive.
The application environment of the switch-mode dc-to-ac
A good steady-state and dynamic performance of the switch-
inverter requires that its output voltage remains dynamically
mode dc-to-ac inverter is desirable for these applications.
stable when the supply voltage or load current suddenly
Traditionally, a bridge configuration is employed for the
changes.
switch-mode dc-to-ac inverters. By using a pulsewidth mod-
Greater attention has been paid to the switch-mode dc-to-ac
ulation (PWM) switching technique, the input dc voltage is
inverter using the dc-to-dc converter topology because of the
transformed into a high-frequency pulse waveform at the
aforementioned advantages. Several efforts have been made to
output of the bridge. Through a filter, this high-frequency
improve the dynamical performance of this type of inverter,
pulsed voltage is smoothed into a sinusoidal waveform, as
i.e., the output voltage remains dynamically unchanged when
shown in Fig. 1 [1], [2].
subjected to large disturbances in supply voltage or load
Recently, switch-mode dc-to-ac inverters using a dc-to-dc
current.
converter topology have been developed [3] [7]. The principle
Direct duty ratio control is the most commonly used control
of operation of this type of inverter is illustrated in Fig. 2(a),
strategy [4]. The principle of the control strategy is illustrated
where the dc-to-dc converter is of buck configuration. The
in Fig. 3. Its duty ratio is controlled by the  error that is
average output voltage of this buck converter, , is the
the difference between the actual output voltage and the
product of duty ratio and the input voltage i.e.,
reference voltage , where the reference signal consists of
If the input voltage is constant and the duty ratio is varied
a fully rectified sinusoidal waveform. The objective of the
slowly, relative to the switching frequency, in the form of a
direct duty ratio control is to stabilize the output voltage
fully rectified sinusoidal wave, the output will naturally be
when the system is subjected to disturbances. However, this
a fully rectified sine wave. Through a bridge circuit which is
control method cannot achieve the dynamical stabilization of
synchronized with the fully rectified sine waveform of the
the voltage, because the output voltage changes before the
output is  unfolded into a sinusoidal waveform , as
control action begins. A sharp overshoot will occur and a
shown in Fig. 2(b).
considerable time will be taken before the voltage returns to
its steady-state value.
The application of current mode control to the switch-
Manuscript received May 7, 1997; revised February 7, 1998. Abstract
published on the Internet May 1, 1998.
mode of the dc-to-ac inverter using the dc-to-dc converter
The authors are with the Department of Electrical and Computer Engineer-
configuration was presented in [6] and is shown in Fig. 4. In
ing, Queen s University, Kingston, Ont., K7L 3N6, Canada.
Publisher Item Identifier S 0278-0046(98)05681-0. this control strategy, the inductor current is forced to follow
0278 0046/98$10.00 © 1998 IEEE
YANG AND SEN: A NOVEL SWITCH-MODE DC-TO-AC INVERTER WITH NONLINEAR ROBUST CONTROL 603
(a)
(b)
Fig. 1. PWM bridge-type inverter. (a) Bridge-type inverter and PWM waveform at the output. (b) Bridge circuit followed by a filter to generate sine wave.
(a)
(b)
Fig. 2. Switch-mode dc-to-ac inverter using buck converter configuration. (a) Buck converter with duty ratio varying in the form of a fully rectified
sine wave. (b) A bridge synchronizer following the buck converter.
the current control signal , which is in proportion to the strategy. When the supply voltage or load current changes, the
difference between output voltage and reference signal output voltage will change at first. The current control signal
This type of control strategy has many advantages over direct changes to accommodate the new operating condition only
duty ratio control, such as a wide bandwidth, fast response, after the output voltage changes.
and automatic current protection [10], [11]. However, robust Discrete data sampling control has also been tried with a
control of the output voltage is still not achieved by this control switch-mode dc-to-ac inverter using the dc-to-dc converter
604 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 45, NO. 4, AUGUST 1998
Fig. 5. General block diagram of PWM dc-to-dc converter.
Fig. 3. Block diagram of the direct duty ratio control.
(a)
Fig. 4. Block diagram of the current-mode control.
configuration [7]. Unfortunately, the digital control is slower in
instantaneous response than the analog control. The transient
performance of the output voltage is not improved. Moreover,
this control system is very complicated and is difficult to
implement in a practical circuit.
(b)
The previously proposed control strategies for a dc-to-
Fig. 6. Buck converter: (a) topology and (b) its low-frequency average
ac inverter have not yet achieved the desirable dynamical
model.
stabilization of the output voltage. In this paper, a nonlinear
control strategy which is based on the control law presented in
A nonlinear control strategy can be applied to the buck-
[8] is proposed and implemented to achieve the robust control
type dc-to-dc converter to realize the above objective. The
of the output voltage. The principle of operation of the control
low-frequency averaged equivalent model of a buck converter
technique is discussed in Section II. The simulation results
is shown in Fig. 6. This equivalent circuit can be derived from
are presented in Section III. The experimental implementation
the state-space average method [9]. This model is valid only
is described in Section IV. Finally, Section V gives the
for continuous conduction mode operation.
conclusions.
In this averaged-circuit model, the active switch is modeled
by a controlled current source with its value equal to the
II. PRINCIPLE OF OPERATION
average current flowing through it over one switching cycle,
A switch-mode dc-to-dc converter is generally composed
i.e., for the buck converter, where   is the
of two basic parts. One is the power stage, or the switching
averaged inductor current and is the duty ratio. The average
converter; the other is the control circuit, as shown in Fig. 5,
output voltage across the diode over one switching cycle is
where is the reference voltage, denotes the combination
modeled as a controlled voltage source with its value equal to
of the feedbacks, and is the duty ratio.
for the buck converter.
The power stage controls the power absorbed from the
From Fig. 6(b), the output voltage can be expressed as
unregulated supply voltage and provides a regulated
(1)
constant output voltage at the load. The main purpose of
the control circuit is to generate a proper duty ratio according
where is the averaged value of the inductor voltage and
to the conditions of the circuit so that the variation of the
is the duty ratio required for the switching converter. This
output voltage is reduced as much as possible when the supply
can be expressed as
voltage or load current changes. In order to achieve robust
control of the output voltage, i.e., to eliminate the effect of the
(2)
supply voltage or load current disturbance, the control strategy
and feedbacks should be properly selected so that the closed- Equation (2) defines the duty ratio required by the buck
loop output voltage is independent of either the supply voltage converter at a specific operating point of and
or the load current and is determined only by the reference The control circuit can now be constructed to generate the
voltage duty ratio. Let the input and output relation of the control
YANG AND SEN: A NOVEL SWITCH-MODE DC-TO-AC INVERTER WITH NONLINEAR ROBUST CONTROL 605
(a)
(b)
Fig. 7. The proposed dc-to-ac inverter using nonlinear robust control system. (a) The diagram of the proposed inverter. (b) The sinusoidal output voltage
is obtained by the bridge-type synchronizer.
circuit be formulated as In the switch-mode dc-to-ac inverter using the buck con-
verter topology, the reference is chosen to be a fully rectified
(3)
sinusoidal wave, i.e., (the frequency is
much lower than the switching frequency). The output voltage
where is the reference voltage, is the gain of the of the buck converter can be derived as
proportional error amplifier, and denotes the duty ratio
(6)
generated by the control circuit. The implementation is shown
in Fig. 7(a).
and represents a fully rectified sinusoidal waveform having the
In the practical circuit, the output of the control circuit is
same frequency as the reference signal
connected to the gate of the active switch in the power stage,
The bridge-type synchronizer composed of  as shown
making Therefore, the closed-loop characteristic can
in Fig. 7(a), is used to generate a sinusoidal ac voltage
be obtained by equating (2) and (3) as
waveform. In this synchronizer, the switching cycle of the
diagonal pair of switches, or is synchronized
(4)
with that of the reference signal For example, and
are turned on at 0, , etc., and and are
From (4), the output voltage can be found as
turned on at etc., as shown in Fig. 7(b). Therefore,
the fully rectified sinusoidal voltage can be unfolded
(5) into a sinusoidal output voltage This sinusoidal output
voltage is immune to disturbances in the input voltage
Equation (5) shows that, by the control law (3), the closed- or output current. The proposed closed-loop control system
loop averaged output voltage is forced to be proportional to of the switch-mode dc-to-ac inverter using the buck converter
a reference voltage. topology is illustrated in Fig. 7.
606 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 45, NO. 4, AUGUST 1998
(a) (b)
(c)
Fig. 8. Computer simulation of the dc-to-ac inverter with nonlinear robust controller. (a) Effect of the input voltage step changes on the output voltage. (b)
Effect of the output load step changes on the output voltage. (c) Response of the output voltage to a step change of the reference signal.
The result of (6) means that the closed-loop output voltage in Fig. 8(b). The simulation result reveals that when the load
of the buck converter is independent of the supply voltage and steps between 20 and 10 the output voltage of the inverter
the load current. In other words, the averaged output voltage under the proposed control technique is not affected by the
remains unchanged, even when there is either a supply voltage deviations in the load.
or load current disturbance. The robust control of the output Finally, the response of the control system to a step change
voltage of the switch-mode inverter is, therefore, achieved.
in the reference signal is simulated. The result shown in
Fig. 8(c) demonstrates that this control system has fast dy-
namic response.
III. SIMULATION RESULTS
IV. EXPERIMENTAL RESULTS
The proposed switch-mode dc-to-ac inverter using a buck
To verify the theoretical analysis and simulation results,
converter topology with the nonlinear robust control strategy
a prototype model of the inverter shown in Fig. 7 has been
shown in Fig. 7 is simulated using PSPICE. The parameters of
breadboarded. The proposed control strategy is implemented.
the buck converter are as follows: input voltage 20 30 V;
The parameters of the power converter are as follows: buck
buck filtering inductor H; buck filtering capacitor
filtering inductor H, buck filtering capacitor
F.
F (two 47 F in parallel), input voltage 20 30 V.
The effect of step changes in the supply voltage have been
The reference voltage is a fully rectified sinusoidal waveform
analyzed for the proposed inverter. The simulated result is
shown in Fig. 8(a). This result shows that, when the supply V.
voltage steps from 20 to 27 V, the output voltage of the inverter Fig. 9(a) shows the waveform of the output voltage of the
does not change. inverter when the supply voltage steps between 20 and 27
The response of the control system to a large disturbance in V. The oscillogram indicates that the output voltage is not
the load is also studied by simulation. The result is illustrated affected by the large deviations in the supply voltage.
YANG AND SEN: A NOVEL SWITCH-MODE DC-TO-AC INVERTER WITH NONLINEAR ROBUST CONTROL 607
(a) (b)
(c)
Fig. 9. Experimental results. (a) Effect of the input voltage step changes on the output voltage. Upper: input voltage, 5 V/div; lower: output voltage 5
V/div; time: 5 ms/div. (b) Effect of the output load step changes on the output voltage, the load resistance steps between 20 and 10 . Upper: output
voltage, 5 V/div; lower: output current, 0.4 A/div; time: 5 ms/div. (c) Dynamic response of the output voltage to a step change of the reference. Upper:
reference voltage, 5 V/div; lower: output voltage, 5 V/div; time: 5 ms/div.
Fig. 9(b) shows the effect of a large load step change on A buck converter followed by a bridge synchronizer was
the output voltage. The output voltage of the inverter remains used to implement the nonlinear robust control. Computer
almost unchanged when the load impedance experiences a
simulations using PSPICE show that the output voltage is
large step change.
immune to large deviations in the supply voltage and load
The response of the output voltage of the inverter to a step
current and the system has a fast dynamic response.
change in reference voltage has been observed experimentally.
A prototype of the switch-mode dc-to-ac inverter with a
The oscillograms shown in Fig. 9(c) reveal that the output
buck topology has been breadboarded. The experimental re-
voltage of the inverter follows the change in reference very
sults agree well with computer simulations, thus demonstrating
quickly, and only a small transient period is observed.
that the proposed robust control method can improve the
The above experimental results agree well with the those
dynamic performance of the inverter.
derived from the computer simulation.
Some distortions appear on the output voltage in the zero-
REFERENCES
crossing regions. This is due the discontinuous inductor current
[1] P. C. Sen, Principles of Electric Machines and Power Electronics. New
around the output voltage zero crossing.
York: Wiley, 1989.
[2] N. Mohan, T. M. Undeland, and W. P. Robbins, Power Electronics,
V. CONCLUSIONS
Converters, Applications and Design. New York: Wiley, 1989.
[3] J. G. Kassakian, M. F. Schlecht, and G. C. Verghese, Principles of Power
A switch-mode dc-to-ac inverter using a nonlinear robust
Electronics. Reading, MA: Addison-Wesley, 1991.
control technique has been presented in this paper. The analy-
[4] J. Jalade, J. Marpinard, and M. Valentin,  DC/AC high power cell
sis of the control technique reveals that the output voltage of
structure improves sine generator performance, IEEE Trans. Aerosp.
the inverter is not affected by supply and load disturbances. Electron. Syst., vol. AES-17, pp. 373 378, May 1981.
608 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 45, NO. 4, AUGUST 1998
[5] C. Y. Hsu,  Stability analysis of a switched mode inverter using Cuk Paresh C. Sen (S 67 M 67 SM 74 F 89) was born
converters, in Conf. Rec. IEEE PESC 94, 1994, pp. 785 795. in Chittagong, Bangladesh. He received the B.Sc.
[6] A. Capel, J. Jalade, M. Valentin, and J. C. Marpinard,  Large signal
degree (Hons.) in physics and the M.Sc. degree
dynamic stability analysis of synchronised current controlled modula-
(Tech.) in applied physics from the University of
tors, application to sine wave high power inverters, in Conf. Rec. IEEE
Calcutta, Calcutta, India, in 1958 and 1961, respec-
PESC 82, 1982, pp. 101 110.
tively, and the M.A.Sc. and Ph.D. degrees in elec-
[7] J. Jalade and S. Senanyake,  Reversible power cell contributes to
trical engineering from the University of Toronto,
efficient light weight inverter, in Conf. Rec. IEEE PESC 86, 1986, pp.
Toronto, Ont., Canada, in 1965 and 1967, respec-
375 380.
tively.
[8] Y. F. Liu and P. C. Sen,  A novel method to achieve zero-voltage
He is currently a Professor of Electrical Engineer-
regulation in Buck converter, IEEE Trans. Power Electron., vol. 10,
ing at Queen s University, Kingston, Ont., Canada.
pp. 292 301, May 1995.
He has written more than 100 research papers in the general areas of power
[9] R. D. Middlebrook and S. Cuk,  A general unified approach to modeling
electronics and drives. He is the author of two books, Thyristor DC Drives
switching power converter stages, in Conf. Rec. IEEE PESC 76, 1976,
(New York: Wiley, 1981) and Principles of Electric Machines and Power
pp. 18 34.
Electronics (New York: Wiley, 1989). His fields of interest include power
[10] R. D. Middlebrook,  Modeling current-programmed Buck and Boost
electronics and drives, modern control techniques for high-performance drive
converter, IEEE Trans. Power Electron., vol. 4, pp. 36 52, Jan. 1989.
systems, and switching power supplies.
[11] D. M. Sable, R. B. Ridley, and B. H. Cho,  Comparison of performance
Dr. Sen has served as an Associate Editor of the IEEE TRANSACTIONS ON
of single loop and current injection control for PWM converters that
INDUSTRIAL ELECTRONICS AND CONTROL INSTRUMENTATION and as Chairman
operate in both continuous and discontinuous modes of operation, IEEE
of the Technical Committees on Power Electronics (1979 1980) and Energy
Trans. Power Electron., vol. 7, pp. 136 142, 1992.
Systems (1980 1982) of the IEEE Industrial Electronics Society. At present,
he is an active member of the Industrial Drives Committee and the Industrial
Power Converter Committee of the IEEE Industry Applications Society. He
received a Prize Paper Award for technical excellence from the Industrial
Drive Committee of the IEEE Industry Applications Society in 1986.
Zaohong Yang (S 96) received the B.Sc. and M.Sc.
degrees in electrical engineering from Zhejiang Uni-
versity, Hangzhou, China, in 1984 and 1987, re-
spectively. He is currently working towards the
Ph.D. degree at Queen s University, Kingston, Ont.,
Canada.
From 1987 to 1994, he was an Assistant Professor
at Hangzhou Institute of Electronics Engineering,
Hangzhou, China. Since 1994, he has been a Re-
search Assistant at Queen s University. His research
interests include high-frequency power conversion,
power factor correction circuits, and high-power resonant converters for
induction heating.