A Novel Switch-Mode Dc-To-Ac Inverter With Nonlinear Robust Control.pdf

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

Compared to the bridge-type inverter, the inverter using

a dc-to-dc converter conﬁguration has several advantages.

Only one switch operates at high frequency and, as a result,

switching losses will be signiﬁcantly less. The conduction

loss will be slightly higher because of one extra switch

compared to the bridge conﬁguration. The overall losses will

be less, thereby increasing efﬁciency. In addition, the output

ﬁltering capacitors in the dc-to-dc converters can be a dc-type

capacitor, e.g., an electrolytic capacitor which is smaller and

less expensive than the ac-type capacitor for the same capacity

required in the bridge conﬁguration. However, the inverters

using bridge conﬁguration must use an ac-type capacitor as

a ﬁlter. More important is that, with a dc-to-dc converter

topology, the advanced control techniques, such as current-

mode control, digital data sampling control, and sliding-mode

control, etc., developed from the investigations of dc-to-dc

converters can be directly applied to the dc-to-ac switch-

mode inverter. Therefore, a good dynamic performance can

be achieved.

The application environment of the switch-mode dc-to-ac

inverter requires that its output voltage remains dynamically

stable

Abstract— A switch-mode dc-to-ac inverter based on a dc-to-

dc converter topology using a novel nonlinear robust control to

generate a sinusoidal output waveform is presented. The control

scheme is based on simultaneous feedback of the output voltage

and feedforward of the input voltage and inductor voltage. As a

result, the output voltage remains dynamically unchanged when

there are large disturbances in input voltage or load current.

The nature of the control law is explained. Computer simulation

results show the robustness and fast dynamical response of

the control system. The experimental results are presented to

verify the analysis and demonstrate the feasibility of the control

strategy.

Index Terms— Control techniques, dc–ac power conversion,

dynamic response, pulsewidth modulated inverters.

I. I NTRODUCTION

S WITCH-MODE dc-to-ac inverters have been used in var-

ious types of applications, such as uninterruptible power

supplies, communication ring generators, aerospace power

systems, and variable-speed ac machine drives. The loads in

the aforementioned applications are either critical or sensitive.

A good steady-state and dynamic performance of the switch-

mode dc-to-ac inverter is desirable for these applications.

Traditionally, a bridge conﬁguration is employed for the

switch-mode dc-to-ac inverters. By using a pulsewidth mod-

ulation (PWM) switching technique, the input dc voltage is

transformed into a high-frequency pulse waveform at the

output of the bridge. Through a ﬁlter, this high-frequency

pulsed voltage is smoothed into a sinusoidal waveform, as

shown in Fig. 1 [1], [2].

Recently, switch-mode dc-to-ac inverters using a dc-to-dc

converter topology have been developed [3]–[7]. The principle

of operation of this type of inverter is illustrated in Fig. 2(a),

where the dc-to-dc converter is of buck conﬁguration. The

average output voltage of this buck converter,

when

the

supply

voltage

load

current

suddenly

changes.

Greater attention has been paid to the switch-mode dc-to-ac

inverter using the dc-to-dc converter topology because of the

aforementioned advantages. Several efforts have been made to

improve the dynamical performance of this type of inverter,

i.e., the output voltage remains dynamically unchanged when

subjected to large disturbances in supply voltage or load

current.

Direct duty ratio control is the most commonly used control

strategy [4]. The principle of the control strategy is illustrated

in Fig. 3. Its duty ratio is controlled by the “error” that is

the difference between the actual output voltage and the

reference voltage , where the reference signal consists of

a fully rectiﬁed sinusoidal waveform. The objective of the

direct duty ratio control is to stabilize the output voltage

when the system is subjected to disturbances. However, this

control method cannot achieve the dynamical stabilization of

the voltage, because the output voltage changes before the

control action begins. A sharp overshoot will occur and a

considerable time will be taken before the voltage returns to

its steady-state value.

The application of current mode control to the switch-

mode of the dc-to-ac inverter using the dc-to-dc converter

conﬁguration was presented in [6] and is shown in Fig. 4. In

this control strategy, the inductor current

, is the

product of duty ratio and the input voltage i.e.,

If the input voltage is constant and the duty ratio is varied

slowly, relative to the switching frequency, in the form of a

fully rectiﬁed sinusoidal wave, the output will naturally be

a fully rectiﬁed sine wave. Through a bridge circuit which is

synchronized with the fully rectiﬁed sine waveform of

the

output

is “unfolded” into a sinusoidal waveform

,as

shown in Fig. 2(b).

Manuscript received May 7, 1997; revised February 7, 1998. Abstract

published on the Internet May 1, 1998.

The authors are with the Department of Electrical and Computer Engineer-

ing, Queen’s University, Kingston, Ont., K7L 3N6, Canada.

Publisher Item Identiﬁer S 0278-0046(98)05681-0.

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

difference between output voltage and reference signal

This type of control strategy has many advantages over direct

duty ratio control, such as a wide bandwidth, fast response,

and automatic current protection [10], [11]. However, robust

control of the output voltage is still not achieved by this control

strategy. When the supply voltage or load current changes, the

output voltage will change at ﬁrst. The current control signal

changes to accommodate the new operating condition only

after the output voltage changes.

Discrete data sampling control has also been tried with a

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.

The previously proposed control strategies for a dc-to-

ac inverter have not yet achieved the desirable dynamical

stabilization of the output voltage. In this paper, a nonlinear

control strategy which is based on the control law presented in

[8] is proposed and implemented to achieve the robust control

of the output voltage. The principle of operation of the control

technique is discussed in Section II. The simulation results

are presented in Section III. The experimental implementation

(b)

Fig. 6.

Buck converter: (a) topology and (b) its low-frequency average

model.

A nonlinear control strategy can be applied to the buck-

type dc-to-dc converter to realize the above objective. The

low-frequency averaged equivalent model of a buck converter

is shown in Fig. 6. This equivalent circuit can be derived from

the state-space average method [9]. This model is valid only

for continuous conduction mode operation.

In this averaged-circuit model, the active switch is modeled

by a controlled current source with its value equal to the

average current ﬂowing through it over one switching cycle,

i.e., for the buck converter, where “ ” is the

averaged inductor current and is the duty ratio. The average

output voltage across the diode over one switching cycle is

modeled as a controlled voltage source with its value equal to

for the buck converter.

From Fig. 6(b), the output voltage can be expressed as

described

Section

IV.

Finally,

Section

gives

the

conclusions.

II. P RINCIPLE OF O PERATION

A switch-mode dc-to-dc converter is generally composed

of two basic parts. One is the power stage, or the switching

converter; the other is the control circuit, as shown in Fig. 5,

where is the reference voltage, denotes the combination

of the feedbacks, and is the duty ratio.

The power stage controls the power absorbed from the

unregulated supply voltage and provides a regulated

constant output voltage at the load. The main purpose of

the control circuit is to generate a proper duty ratio according

to the conditions of the circuit so that the variation of the

output voltage is reduced as much as possible when the supply

voltage or load current changes. In order to achieve robust

control of the output voltage, i.e., to eliminate the effect of the

supply voltage or load current disturbance, the control strategy

and feedbacks should be properly selected so that the closed-

loop output voltage is independent of either the supply voltage

or the load current and is determined only by the reference

voltage

(1)

where is the averaged value of the inductor voltage and

is the duty ratio required for the switching converter. This

can be expressed as

(2)

Equation (2) deﬁnes the duty ratio required by the buck

converter at a speciﬁc operating point of and

The control circuit can now be constructed to generate the

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

sinusoidal wave, i.e., (the frequency is

much lower than the switching frequency). The output voltage

of the buck converter can be derived as

(3)

where is the reference voltage, is the gain of the

proportional error ampliﬁer, and denotes the duty ratio

generated by the control circuit. The implementation is shown

in Fig. 7(a).

In the practical circuit, the output of the control circuit is

connected to the gate of the active switch in the power stage,

making Therefore, the closed-loop characteristic can

be obtained by equating (2) and (3) as

(6)

and represents a fully rectiﬁed sinusoidal waveform having the

same frequency as the reference signal

The bridge-type synchronizer composed of – as shown

in Fig. 7(a), is used to generate a sinusoidal ac voltage

waveform. In this synchronizer, the switching cycle of the

diagonal pair of switches, or is synchronized

with that of the reference signal For example, and

are turned on at 0, , etc., and and are

turned on at etc., as shown in Fig. 7(b). Therefore,

the fully rectiﬁed sinusoidal voltage can be unfolded

into a sinusoidal output voltage This sinusoidal output

voltage is immune to disturbances in the input voltage

or output current. The proposed closed-loop control system

of the switch-mode dc-to-ac inverter using the buck converter

topology is illustrated in Fig. 7.

(4)

From (4), the output voltage can be found as

(5)

Equation (5) shows that, by the control law (3), the closed-

loop averaged output voltage is forced to be proportional to

a reference voltage.

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

of the buck converter is independent of the supply voltage and

the load current. In other words, the averaged output voltage

remains unchanged, even when there is either a supply voltage

or load current disturbance. The robust control of the output

voltage of the switch-mode inverter is, therefore, achieved.

in Fig. 8(b). The simulation result reveals that when the load

steps between 20 and 10 the output voltage of the inverter

under the proposed control technique is not affected by the

deviations in the load.

Finally, the response of the control system to a step change

in the reference signal is simulated. The result shown in

Fig. 8(c) demonstrates that this control system has fast dy-

namic response.

III. S IMULATION R ESULTS

The proposed switch-mode dc-to-ac inverter using a buck

converter topology with the nonlinear robust control strategy

shown in Fig. 7 is simulated using PSPICE. The parameters of

the buck converter are as follows: input voltage

IV. E XPERIMENTAL R ESULTS

To verify the theoretical analysis and simulation results,

a prototype model of the inverter shown in Fig. 7 has been

breadboarded. The proposed control strategy is implemented.

The parameters of the power converter are as follows: buck

ﬁltering inductor H, buck ﬁltering capacitor

F (two 47 F in parallel), input voltage 20–30 V.

The reference voltage is a fully rectiﬁed sinusoidal waveform

Fig. 9(a) shows the waveform of the output voltage of the

inverter when the supply voltage steps between 20 and 27

V. The oscillogram indicates that the output voltage is not

affected by the large deviations in the supply voltage.

20–30 V;

buck ﬁltering inductor

H; buck ﬁltering capacitor

The effect of step changes in the supply voltage have been

analyzed for the proposed inverter. The simulated result is

shown in Fig. 8(a). This result shows that, when the supply

voltage steps from 20 to 27 V, the output voltage of the inverter

does not change.

The response of the control system to a large disturbance in

the load is also studied by simulation. The result is illustrated

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