Home > DC-DC Converters Via MATLAB/SIMULINK

DC-DC CONVERTERS
VIA MATLAB**/**SIMULINK

MOHAMED ASSAF, D. SESHSACHALAM, D. CHANDRA, R. K. TRIPATHI

Electrical Engineering Department

Motilal Nehru National Institute of Technology

Allahabad, Utter Pradesh- 211004

INDIA

Index Terms—Switching converters, MATLAB/SIMULINK, system modeling, cascade control, subsystems

**1
Introduction **

Controller design for any system
needs knowledge about system behavior. Usually this involves a mathematical
description of the relation among inputs to the process, state variables,
and output. This description in the form of mathematical equations which
describe behavior of the system (process) is called model of the system.
This paper describes an efficient method to learn, analyze and simulation
of power electronic converters, using system level nonlinear, and switched
state- space models. The MATLAB/SIMULINK software package can be advantageously
used to simulate power converters. This study aims at development of
the models for all basic converters and studying its open loop response,
so these models can be used in case of design of any close loop scheme.
Also as a complete exercise a closed scheme case has
been studied using cascaded control for a boost converter.

**2 Simulink Model Construction
of DC-DC Switching Converter**

System modeling is probably the most important phase in any form of system control design work. The choice of a circuit model depends upon the objectives of the simulation. If the goal is to predict the behavior of a circuit before it is built. A good system model provides a designer with valuable information about the system dynamics. Due to the difficulty involved in solving general nonlinear equations, all the governing equations will be put together in block diagram form and then simulated using Matlab’s Simulink program. Simulink will solve these nonlinear equations numerically, and provide a simulated response of the system dynamics.

*A. Modeling Procedure*

To obtain a nonlinear model for power electronic circuits, one needs to apply Kirchhoff's circuit laws. To avoid the use of complex mathematics, the electrical and semiconductor devices must be represented as ideal components (zero ON voltages, zero OFF currents, zero switching times). Therefore, auxiliary binary variables can be used to determine the state of the switches. It must be ensure that the equations obtained by the use of Kirchhoff's laws should include all the permissible states due to power semiconductor devices being ON or OFF.

The steps to obtain a system-level modeling and simulation of power electronic converters are listed below.

* *
1) Determine the state variables of the power circuit in order to write
its switched state-space model, e.g., inductor current and capacitor
voltage.

*2)*
Assign integer variables to the power semiconductor (or to each switching
cell) ON and OFF states.

*3)*
Determine the conditions governing the states of the power semiconductors
or the switching cell.

*4)*
Assume the main operating modes of the converter (continuous or discontinuous
conduction or both) or the modes needed to describe all the possible
circuit operational modes. Then, apply Kirchhoff's laws and combine
all the required stages into a switched state-space model, which is
the desired system-level model.

*5)*
Write this model in the integral form, or transform the differential
form to include the semiconductors logical variables in the control
vector: the converter will be represented by a set of nonlinear differential
equations.

*6)*
Implement the derived equations with "SIMULINK" blocks (open
loop system simulation is then possible to check the obtained model).

*7)*
Use the obtained switched space-state model to design linear or nonlinear
controllers for the power converter.

*8)*
Perform closed-loop simulations and evaluate converter performance.

9)
The algorithm for solving the differential equations and the step size
should be chosen before running any simulation. The two last steps are
to obtain closed-loop simulations [2].

**3 Simulation Open-Loop Modeling
of DC-DC Converters**

*A. Buck
Converter Modeling*

The buck converter
with ideal switching devices will be considered here which is operating
with the switching period of T and duty cycle D Fig. 1, [1]. The state
equations corresponding to the converter in continuous conduction mode
(CCM) can be easily understood by applying Kirchhoff's voltage law on
the loop containing the inductor and Kirchhoff's current law on the
node with the capacitor branch connected to it. When the ideal switch
is ON, the dynamics of the inductor current and the capacitor voltageare
given by,

and when the
switch is OFF are presented by,

**Fig 2 Open-loop
modeling of Buck DC-DC converters**

**Fig.1 DC-DC Buck Converter**

** These equations ar**e
implemented in Simulink as shown in Fig. 2 using multipliers, summing
blocks, and gain blocks, and subsequently
fed into two integrators to obtain the states and [2][3] [4].

*B. Boost Converter
Modeling*

The boost converter
of Fig. 3 with a switching period of T and a duty cycle of D is given.
Again, assuming continuous conduction mode of operation, the state space
equations when the main switch is ON are shown by, [1].

and when the switch is OFF

Fig. 4 shows These equations
in Simulink using multipliers, summing blocks, and gain
blocks, and subsequently fed into two integrators to obtain the states
and , [2][3][4]

**Fig. 4 Open-loop
modeling of Boost DC-DC converters**

In Fig. 5 a
DC-DC buck-boost converter is shown. The switching period is T and the
duty cycle is D. Assuming continuous conduction mode of operation, when
the switch is ON, the state space equations are given by, [1]

and when the
switch is OFF

These equations are implemented in Simulink as shown in Fig. 6 using multipliers, summing blocks, and gain blocks, and subsequently fed into two integrators to obtain the states and , [2] [3] [4].

**Fig. 6 Open-loop
of Buck-Boost DC-DC Converters**

*D. Cuk Converter Modeling*

The Cuk converter
of Fig. 7 with switching period of T and duty cycle of D is considered.
During the continuous conduction mode of operation, the state space
equations are as follows, [1]

When the switch
is OFF
the state space equations are represented by

**Fig.7 DC-DC
Cuk converter**

these equations
are implemented in Simulink as shown in Fig. 8 using multipliers, summing
blocks, and gain blocks, and subsequently
fed into two integrators
to obtain the states and , [2] [3] [4].

Each of the power electronic models represents subsystems within the simulation environment. These blocks have been developed so they can be interconnected in a consistent and simple manner for the construction of complex systems. The subsystems are masked, meaning that the user interface displays only the complete subsystem, and user prompts gather parameters for the entire subsystem. Relevant parameters can be set by double-clicking a mouse or pointer on each subsystem block, then entering the appropriate values in the resulting dialogue window [4].

To
facilitate the subsequent simulation analysis and feedback controller
verification, the pulse-width-modulation signal to control the ideal
switch can also be built into the masked subsystem Fig. 9(a) and Fig.
9(b). For each converter to verity it’s working in open loop configuration
trigger pulses have been derived using a repeating sequence generator
and duty cycle block. Function block compares the duty cycle and saw
tooth from repeating sequence- derived trigger pulses are connected
as

an input to
the switch control. Hence inputs for the masked subsystem are duty ratio
and input voltage, and the outputs are chosen to be inductor current,
capacitor voltage, and output voltage. When double-clicking the pointer
on the masked subsystem, one enters parameter values of the switching converter circuit in
a dialogue window. The intuitive signal flow interface in SIMULINK makes
this mathematical model and its corresponding masked subsystem very
easy to create.

**4
Simulation Closed-Loop of DC-DC Converters Using Cascaded Control**

The simulation model for cascaded control of DC-DC switching converters is build using the above-mentioned steps is as shown in Fig. 10. The DC-DC buck, boost, buck-boost, and Cuk converters was previously designed, and simulated on digital computer using Matlab package with the parameters given in Table 1, and Table 2. Inductor current and capacitor voltage for open loop simulation of all converters are as shown in Fig.11 (a, b, c, and d).

Table 1 Buck, Boost, and Buck-Boost converters parameters | Table 2 Cuk converter parameters | |||||||||||||

24, 10, 24 Respectively | 69 | 220 | 13 | 100 | 12, 20, -24
Respectively |
24 | 69 | 19 | 47 | 220 | 100 | 15 | 31.8 |

**Fig. 9(a) Subsystem for
Buck, Boost and Buck-Boost converters**

Results of Closed loop using
a cascaded control scheme for a boost converter is shown in Fig. 12(a).
Here the output voltage rises up to 21.3V (6.5%) for the step variation
of load from 10
to 13
(30%). The output voltage resumes its reference value (of 20V) within
15ms after the transient variation of load. As per fig 12(b), for a
step change at the input voltage from 10V to18 V (80%) (at 0.5 Sec instant),
a satisfactory performance is obtained in the output voltage which has
a rise up to 22.8V (14%), but it is quickly dropped to its set value
(20V) within 16 ms. Simulation results verify that the control scheme
in this section gives stable operation of the power supply. The output
voltage and inductor current can return to the steady state even when
it is affected by line and load variation.

**5
Conclusions**

**Fig.10 Simulink block diagram
representing close loop**

** Scheme of Boost
converter using cascaded control**

This paper analysis nonlinear,
switched, state-space models for buck, boost, buck-boost, and Cuk converters.
The simulation environment MATLAB/SIMULINK is quite suitable to design
the modeling circuit, and to learn the dynamic behavior of different
converter structures in open loop. The simulation model in MATLAB/SIMULINK
for the boost converter is build for close loop. The simulation results
obtained, show that the output voltage and inductor current can return
to steady state even when it is

affected by input voltage and load variation, with a very small over shoot and settling time.

**Fig. 9(b)
Subsystem for Cuk converters**

(a)

Ripple (peak-to-peak
= 0.11%)

(b)

Ripple (peak-to-peak = 0.43%)

(c)

Ripple (peak-to-peak = 0.12%)

(d)

**Fig. 11 Output
voltage and inductor current Open-loop for
(a) Buck (b) Boost (c) Buck-Boost (d) Cuk Converters**

Ripple (peak-to-peak = 1.96%)

(a)

**Fig. 12 Output
voltage of SMC Boost Converter when (a) load variation (b) input** **voltage
variation**

**6
References**

[1] J.Mahdavi, A.Emadi, H.A.Toliyat, Application of State Space Averaging Method to Sliding Mode Control of PWM DC/DC Converters, IEEE Industry Applications Society October 1997.

[2] Vitor Femao
Pires, Jose Fernando A. Silva, Teaching Nonlinear Modeling, Simulation,
and Control of Electronic Power Converters Using MATLAB/SIMULINK, IEEE
Transactions on Education, vol. 45, no. 3, August 2002.

(b)

[3] Juing-Huei Su, Jiann-Jong Chen, Dong-Shiuh Wu, Learning Feedback Controller Design of Switching Converters Via MATLAB/SIMULINK, IEEE Transactions on Education, vol. 45, November 2002.

[4] Daniel
Logue, Philip. T. Krein, Simulation of Electric Machinery and Power
Electronics Interfacing Using MATLAB/SIMULINK, in 7^{th} Workshop
Computer in Power Electronics, 2000,pp. 34-39.

[5] N.
Mohan, T. Undeland, W. Robbins, Power Electronics Converters, Applications
and Design, ISBN 9814-12-692-6.

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