672

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 45, NO. 4, AUGUST 1998

Letters to the Editor

A Digital Control Technique for a

Single-Phase PWM Inverter

K. S. Low

Abstract—This paper describes the closed-loop control of a single-phase

pulsewidth modulated (PWM) inverter using the generalized predictive
control (GPC) algorithm. This approach determines the desired switching
signals by minimizing a cost function that reduces the tracking error
and the control signals. Experimental results have demonstrated that the
prototype system performs well.

Index Terms—Digital control, pulsewidth modulated inverters.

I. I

NTRODUCTION

Uninterruptible power supplies (UPS’s) are used in many industrial

systems to reduce power line disturbances and interruption. For
critical loads, such as communication systems in the airport, medical
equipment in the hospital, workstations in the computer centers, etc.,
a highly reliable and stable voltage supply is required. One of the
important mechanisms of the UPS is to convert the dc voltage of the
battery to sinusoidal ac output through an inverter LC filter block.
To achieve the desired dynamic response and attain good robustness
with respect to disturbances or parameter variations, various advanced
control techniques have been applied to control the inverter [1]–[4].

In this letter, we propose a new approach using the generalized

predictive control (GPC) scheme. The main characteristic of the
proposed control scheme is that it employs the receding-horizon
strategy [5]. Based on the system model, the GPC scheme predicts
the output of the plant over a time horizon based on the assumption
about future controller output sequences. An appropriate sequence
of the control signals is then calculated to reduce the tracking error
by minimizing a quadratic cost function. This process is repeated
for every sample interval. Thus, new information can be updated at
every sampling interval. Due to this approach, it gives good rejection
against modeling errors and disturbances.

The GPC scheme has been used successfully in many applications,

especially in the process control industries, such as steel casting,
glass processing, oil refinery, pulp and paper industries, etc. In this
letter, we explore its application in the control of the inverter. Some
experimental results of a prototype system are demonstrated.

II. T

HE

M

ODEL OF THE

S

YSTEM

The block diagram of the system is shown in Fig. 1. It consists of a

single-phase full-bridge inverter with an LC output filter. The inverter
switching sequence is controlled by a digital signal processor (DSP),
such that the output voltage follows the desired sinusoidal waveform.
The resistor

r in the circuit is the equivalent series resistor (ESR) of

the inductor. The ESR of the capacitor is neglected in the circuit, as
it is small. Define the state variables as the output voltage

V

o

and

Manuscript received April 21, 1997; revised September 24, 1997. Abstract

published on the Internet May 1, 1998.

The author is with the School of Electrical and Electronic Engineering,

Nanyang Technological University, Singapore 639798.

Publisher Item Identifier S 0278-0046(98)05690-1.

Fig. 1.

The overall experimental setup.

its derivative, i.e.,

z(t) = V

o

_V

o

:

(1)

Then, the system in Fig. 1 can be modeled using the following

second-order state-space model:

_z(t) = az(t) + bu(t) + h(t)

(2)

y(t) = cz(t)

(3)

where

a =

0

1

0 1

LC

0 r

L

; b =

0

1

LC

;

h(t) =

0

0 1

C

di

o

dt

0 ri

o

LC

; c = [1 0]:

In (2),

u is the input voltage and i

o

is the output current. By treating

the disturbance as an unmeasurable variable, the discrete-time state
model of the system can be expressed as

1z(kT + t) = G1z(kT ) + H1u(kT)

(4)

where

T is the sampling time of the system, k is the discrete-time

index, and

G = eaaa

T

;

H =

T

0

eaaa



d b:

(5)

1 is the difference operator, such that

1z(kT ) = z(kT ) 0 z(kT 0 T )

(6)

1u(kT ) = u(kT ) 0 u(kT 0 T ):

(7)

To eliminate steady-state error, the system (4) is augmented to the

following new system:

1z(kT + T )

V

o

(kT )

= G 0

c 1

1z(kT )

V

o

(kT 0 T ) +

H

0 1u(kT ):

(8)

Define

X(kT ) =

1z(kT )

V

o

(kT 0 T ) :

Then, (8) can be expressed as

X(kT + T ) = GX(kT ) + H1u(kT)

(9)

0278–0046/98$10.00

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1998 IEEE

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 45, NO. 4, AUGUST 1998

673

(a)

(b)

Fig. 2.

Experimental result under rated load. (a) Output voltage (vertical:

25 V/div; horizontal: 5 ms/div). (b) Harmonic spectrum of (a) (vertical: 1
percent/div; horizontal: 100 Hz/div).

where

G = G 0

c 1

and

H = H

0 :

The output variable now becomes

u(kT ) = CX(kT ) = V

o

(kT )

(10)

where

C = [1 0 1]:

III. C

ONTROLLER

D

ESIGN

To develop the GPC controller for the inverter, we employ the

receding-horizon control strategy. In this strategy, a sequence of
future control signals is calculated by minimizing a cost function
defined over a prediction horizon. However, only the first element
of the future control signals is applied to the system. At the next
sampling interval, the control calculation is repeated again. In this
letter, we define the control law as

1u(kT ) = K

1

V

3

o

(kT ) + K

2

X(kT )

(11)

where

K

1

and

K

2

are the controller gains, and

V

3

o

is the reference

output voltage.

(a)

(b)

Fig. 3.

Experimental result under triac load. (a) Output voltage (vertical:

25 V/div; horizontal: 5 ms/div). (b) Harmonic spectrum of (a) (vertical: 1
percent/div; horizontal: 100 Hz/div).

Denoting ^

V

o

(kT + jT jkT ) as the prediction of V

o

(kT + jT ) at

time

kT; the controller gains can be obtained by minimizing the

following cost function:

J

c

=

N

j=1

kV

3

o

(kT + jT ) 0 ^

V

o

(kT + jT jkT )k

2

+ k1u(kT )k

2

(12)

with respect to

1u: The parameter N

y

in (12) is known as the

prediction horizon. It is defined as the interval over which the
tracking error is minimized. The control weighting factor

 is used

to penalize excessive control activity and to ensure a numerically
well-conditioned algorithm. In this paper,

N

y

and

 are chosen as 25

and 1, respectively. Their choices affect the dynamics and robustness
of the system. The selection criteria are beyond the present scope of
this letter.

IV. E

XPERIMENTAL

R

ESULTS

To investigate the effectiveness of the proposed scheme in con-

trolling the inverter, a DSP board (TMS320C31) is used to realize
the controller in real time. The DSP board uses a slave processor
TMS320P14, which is capable of generating a 10-b pulsewidth modu-

674

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 45, NO. 4, AUGUST 1998

lated (PWM) waveform with a switching frequency of 25 kHz. As the
controller requires approximately 50

s for execution, the sampling

period is set to 80

s, resulting in two PWM pulses per controller

output. The filter is designed to have a cutoff frequency of 1.8 kHz.
The inverter is designed to produce a sinusoidal voltage of 100 V
(pp) at 50 Hz with a rated current of 5 A (pp). In the experiment,
the dc-link voltage is 60 V. Fig. 2(a) shows the experimental results
of the output voltage under rated load. The corresponding harmonic
spectrum is depicted in Fig. 2(b). The results show that the harmonic
distortion is less than 1%. To study the transient response of the
proposed scheme, a nonlinear load using a triac with rated load is
connected. Experimental results are demonstrated in Fig. 3. In this
case, a firing angle of 60



has been used. Thus, no load is connected

from 0



to 60



and a full load is connected from 60



to 180



.

Similarly, the same loading condition is applied in the negative cycle.
In spite of the rough load condition, the results show that the harmonic
distortion is still less than 2%, and the performance remains good.

V. C

ONCLUSIONS

A GPC algorithm has been developed to control a single-phase

inverter. The approach uses the receding-horizon strategy. The gains
are obtained by minimizing a cost function, which can be adjusted by
changing the prediction horizon and the control weighting factor. The
experimental results have demonstrated that the proposed controller
performs well under various loading conditions.

R

EFERENCES

[1] S. L. Jung and Y. Y. Tzou, “Discrete sliding-mode control of a PWM

inverter for sinusoidal output waveform synthesis with optimal sliding
curve,” IEEE Trans. Power Electron., vol. 11, pp. 567–577, July 1996.

[2] M. Carpita and M. Mar.esoni, “Experimental study of a power condition-

ing system using sliding mode control,” IEEE Trans. Power Electron.,
vol. 11, pp. 731–742, Sept. 1996.

[3] A. Kawamura, R. Chuarayapratip, and T. Haneyoshi, “Deadbeat control

of PWM inverter with modified pulse patterns for uninterruptible power
supply,” IEEE Trans. Ind. Electron., vol. 35, pp. 295–300, May 1988.

[4] A. V. Jouanne, P. N. Enjeti, and D. J. Lucas, “DSP control of high-power

UPS systems feeding nonlinear loads,” IEEE Trans. Ind. Electron., vol.
43, pp. 121–125, Feb. 1996.

[5] H. Demircioglu and D. W. Clarke, “Generalized predictive control with

end-point state weighting,” Proc. Inst. Elect. Eng., vol. 140, pt. D, no.
4, pp. 275–282, 1993.

On the ZVT-PWM C ´uk Converter

Ching-Jung Tseng and Chern-Lin Chen

Abstract— A modified zero-voltage-transition pulsewidth modulation

(ZVT-PWM) C ´uk converter is proposed in this letter. Better robustness,
smaller minimum duty ratio, and lower turn-on loss are obtained in
this converter. No additional component is needed compared with the
conventional ZVT-PWM C ´uk converter.

Index Terms—Converters, pulsewidth modulation, switching circuits.

I. I

NTRODUCTION

Various soft-switching techniques have been proposed to reduce

switching losses and EMI noises of pulsewidth modulation (PWM)
converters in recent years. Zero-voltage-transition (ZVT)-PWM con-
verters [1], [2], which achieve zero-voltage switching (ZVS) for both
the transistors and the diodes, while minimizing their voltage and
current stresses, are deemed desirable. However, circuit operations
are easily interfered with by the nonidealities of circuit components.
The minimum duty ratio is also limited by the discharging time of the
resonant inductor. A modified ZVT-PWM C´uk converter is proposed
to improve these disadvantages of the conventional ZVT-PWM C´uk
converter [1], shown in Fig. 1.

II. T

HE

M

ODIFIED

ZVT-PWM C

´

UK

C

ONVERTER

The circuit diagram and key waveforms of the modified ZVT-

PWM C´uk converter are shown in Fig. 2. The modified converter
differs from the conventional one by connecting the

D)2 anode to the

output terminal instead of to the

D

1

anode. The following benefits

are obtained.

1) Better robustness: In the conventional converter, voltage across

the auxiliary diode

D

2

is zero when the main diode

D

1

is

conducting.

D

1

and

D

2

are essentially in parallel.

D

2

may

be easily turned on by small disturbances and, thus, a certain
percentage of current will flow through it. This phenomenon
may generate serious reverse-recovery loss when the auxiliary
switch

S

2

turns on unless an additional saturable reactor is

placed in series with the resonant inductor. In the modified
ZVT-PWM C´uk converter,

D

2

is reverse biased by the output

voltage when

D

1

is conducting. It prevents

D

2

and

L

r

from

conducting and, thus, avoids the reverse-recovery loss.

2) Smaller minimum duty ratio: In ZVT-PWM converters, the

minimum duty ratio can be defined as the minimum time ratio
that either

S

1

or

S

2

is on. In the conventional ZVT-PWM C´uk

converter,

I

Lr

has to discharge to zero before

S

1

turns off to

prevent

D

2

and

L

r

from conducting for the entire switching

period. Otherwise, the same switching loss as mentioned above
will be generated. The minimum duty ratio of the conventional

Manuscript received May 26, 1997; revised February 11, 1998. Abstract

published on the Internet May 1, 1998.

The authors are with the Power Electronics Laboratory, Department of

Electrical Engineering, National Taiwan University, Taipei, 10764 Taiwan,
R.O.C.

Publisher Item Identifier S 0278-0046(98)05691-3.

0278–0046/98$10.00



1998 IEEE