1.
Research Skills
ME(Electrical) Semester 1
By
YAGNIK UTSAV (Roll No. 2004)
A HYBRID CONTROL
ALGORITHM FOR
VOLTAGE REGULATION
IN DC-DC BOOST
CONVERTER
1

2.
 Innovated by
C. Sreekumar and Vivek Agarwal, Senior Member,
IEEE
 IEEE transactions on industrial electronics, Volume
55, No. 6, June 2006
 Presented by:
 Utsav Yagnik
 M.E. Electrical(Roll No. 2004)
 Shantilal Shah Engineering College, Bhavnagar
ABOUT THE PAPER
2

3.
3
Sr. Slide title From To
1 Abstract 4 6
2 Introduction 7 7
3 Earlier Approaches 8 11
4 Typical DC-DC Boost Converter 12 12
5 Hybrid Modelling & Automation Representation 13 21
6 Guard Selection Problem 22 22
7 CCM Operation 23 28
8 DCM Operation 29 31
9 Guard conditions 32 32
10 Simulation Parameters 33 33
11 Simulation Results 34 34
12 Operation at CCM-DCM boundary 35 36
13 Operation Under Input Voltage Disturbances 37 37
14 Impact of Higher Trap Frequency 38 40
15 Experimental Verification 41 41
16 Conclusion 42 42
17 Salient Features 43 45
I
N
D
E
X

4.
A state trajectory approximation based
switching control to regulate the output
voltage of a representative second order dc-dc
converter.
Main objective is to trap the system in a
stable limit cycle, but without violating the
limits of voltage regulation.
The difference between this method and
earlier methods is the applicability to the CCM
and DCM modes of opration.
ABSTRACT
4

5.
Which makes this algorithm suitable over wide
range of load and various disturbances.
The control problem is simplified to guard
selection problem by introducing the Hybrid
automation representation.
In this Hybrid automation representation, the
guard conditions are derived which are governing
the transition from one discrete state to another.
This algorithm is implemented by State Flow
Chart method in MATLAB.
ABSTRACT
5

6.
The hybrid control law is also validated by
using a laboratory prototype.
So, all in all this whole algorithm and hybrid
model is used to find a single model which
will be suitable for both CCM and DCM modes
of operations.
ABSTRACT
6

7.
DC-DC converters are:
1. Highly non-linear
2. Discontinuous in time
3. Variable in structure(i.e. they work under
various topologies based on the mode of
operation)
4. CCM and DCM
Complete range of converter will include CCM and
DCM
So, we need a common representation that will
cover entire operating range.
INTRODUCTION
7

8.
Using transfer function:
States of system are averaged around a
normal point and linearized via s-domain.
Same thing can be achieved by Langrangian
approach in time domain.
Now a days we can also get Numerical state
space value model for control design.
But all above will describe dynamics around
operating point but will fall short when
disturbances occur
EARLIER APPROACHES 1
8

9.
We can also design State space model
But it will also require different models for
CCM and DCM.
Sometimes DCM is overlooked if persisted for
shorter duration.
EARLIER APPROACHES 2
9

10.
One can also go for PWM(Pulse Width
Modulation) which has which has two types of
control:
1. Voltage mode control
2. Current mode control
But both of above will have inherent instability
and sub harmonic oscillations when operated
under constant frequency PWM.
EARLIER APPROACHES 3
10

11.
We can also do Linear system design
techniques in frequency domain.
But it also has constraints of right hand
plane zero in average model.
And since the location of zero is inversely
proportional to inductor current, as we
increase the load current, the zero will go
towards low frequency.
This will introduce phase lag and result in
less availability of band width.
EARLIER APPROACHES 4
11

12.
A TYPICAL DC-DC BOOST CONVERTER
12

13.
𝑥 = 𝑅 𝑛 is a continuous state space.
𝑄 = 𝑞1, 𝑞2, … 𝑞 𝑛 are finite set of discrete
states.
The continuous state space specifies the
possible values of the continuous states for all
q’s and q ε Q shows ON/OFF configurations.
HYBRID MODELLING AND AUTOMATION
REPRESENTATION
13

14.
The common state space equation is
𝑥 𝑡 = 𝐴𝑞𝑥 𝑡 + 𝐵𝑞 = 𝑓𝑞 𝑥 𝑡
Where
𝑥 ∈ 𝑋, 𝐴𝑞 ∈ 𝑅 𝑛 × 𝑛 𝑎𝑛𝑑 𝐵𝑞 ∈ 𝑅 𝑛 ×1
If k are switching elements then 2 𝑘
are
possible discrete states.
HYBRID MODELLING AND AUTOMATION
REPRESENTATION
14

15.
State SW1 SW2
𝑞1 ON OFF
𝑞2 OFF ON
𝑞3 OFF OFF
𝑞4 ON ON
HYBRID MODELLING AND AUTOMATION
REPRESENTATION
where,
SW1 = main controllable switch
SW2 = power diode
15

16.
Here 𝑞4 is not possible because it will bypass
the load.
∴ 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑄 = 𝑞1, 𝑞2, 𝑞3
∴ total possible events E =
𝑞1, 𝑞2 , 𝑞2, 𝑞1 , 𝑞2, 𝑞3 , 𝑞3, 𝑞1
First two events corresponds to the CCM
operation and 1st, 3rd & 4th events corresponds
to DCM operation.
HYBRID MODELLING AND AUTOMATION
REPRESENTATION
16

17.
States of the system are taken as (𝑖 𝐿, 𝑣 𝑜).
Where,
𝑖 𝐿 = Instantaneous Inductor Current &
𝑣 𝑜 = Instantaneous Output Voltage
Let,
𝑉 𝑚 = Input voltage
L = Input inductor
C = Output capacitor
R = Load resistance
HYBRID MODELLING AND AUTOMATION
REPRESENTATION
17

18.
Thus, the system can be represented in terms
of three state equations corresponding to the
𝑞 𝑖(1,2,3) as below…
HYBRID MODELLING AND AUTOMATION
REPRESENTATION
18

19.
Under closed loop conditions, control
operation can be considered as an interacting
combination of two hybrid automations.
In which, the discrete evaluation depends
upon continuous signal 𝑥(𝑡) and the
continuous evaluation depends upon discrete
symbol 𝜎 = 𝜎1, 𝜎2, 𝜎3
HYBRID MODELLING AND AUTOMATION
REPRESENTATION
19

20.
Here, the control problem is to find guard
conditions 𝐺 𝑖𝑗 which cause transition from 𝑖 𝑡ℎ
discrete state to 𝑗 𝑡ℎ discrete state while
satisfying the system requirements.
In this paper, approach is to determine
appropriate switching guards for trapping the
system in to a limit cycle satisfying the
Voltage regulation constraints.
HYBRID MODELLING AND AUTOMATION
REPRESENTATION
20

21.
HYBRID AUTOMATION REPRESENTATION
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 For CCM, we need to determine two guards. i.e. 𝐺12
and 𝐺21.
 For DCM, we need to determine three guard. i.e.
𝐺12, 𝐺23 𝑎𝑛𝑑𝐺31.
 The generation of control pulses depends upon
similar conditions based on the respective guards
except that in the CCM mode, the third mode is not
present, and transitions from mode 2 to mode 3
and mode 3 to mode 1 are not defined.
 Transition from one mode to other mode takes
place when the sensed state variables exceed the
relevant guard conditions.
GUARD SELECTION PROBLEM
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23.
CCM OPERATION
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24.
At dT, system dynamics changes from mode 1
and mode 2.
At T, system switches back to mode 1.
During 0 ≤ 𝑡 ≤ 𝑑𝑇
𝑑𝑖 𝐿
𝑑𝑡
=
𝑉𝑖𝑛
𝐿
∴ 2∆𝑖 𝐿 =
𝑉𝑖𝑛
𝐿
𝑑𝑇 … (1)
CCM OPERATION
24

25.
Also,
𝑑𝑣 𝑜
𝑑𝑡
=
−𝑉𝑜
𝑅𝐶
∴ −2∆𝑣 𝑜 =
−𝑉𝑜
𝑅𝐶
dT … 2
From (1) & (2)
∆𝑖 𝐿 =
𝑅𝐶𝑉 𝑖𝑛
𝐿𝑉 𝑜
∆𝑣 𝑜 … (3)
CCM OPERATION
25

26.
The ripples in the output voltage and inductor
current are related by equation 3.
In CCM, for the given voltage swing, the
current swing along with the average inductor
current is used to define the guard conditions,
which governs the transition between two
modes of operation.
CCM OPERATION
26

27.
The average inductor current can be
determined by equating the converter output
power with converter input power as below
𝐼 𝐿 =
𝑉 𝑜
2
𝑅𝑉 𝑖𝑛
… (4)
From equations 3 and 4 the guard conditions
are:
𝐺12 → 𝑖 𝐿 ≥ 𝐼 𝐿 + ∆𝑖 𝐿
𝐺21 → 𝑖 𝐿 ≤ 𝐼 𝐿 − ∆𝑖 𝐿
CCM OPERATION
27

28.
These guards cause the system to settle in
some limit cycle, depending upon the load
conditions of the system.
The load current an the output voltage have
to be sensed to determine the guards.
As the load decreases, the average inductor
current reduces and becomes exactly half of
the current ripple at the CCM-DCM boundary.
Thereafter, voltage regulation is lost and the
algorithm is modified for the DCM operation.
CCM OPERATION
28

29.
DCM OPERATION
29

30.
The output voltage
𝑉𝑜 =
𝑉𝑖𝑛 𝑑1 + 𝑑2
𝑑2
The inductor current
𝐼 𝐿 =
𝑉 𝑜 𝑑1+𝑑2
𝑅𝑑2
Or 𝐼 𝐿 =
𝐼 𝑝 𝑑1+𝑑2
2
Where,
𝐼 𝑝 =
2𝑉 𝑜 𝑉 𝑜 −𝑉 𝑖𝑛
𝑅𝑓𝐿
… (5)
DCM OPERATION
30

31.
To define the guard condition 𝐺12, based on 𝐼 𝑃
should satisfy the equation 5.
Which means that 𝐺12 depends on frequency.
So the condition for the trap frequency can be
obtained as below…
𝑓 𝑇 >
𝑉𝑜 − 𝑉𝑖𝑛
2∆𝑣 𝑜 𝑅𝐶
… (6)
DCM OPERATION
31

32.
𝐺12 → depends on equation 5 and equation 5
depends on equation 6.
𝐺23 → natural guard, i.e. transition from mode
2 to mode 3 is autonomous due to 𝑖 𝐿 = 0.
𝐺31 → the reference voltage 𝑣 𝑜 = 𝑉𝑜 can be
taken as guard condition for controlling ∆𝑣 𝑜
swings.
GUARD CONDITIONS
32

33.
The proposed algorithm is tested in MATLAB
with following parameters:
1. 𝑉𝑖𝑛 = 15 𝑉
2. 𝑉𝑜𝑢𝑡 = 30 𝑉
3. 𝑅 = 20 Ω
4. 𝐿 = 350 𝜇𝐻
5. 𝐶 = 10 𝜇𝐹
6. ∆𝑣 𝑜 = 0.5 𝑉
SIMULATION PARAMETERS
33

34.
SIMULATION RESULTS
34

35.
OPERATION AT CCM-DCM BOUNDARY
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36.
At 6ms, when the load is abruptly changed
from 45 Ω to 95 Ω, the voltage jumps to 31.2
V but soon settles down the desired value of
30 V as shown in the figure earlier.
So, the transient response during transition
from CCM to DCM is found satisfactory and
the system does not become UNSTABLE.
OPERATION AT CCM-DCM BOUNDARY
36

37.
According to slide no. 35,
A step rise of 5V in the input is given at 18
ms.
A Sinusoidal disturbance of peak 2 V at
frequency of 4000 rad/s is given.
But the system can withstand these as it
doesn’t become unstable.
OPERATION UNDER INPUT VOLTAGE
DISTURBANCES
37

38.
For earlier waveforms, the trap frequency was
20 kHz.
Trap frequency has minimum value of 3.9 kHz
for 400 Ω and is as high as 16.6 kHz for load
of 95 Ω.
And now trap frequency of 30kHz is applied
for the load of 440 Ω and it is observed that
system remains stable.
IMPACT OF HIGHER TRAP FREQUENCY(𝑓 𝑇)
38

39.
IMPACT OF HIGHER TRAP FREQUENCY(𝑓 𝑇)
39

40.
A higher trap frequency is desirable as far as
the speed of response, voltage ripple, current
ripple and regulations are considered.
But such frequency should be considered only
and only if the other parameters such as
power loss, driver circuit limitations, device
speed etc. permit.
IMPACT OF HIGHER TRAP FREQUENCY(𝑓 𝑇)
40

41.
Experimental verification of control circuit in
real time is done by using analogue and
digital ICs and other discrete components and
similar waveforms are observed.
For SW1 MOSFET IRF450 and for SW2 CSD
10030 ultrafast diode are used.
EXPERIMENTAL VERIFICATION
41

42.
A new technique for hybrid control of dc-dc
boost converter is proposed in which the
control problem is simplified in to guard
selection problem in a hybrid automation
system to obtain required voltage regulation.
Simulation is done in MATLAB/SIMULINK
using the state flow chart feature.
CONCLUSION
42

43.
Minimal computations in algorithm making it
good choice for real time control.
Complete cycle of operation i.e. CCM and
DCM are covered.
The approach is generic and can be
implemented for other similar second order
converters.
The proposed control has variable switching
frequency with the maximum allowable
output voltage ripple in the CCM operation.
SALIENT FEATURES
43

44.
The operation in the DCM is very smooth
even under disturbances, but since the guard
conditions depend upon the load value,
accurate load sensor is required.
PWM control is not applied.
Here, the output filter capacitor value is
taken as 10 𝜇𝐹. A higher value of filter
capacitor will improve transient response but
finer tuning of trap frequency might be
required in DCM operation.
SALIENT FEATURES
44

45.
The load is varied by toggle switch in this
experiment so the change in the switch will
change in its dynamics and will effect
operation.
The parasitic elements are not considered to
reduce the computational complexity.
Nevertheless, it is proved through practical
experiments that the given scheme gives
good regulation characteristics over a wide
range of load and line disturbances.
SALIENT FEATURES
45

46.
THANK YOU
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