International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 6 (2016) pp 3819-3827
© Research India Publications. http://www.ripublication.com
Class D Series Resonant Inverter with PDM Scheme For Induction Heating
Application
S. Jaanaa Rubavathy*
Research Scholar, Faculty of Electrical Engineering, Sathyabama University, Chennai, Tamil Nadu, India.
Dr. P. Murugesan
Professor, Department of EEE, S.A. Engineering College, Chennai, Tamil Nadu, India.
transferred to it. For applications like steel melting, brazing
and surface hardening high operating temperature is required
for which the operating frequency must be selected based on
work piece size and skin depth requirement [4]. The inverter
topologies used in induction appliances are resonant
inverters, like full-bridge, half bridge and single switch
inverters [5-9]. In this study, Class D inverter topology is
used for supplying the induction heating load.
Recently, voltage source series resonant inverter (SRI) has
been suggested for induction heating [10 &11] with various
modulation schemes to vary the output power. In the
conventional fixed frequency modulation techniques, ZVS is
ensured only for a limited range of duty cycle[12]. Power
frequency modulation (PFM) can also be employed for
controlling the output power by controlling the switching
frequency [13-16]. The two output fixed frequency control
techniques employ asymmetrical duty-cycle or asymmetrical
Pulse Width Modulation (PWM) control. It is based on an
unequal duty-cycle operation of the switches in inverter [17].
A two output resonant inverter for cooking application was
given by Jose [18]. Later this was modified into an inverter
designed to give three outputs for induction heating cooking
appliances [19] and now it is designed as two output solution
for induction heating cooking applications with full bridge
inverter topology and fixed frequency control which reduces
the number of switching devices to 2n+2 instead of 4n [20].
Thus, the use of multi-output inverters is better for multiburner cookers: higher utilization of electronics, higher
maximum power and it is possible to share some components
of the converter. In addition to this, they also employ fixed
frequency control technique [21 & 22], in particular
Asymmetrical Voltage Cancellation Control (AVC). The
Finite Element Method (FEM) and the heat generating rate
was derived from the theoretical results [23]. Analysis and
design of a new AC-AC resonant converter applied to
domestic induction heating was employed using half bridge
series resonant inverter, which can be operated with Zero
Voltage Switching (ZVS) during both switch on and switch
off transitions. Hence the output voltage was doubled and the
current in the load was reduced for the same output power
[24]. A quantitative analysis of domestic induction heating
appliances was proposed by considering different parameters
which led to efficiencies higher than 95% [25]. The direct
AC-AC boost resonant converter not only reduces the
component count, but also exhibits higher efficiency levels,
making it appropriate for the domestic IH applications [26].
Abstract
This paper proposes a unique topology of Class D series
resonant inverter with output power control schemes for
Induction Heating (IH) application. The main aim of this
work is to reduce the steady state error so as to get better
performance for induction heating applications under varying
load conditions. The power control strategy allows the class
D series resonant inverter to operate nearly at the resonance
frequency and enhances the power quality of inverter output
power waveform. The class D series resonant inverter here
employs constant frequency Pulse Density Modulation
(PDM) scheme to reduce the switching losses. It also
compares the performance of closed loop output power
control using conventional PID controller and Load Adaptive
Fuzzy logic controller (LAFLC) for reducing steady state
error. To verify the results, the proposed Class D inverter
system
is
designed
and
simulated
using
MATLAB/SIMULINK simulation tool. The PDM method is
implemented by using the PIC16F84A microcontroller. The
proposed system is simulated and validated by experiments
in the laboratory.
Keywords: Pulse Density Modulation, PID controller, Fuzzy
logic controller, Induction heating system, Class D series
resonant inverter.
Introduction
Induction heating is employed in industries due to its various
advantages like safety, cleanliness, non-contact and
efficiency compared with the other classical methods of
heating. Electrical energy supplied to the coil is converted to
thermal energy in the work piece through the
electromagnetic field, without any physical electrical
connection to the work piece. The induced „eddy‟ current
intensity is maximum at the surface of the work piece and
decreases towards its center as a function on the ratio:
thickness/skin depth. As the ratio increases, a greater
proportion of the total power is dissipated in the outer
surface; this phenomenon is called the skin depth.
In general, the electromagnetic induction heating is a clean,
non-contact and low loss heating method due to
semiconductor devices based on Faraday‟s law and Joule‟s
heating principle [1]. In order to have desired temperature
level at work piece, IH load has to be controlled smoothly
and accurately [2 & 3] by means of electric power that is
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 6 (2016) pp 3819-3827
© Research India Publications. http://www.ripublication.com
Also a new power control based Phase Shift (PS) technique
has been implemented in full-bridge inverter fed series
resonant load circuit for IH applications, which ensures ZVS
operation for all output power levels and load conditions
[27]. The above literature, however, does not deal with the
power control strategy. In PDM control method, Zero
Voltage Switching (ZVS) condition is maintained throughout
the operation, which satisfies the variable power requirement
of the load with reduced switching losses. Switching losses
are kept minimum due to its constant frequency mode of
operation. This paper discusses the output power control of
Class D resonant inverter fed induction heating system using
PDM technique in open loop as well as in closed loop
controls. In closed loop control, conventional PID controller
performance is compared with load adaptive Fuzzy logic
controller for Class D resonant inverter in terms of output
power and temperature rise.
The paper is organized as follows: In section 2, the
description of Class D series resonant inverter topology is
presented. In section 3, open loop simulation results of a
Class D series resonant inverter are presented. In section 4,
Closed loop simulation results with PID controller & Fuzzy
Logic Controller (FLC) are presented and compared. In
section 5, experimental results of the prototype are presented.
Finally, the conclusions of the work are provided in section
6.
Consider the equivalent circuit of series resonant inverter as
shown in Figure 2. Let Io be the current through induction
load, Vo the voltage across induction load, and Vc the voltage
across resonant capacitor.
Figure 2: Circuit model of series resonant inverter
The voltage balance equation is given by
Vin = I0R+ L dI/dt + Vc
(1)
Ic = Cr dVc/dt
(2)
Under resonant condition, (XL = XC), output power of
converter is obtained across the resistor R,
Pout = I02R /2
Description of class D inverter topology
(3)
And the quality factor of the coil is given by,
One of the most popular resonant inverters used for induction
heating application is Class D series resonant inverter. The
circuit configuration of Class D series resonant inverter
topology shown in Figure 1 offers more advantages. It is
basically an AC-AC conversion circuit for producing high
frequency AC (HFAC) from utility frequency AC for
induction heating applications. It consists of an uncontrolled
rectifier which is used to convert the given single phase AC
input voltage (Vin) of 50Hz frequency into its equivalent DC
voltage. The DC output obtained from the uncontrolled
rectifier is then filtered by using a capacitive filter (C1). Pure
DC is now applied to the Class D Series Resonant Inverter to
produce HFAC, which is required for induction heating load
and the induction pan gets heated up. The two MOSFET
switches M1 & M2 are provided with anti-parallel connection
of diodes, which are alternately operated with the high
frequency PDM pulses generated by logic circuit.
Q = ωsL / R
(4)
Hence, whenever there is a variation in load parameters, it is
required to change the operating conditions like duty ratio
and operating frequency of the inverter.
Open loop control of Class-D Series Resonant Inverter
The Class D series resonant inverter fed induction heating
system is modeled and simulated by using the MATLAB/
SIMULINK software. The system data used for simulation
are given in Table. 1. The Pulse Density Modulation (PDM)
pulses for the MOSFET switches M1 & M2 are shown in
Figure 3a. By controlling the duty period DPDM of the low
frequency signal, the output power can be varied. The value
of DPDM considered for this simulation is 80%. Figs. 3b & 3c
illustrate the output voltage waveform and RMS voltage
waveform for 0. 8 DPDM. The output current waveform and
RMS current waveform for 0. 8 DPDM are presented in Figs.
3d & 3e respectively. The output voltage and the output
current waveforms are discontinuous in nature, hence the
output power and mean power are measured and they are
given in Figs. 3f & 3g respectively. The average power
output obtained is 80watts since the DPDM= 80%. The value of
average output voltage increases with increase in DPDM.
Figure 1: Class D Series Resonant Inverter
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 6 (2016) pp 3819-3827
© Research India Publications. http://www.ripublication.com
Table 1: Design parameters
8
6
Pulses
Parameter’s Name
AC input voltage
DC link capacitance
Load Inductance
Resonant Capacitance
Load Resistance
Duty ratio
Switching Frequency
Resonant frequency
2
1
0
-1
Class D inverter
50V (Peak)
90000e-5F
50. 92e-6H
0. 65µF
1Ω
80%
22kHz
20kHz
Current (A)
4
Pulses
-8
0
0.05
0.1
0.15
0.2
0.25
Time (s)
0.3
0.35
0.4
0.45
0.5
Figure 3d: Output current waveform with PDM technique
for DPDM =0. 8
0
0.1
0.2
0.3
0.4
4.5
0.5
4
3.5
0
0.1
0.2
0.3
0.4
3
0.5
2
1
0
-1
0
0.05
0.1
0.15
0.2
Current (A)
Pulses
Pulses
-2
-6
Time (s)
2
1
0
-1
0
-4
Time (s)
2
1
0
-1
2
0.25
0.3
Time (s)
0.35
0.4
0.45
2.5
2
1.5
0.5
1
0.5
0
0.1
0.2
0.3
0.4
0.5
0
Time (s)
0
0.05
0.1
0.15
0.2
0.25
Time (s)
0.3
0.35
0.4
0.45
0.5
0.45
0.5
Figure 3e: RMS current waveform
Figure 3a: Switching pulses waveform
100
120
100
50
Power (W)
Voltage (V)
80
0
60
40
20
-50
0
-100
0
0.1
0.2
0.3
Time (s)
0.4
-20
0.5
0
0.05
0.1
0.15
0.2
0.25
Time (s)
0.3
0.35
0.4
Figure 3f: Output power waveform with PDM technique for
DPDM =0. 8
Figure 3b: Output voltage waveform with PDM technique
for DPDM = 0. 8
100
35
90
30
80
70
60
Power (W)
Voltage (V)
25
20
15
50
40
30
20
10
10
5
0
0
-10
0
0.05
0.1
0.15
0.2
0.25
0.3
Time (s)
0.35
0.4
0.45
0.5
0
0.05
0.1
0.15
0.2
0.25
Time (s)
0.3
0.35
0.4
Figure 3g: Mean power waveform
Figure 3c: RMS voltage waveform
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0.45
0.5
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 6 (2016) pp 3819-3827
© Research India Publications. http://www.ripublication.com
Closed loop control of Class-D Series Resonant Inverter
With PID Controller
Simulink model of closed loop controlled Class D series
resonant inverter fed induction heating system with PID
controller is carried out by means of MATLAB simulink.
Any change in load parameters causes dip in the inverter
output voltage. Thus error e(s) is processed by the PID
controller. The control signal obtained from the output of
PID controller is designed with gains Kp=1e-4, Ki=5e-4 &
Kd=1e-7 as follows:
C(s) = {Kp + (Ki/s) + SKd}*e(s)
(5)
The PID controller regulates the output voltage with a large
peak overshot, settling time, and the steady state error. The
main drawback of this controller is the non-linear variation in
IH load parameters. Hence to improve the dynamic response
of the system, fuzzy-logic control scheme is proposed. The
simulation is done for different values of set power. Output
voltage, RMS value, and output current are shown in Figs.
4a, 4b, & 4c respectively. RMS output current, output power
waveform, and mean power are shown in Figs. 4d, 4e, & 4f
respectively. The RMS current is 3. 5 amperes. The RMS
power is approximates to 60 watts.
8
6
Current (A)
4
2
0
-2
-4
-6
-8
0
0.05
0.1
0.15
0.2
0.25
Time (s)
Figure 4c: Output current waveform for set power equal to
60 W
Figure 4d: RMS output current waveform
Figure 4a: Output voltage waveform for set power equal to
60W
Figure 4e: Output power waveform for set power equal to
60 W
30
Voltage (V)
25
20
15
10
5
0
0
0.1
0.2
0.3
0.4
0.5
Time (s)
Figure 4f: Mean power waveform for set power 60 W
Figure 4b: RMS output voltage waveform
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 6 (2016) pp 3819-3827
© Research India Publications. http://www.ripublication.com
Table 2: Rule base with 25 rules
With fuzzy controllers
In recent years, FLC has been widely used for many
domestic and industrial applications because it is defined as a
theory of vagueness & uncertainties. It is a non-linear control
technique which is employed to the controling of inverter to
improve the dynamic response of the system as suggested in
the literature [28]. The centroid defuzzification technique is
employed in this work. The output power is required to be
varied in accordance with reference power set by the user.
The output of FLC is used to vary the DPDM of MOSFET
switches. FLC with 2 inputs (Error and Change in error) and
one output are converted into 5 triangular functions as shown
in Figs. 5a, 5b, & 5c respectively. And the Rule Base is
given in Table. 2. The surface plot is shown in Figure 5d.
e /Δe
NB
NS
Z
PS
PB
NB
Z
PB
NB
NB
NS
NS
PS
Z
NS
NS
PB
Z
PB
NB
Z
PB
NB
PS
NB
PS
PS
Z
PS
PB
NS
NS
PB
PS
Z
Figure 5d: Surface plot
The fuzzy controlled Class D series resonant inverter system
is also simulated using MATLAB simulink Fuzzy toolbar.
Actual power is measured using P-Q block and it is
compared with reference power. The error and its derivative
are applied to the fuzzy block. The pulse is adjusted such that
the actual power is equal to the set power. Output voltage
waveform, RMS voltage, output current waveform, RMS
output current and output power waveforms are shown in
Figs. 5e, 5f, 5g, 5h, & 5i respectively. The mean power is
shown in Figure 5j. The comparison of time domain
specifications of PID & Fuzzy controlled systems is given in
Table 3. It can be seen that fuzzy controlled system settles
faster than PID controlled system. The steady state error in
power is less with FLC.
Figure 5a: Triangular membership function for error
80
60
Figure 5b: Triangular membership function for change in
error
Voltage (V)
40
20
0
-20
-40
-60
-80
0
0.1
0.2
0.3
0.4
0.5
Time (s)
Figure 5e: Output voltage waveform for set power equal to
60W
Figure 5c: Triangular membership function for control
output
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 6 (2016) pp 3819-3827
© Research India Publications. http://www.ripublication.com
80
30
70
25
60
Power (W)
Voltage (V)
20
15
10
50
40
30
20
10
5
0
0
0
0.1
0.2
0.3
0.4
0
0.05
0.1
0.15
0.2
0.25
Time (s)
0.3
0.35
0.4
0.45
0.5
0.5
Time (s)
Figure 5j: Mean power waveform for set power 60 W
Figure 5f: RMS output voltage waveform
Table 3: Comparison of time domain specifications
8
Controllers
Settling time (s) Steady state error (W)
4
PI Controller 1. 5
0. 8
0. 1
FLC
6
Current (A)
4
2
0
-2
Multiple Power Settings using FLC
Simulation studies with multiple power settings are also
performed. Set power of 60W upto 0. 25 sec and then 20W is
used. FLC is adaptive for multiple set powers, whereas PID
requires gain adjustment for different output levels. The
output voltage waveform, RMS output voltage, output
current waveform, and RMS output current are shown in
Figures 5k, 5l, 5m, & 5n respectively. The output power
waveform and the mean power waveform are shown in
Figures 5o & 5p respectively. It is observed from Figure 5p
that the power reduces from 60W to 20W.
-4
-6
-8
0
0.1
0.2
0.3
0.4
0.5
Time (s)
Figure 5g: Output current waveform for set power equal to
60W
3.5
3
80
60
2
40
1.5
Voltage (V)
Current (A)
2.5
1
0.5
0
0
20
0
-20
-40
-60
0.1
0.2
0.3
0.4
0.5
-80
Time (s)
Figure 5h: RMS output current waveform
0
0.05
0.1
0.15
0.2
0.25
Time (s)
0.3
0.35
0.4
0.45
0.5
Figure 5k: Output voltage waveform for set power equal to
60 W till 0. 25s and then 20W
100
40
80
30
40
Voltage (V)
Power (W)
35
60
20
25
20
15
10
0
5
-20
0
0.1
0.2
0.3
0.4
0
0.5
Time (s)
0
0.05
0.1
0.15
0.2
0.25
Time (s)
0.3
0.35
0.4
0.45
0.5
Figure 5l: RMS voltage waveform for set power equal to 60
W till 0. 25s and then 20W
Figure 5i: Output power waveform for set power equal to
60W
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 6 (2016) pp 3819-3827
© Research India Publications. http://www.ripublication.com
full bridge uncontrolled rectifier was constructed by using
four IN4007 diodes to give DC supply to the Class D
inverter. Then Class D inverter was constructed by using two
IRF840 MOSFETs for the conversion of DC into HFAC.
The control logic for PDM technique was implemented by
using a PIC 16F84 micro-controller, which gives driving
pulses for MOSFETs 1 & 2. These control pulses were
amplified using IR2110 drivers. The output pulses from the
driver are shown in Figure 6b. The output voltage is shown
in Figure 6c. And the Output voltage along with driving
pulse waveform is given in Figure 6d. The 10cm heating coil
of gauge 18 having 90 turns per coil and a resistance of 0.
0645 ohms was considered. Temperature was measured
using industrial thermometer and it reached 500ºC in 125
seconds for class D inverter system. It could be noticed that
the oscillograms were in agreement the simulation results.
8
6
Current (A)
4
2
0
-2
-4
-6
-8
0
0.05
0.1
0.15
0.2
0.25
Time (s)
0.3
0.35
0.4
0.45
0.5
Figure 5m: Output current waveform for set power equal to
60 W till 0. 25s and then 20W
3.5
3
Current (A)
2.5
2
1.5
1
0.5
0
0
0.05
0.1
0.15
0.2
0.25
Time (s)
0.3
0.35
0.4
0.45
0.5
Figure 5n: RMS current waveform for set power equal to 60
W till 0. 25s and then 20W
120
100
Power (W)
80
Figure 6a: Hardware layout of Class D inverter fed IH
system
60
40
20
0
-20
0
0.05
0.1
0.15
0.2
0.25
Time (s)
0.3
0.35
0.4
0.45
0.5
Figure 5o: Power waveform for set power equal to 60 W till
0. 25s and then 20W
80
70
60
Power (W)
50
Figure 6b: Driving pulses of switches M1 & M2 (X-axis
100μs/div, Y-axis 10v/div)
40
30
20
10
0
-10
0
0.05
0.1
0.15
0.2
0.25
Time (s)
0.3
0.35
0.4
0.45
0.5
Figure 5p: Mean power waveform for set power equal to 60
W till 0. 25s and then 20W
Experimental Results
The laboratory model for class D Series resonant inverter fed
induction heater system rated 100W was fabricated and
tested to validate the PDM scheme. The hardware layout of
Class D inverter fed IH system is shown in Figure 6a. The
Figure 6c: Output voltage waveform (X-axis 100μs/div, Yaxis 30v/div)
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 6 (2016) pp 3819-3827
© Research India Publications. http://www.ripublication.com
[6]
[7]
Figure 6d: Channel 2: Driving pulse (X-axis 100μs/div, Yaxis 10v/div), Channel 1: Output voltage(X-axis 100μs/div,
Y-axis 50v/div)
[8]
Conclusion
The open loop response of Class D resonant inverter, closed
loop response of PID controlled and fuzzy controlled
systems were simulated and the results were presented.
Hardware implementation of Class D resonant inverter fed
induction heating system was performed to study the
controller response. It was found that the Fuzzy controlled
system settled quickly as compared with PID controlled
system and that the RMS value of square shaped output
voltage & output current waveform was higher than sine
wave output and hence quick heating became possible. The
result showed that the system with FLC improved the time
response with lower settling time and lower steady state
error. The drawback of fuzzy controlled system is that it
requires data from PID controlled system. The comparison of
response with FLC & ANN is a possible future work.
[9]
[10]
[11]
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