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.
Fig. 1. The overall experimental setup.
I. INTRODUCTION
Uninterruptible power supplies (UPS s) are used in many industrial its derivative, i.e.,
systems to reduce power line disturbances and interruption. For
Vo
z(t) = : (1)
critical loads, such as communication systems in the airport, medical
_
Vo
equipment in the hospital, workstations in the computer centers, etc.,
Then, the system in Fig. 1 can be modeled using the following
a highly reliable and stable voltage supply is required. One of the
second-order state-space model:
important mechanisms of the UPS is to convert the dc voltage of the
battery to sinusoidal ac output through an inverter LC filter block.
_
z(t) = az(t) + bu(t) + h(t) (2)
To achieve the desired dynamic response and attain good robustness
y(t) = cz(t) (3)
with respect to disturbances or parameter variations, various advanced
control techniques have been applied to control the inverter [1] [4].
where
In this letter, we propose a new approach using the generalized
0 1 0
predictive control (GPC) scheme. The main characteristic of the 1 r 1
a = ; b = ;
0 0
proposed control scheme is that it employs the receding-horizon
LC L LC
0
strategy [5]. Based on the system model, the GPC scheme predicts
1 dio rio ; c =[1 0]:
h(t) =
the output of the plant over a time horizon based on the assumption 0 0
C dt LC
about future controller output sequences. An appropriate sequence
In (2), u is the input voltage and io is the output current. By treating
of the control signals is then calculated to reduce the tracking error
the disturbance as an unmeasurable variable, the discrete-time state
by minimizing a quadratic cost function. This process is repeated
model of the system can be expressed as
for every sample interval. Thus, new information can be updated at
every sampling interval. Due to this approach, it gives good rejection
1z(kT + t) = G1z(kT) + H1u(kT) (4)
against modeling errors and disturbances.
The GPC scheme has been used successfully in many applications, where T is the sampling time of the system, k is the discrete-time
especially in the process control industries, such as steel casting, index, and
glass processing, oil refinery, pulp and paper industries, etc. In this T
aT a
a a
G = ea ; H = ea d b: (5)
letter, we explore its application in the control of the inverter. Some
0
experimental results of a prototype system are demonstrated.
1 is the difference operator, such that
1z(kT) = z(kT) 0 z(kT 0 T) (6)
II. THE MODEL OF THE SYSTEM
1u(kT) = u(kT) 0 u(kT 0 T): (7)
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
To eliminate steady-state error, the system (4) is augmented to the
switching sequence is controlled by a digital signal processor (DSP),
following new system:
such that the output voltage follows the desired sinusoidal waveform.
1z(kT + T) G 0 1z(kT) H
The resistor r in the circuit is the equivalent series resistor (ESR) of
= + 1u(kT): (8)
Vo(kT) c 1 Vo(kT 0 T) 0
the inductor. The ESR of the capacitor is neglected in the circuit, as
it is small. Define the state variables as the output voltage Vo and
Define
1z(kT)
X(kT) = :
Manuscript received April 21, 1997; revised September 24, 1997. Abstract
Vo(kT 0 T)
published on the Internet May 1, 1998.
The author is with the School of Electrical and Electronic Engineering,
Then, (8) can be expressed as
Nanyang Technological University, Singapore 639798.
Publisher Item Identifier S 0278-0046(98)05690-1. X(kT + T) = GX(kT) + H1u(kT) (9)
0278 0046/98$10.00 © 1998 IEEE
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 45, NO. 4, AUGUST 1998 673
(a)
(a)
(b)
(b)
Fig. 2. Experimental result under rated load. (a) Output voltage (vertical:
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
25 V/div; horizontal: 5 ms/div). (b) Harmonic spectrum of (a) (vertical: 1
percent/div; horizontal: 100 Hz/div).
percent/div; horizontal: 100 Hz/div).
^
where
Denoting Vo(kT + jTjkT) as the prediction of Vo(kT + jT) at
G 0 H time kT; the controller gains can be obtained by minimizing the
G = and H = :
c 1 0 following cost function:
N
The output variable now becomes
3 2 2
^
Jc = kVo (kT + jT) 0 Vo(kT + jTjkT)k + k1u(kT)k
u(kT) = CX(kT) = Vo(kT) (10)
j=1
(12)
where
C =[1 0 1]: with respect to 1u: The parameter Ny 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
III. CONTROLLER DESIGN
to penalize excessive control activity and to ensure a numerically
To develop the GPC controller for the inverter, we employ the
well-conditioned algorithm. In this paper, Ny and are chosen as 25
receding-horizon control strategy. In this strategy, a sequence of
and 1, respectively. Their choices affect the dynamics and robustness
future control signals is calculated by minimizing a cost function
of the system. The selection criteria are beyond the present scope of
defined over a prediction horizon. However, only the first element
this letter.
of the future control signals is applied to the system. At the next
sampling interval, the control calculation is repeated again. In this
IV. EXPERIMENTAL RESULTS
letter, we define the control law as
To investigate the effectiveness of the proposed scheme in con-
3
1u(kT) = K1 Vo (kT) + K2X(kT) (11)
trolling the inverter, a DSP board (TMS320C31) is used to realize
3
where K1 and K2 are the controller gains, and Vo is the reference the controller in real time. The DSP board uses a slave processor
output voltage. 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 On the ZVT-PWM Cśk Converter
controller requires approximately 50 s for execution, the sampling
period is set to 80 s, resulting in two PWM pulses per controller
Ching-Jung Tseng and Chern-Lin Chen
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,
Abstract A modified zero-voltage-transition pulsewidth modulation
(ZVT-PWM) Cśk converter is proposed in this letter. Better robustness,
the dc-link voltage is 60 V. Fig. 2(a) shows the experimental results
smaller minimum duty ratio, and lower turn-on loss are obtained in
of the output voltage under rated load. The corresponding harmonic
this converter. No additional component is needed compared with the
spectrum is depicted in Fig. 2(b). The results show that the harmonic
conventional ZVT-PWM Cśk converter.
distortion is less than 1%. To study the transient response of the
Index Terms Converters, pulsewidth modulation, switching circuits.
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 .
I. INTRODUCTION
Similarly, the same loading condition is applied in the negative cycle.
Various soft-switching techniques have been proposed to reduce
In spite of the rough load condition, the results show that the harmonic
switching losses and EMI noises of pulsewidth modulation (PWM)
distortion is still less than 2%, and the performance remains good.
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
V. CONCLUSIONS
current stresses, are deemed desirable. However, circuit operations
A GPC algorithm has been developed to control a single-phase
are easily interfered with by the nonidealities of circuit components.
inverter. The approach uses the receding-horizon strategy. The gains
The minimum duty ratio is also limited by the discharging time of the
are obtained by minimizing a cost function, which can be adjusted by
resonant inductor. A modified ZVT-PWM Cśk converter is proposed
changing the prediction horizon and the control weighting factor. The
to improve these disadvantages of the conventional ZVT-PWM Cśk
experimental results have demonstrated that the proposed controller
converter [1], shown in Fig. 1.
performs well under various loading conditions.
II. THE MODIFIED ZVT-PWM CÚK CONVERTER
REFERENCES
The circuit diagram and key waveforms of the modified ZVT-
[1] S. L. Jung and Y. Y. Tzou, Discrete sliding-mode control of a PWM PWM Cśk converter are shown in Fig. 2. The modified converter
inverter for sinusoidal output waveform synthesis with optimal sliding
differs from the conventional one by connecting the D)2 anode to the
curve, IEEE Trans. Power Electron., vol. 11, pp. 567 577, July 1996.
output terminal instead of to the D1 anode. The following benefits
[2] M. Carpita and M. Mar.esoni, Experimental study of a power condition-
are obtained.
ing system using sliding mode control, IEEE Trans. Power Electron.,
vol. 11, pp. 731 742, Sept. 1996.
1) Better robustness: In the conventional converter, voltage across
[3] A. Kawamura, R. Chuarayapratip, and T. Haneyoshi, Deadbeat control
the auxiliary diode D2 is zero when the main diode D1 is
of PWM inverter with modified pulse patterns for uninterruptible power
conducting. D1 and D2 are essentially in parallel. D2 may
supply, IEEE Trans. Ind. Electron., vol. 35, pp. 295 300, May 1988.
be easily turned on by small disturbances and, thus, a certain
[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. percentage of current will flow through it. This phenomenon
43, pp. 121 125, Feb. 1996.
may generate serious reverse-recovery loss when the auxiliary
[5] H. Demircioglu and D. W. Clarke, Generalized predictive control with
switch S2 turns on unless an additional saturable reactor is
end-point state weighting, Proc. Inst. Elect. Eng., vol. 140, pt. D, no.
placed in series with the resonant inductor. In the modified
4, pp. 275 282, 1993.
ZVT-PWM Cśk converter, D2 is reverse biased by the output
voltage when D1 is conducting. It prevents D2 and Lr 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 S1 or S2 is on. In the conventional ZVT-PWM Cśk
converter, ILr has to discharge to zero before S1 turns off to
prevent D2 and Lr 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
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