A POWER ELECTRONICS AND DIGITAL CONTROL EXPERIMENT APPLIED TO TEACHING INTERDISCIPLINARY IN ELECTRICAL

ENGINEERING Kleiton M. Sousa, Filipe Marangoni, Julian K. Moreno, Emerson G. Carati, Mario L. S. Martins,

Carlos M. O. Stein, Jean C. C. Silva UTFPR Federal University of Technology - Parana, ZIP 85503-390, Pato Branco - PR

kleitonms, fi.marangoni, jk.moreno@gmail.com, emerson, mlucio, cmstein, jeanccs@utfpr.edu.br

Abstract - This paper presents a interdisciplinary

teaching experience applied to power electronics and di­

gital control. The boost converter with a discrete-time PI

controller implemented in a microcontroller is used in this

experiment. It is presented a boost converter model and

the controller design, beyond the description of in strum en­

tation circuit used. Finally are presented experimental and

simulated results. This experiment is applied to UTFPR

electrical engineering students.

Keywords - Boost converter, discrete time control, edu­

cation, interdisciplinary.

I. INTRODUCTION

Nowadays, most electrical engineering courses include the

disciplines of power electronics and digital control, since the

demand for technologies using these areas have grown in num­ber of application and become indispensable for the back­

ground knowledge of graduated students motivated the train­

ing of future graduates students. Most of real application have a interdisciplinary characteristic, requiring the integration of

the concepts of both areas, power electronics and digital con­trol. An example of such application is in power supply sys­

tems of electronics equipments. Often, the power of the equip­ment is supplied by a power electronic apparatus known as

switch-mode power supply (SMPS). The SMPS operates in

order to regulate the voltage required for the system. To ac­complish such task there is a control system that handles the

error between the voltage reference and voltage measured. However, in the power electronics discipline on electrical

engineering course are normally studied the static converters operation stages, not considering the techniques of control and

operation of the closed-loop converters. As well as, the im­

pact of the disturbances such as, circuit input variations or load transients, in the converter response. The power elec­

tronics is a discipline of experimental and multidisciplinary character [1] . Moreover, the digital control discipline only

deals with the control isolated, using theoretical simulations tools and mathematical analysis. Often in digital control dis­

cipline, none experimental situations is analyzed, and some aspects such as actuator devices saturation effect are not ob­

served.

The student's education can be improved by integrating in­terdisciplinary areas with practical situations. It will allow the

students capacity of measuring and analyzing real systems be­

havior [2] . For the undergraduate student improvement, uni-

978-1-4577-1646-1/11/$26.00 ©2011 IEEE

versities have developed several didactic platforms for teach­

ing [3,4] . This paper presents a didactic experiment applied to mul­

tidisciplinary teaching to digital control and power electron­ics. This experiment is applied in the digital control course

of electrical engineering graduation program , where the pre­

requisites necessary for the student are knowledge in power

electronics, analog and digital electronics and programming

techniques microcontrolled devices. The approach is proposed to be developed during one semester and must be carried out

from the first classes in the course. For that, the professor must specify this work as the final project of the course.

This paper are organized as follows. Section II, which is

presented to model the converter used, the instrumentation cir­cuit used and control design implemented in the microcon­

troller. Section III shows the results and discussions obtained

in simulation and experimentally, followed by conclusions and

final considerations shows in Section IV .

II. DESCRIPTION OF THE PROPOSED SYSTEM

The diagram of the system structure is shown in Fig. 1, comprising a static converter feeding a load, the circuit instru­mentation and the digital controller implemented in a micro­

controller. Initially the student should analyze the converter

desired to be controlled, by finding the converter simulation model. After modeling the converter, the student should de­

velop an instrumentation circuit to provide the adequation of the signal in the range of values appropriate for the AID con­

version of the microcontroller. The digital control discipline is applied during the controller development and design, be­

ing the student to decide which type of controller should be employed.

As an example of the use of multidisciplinary didactic ex­

periment will be shown a boost converter and a PI controller

in discrete time. The experiment begin with the modeling of the boost converter, after that, the instrumentation circuit is presented. Following is described a discrete time PI con­

troller used, obtained by discretization of a continuous-time controller. The controller is implemented with a micro con­

troller MC9S08AW60, manufactured by Freescale. Finally,

the simulation and experiments results obtained are presented. Due to the versatility of the platform, could be used with other

topologies of controllers in discrete time or another static con­verter for quick and inexpensive way.

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Converter Load

, , L __________ --.J

Microcontroller

Fig. 1. : Block diagram of experiment.

Fig. 2. : Simplified diagram of the boost converter.

Fig. 3. : Diagram of the boost converter connected with switch on.

A. Modeling of Boost Converter

The simplified diagram of a boost converter is shown in Fig. 2. This converter may operate in two distinct forms, de­

pending on the state of the current through the inductor L. In this paper, only the continuous current conduction mode (CCM) is regarded. In CCM operation, the converter operates

in two stages, when the switch S is closed and when the switch

S is open. The converter static gain depends of the switch S conduc­

tion time te. Therefore, the converter output voltage is given

by: E

Vo = 1- tc/T ' (1)

where Vo is the converter output voltage, tc is the switch S conduction time and T is the switching period.

In order to provide more accurate simulation, the boost con­

verter model considering the inductor windings resistance rL, the capacitor equivalent series resistance re and the switch on­

resistance RDs should be developed. The Fig. 3 represents the

converter with the switch on, and Fig. 4 shows the converter with the switch off.

The equations describing the circuit dynamics, choosing as state variables the capacitor voltage Ve and the inductor cur-

Fig. 4. : Diagram of the boost converter connected with switch

off.

rent h, are shown in (10) to the switch on and (11) to the

switch off.

The output voltage can be obtained using the space state equations. For the switch on the output voltage expression is shown in (2) and to the switch off the output voltage is shown

in (3). R

VOon = Ve re + R

(2)

R reR VOoff = Ve

re + R + h

re + R (3)

The converter equation change according to the state of the switch. Therefore, it is a time-varying system. The average

transfer function of the boost converter should be determine to

design of the propose controller. According to [5], the average transfer function is:

G(s) = va(s)

= _ Vore (s + Wzn ) (S - Wzp )

d(s) (1-D)(R+re) s2+2�wos+w� (4)

where Va (s) represents the behavior of the converter output voltage, the converter average output voltage in regime is re­

presented by Vo. The duty cycle is represented by D, d(s) represents a step of duty cycle. For the simulation of the con­verter should be calculated the converter output voltage Vo by

(1), for a duty cycle D, and the system input d(s) will be a step with the same amplitude value of D. Therefore, the trans­

fer function used will serve to represent the converter output

in just one operation point. The remaining terms of (4) are:

1 Wzn = --Gre

Wzp = ± [(1-D)2 R + r]

Wo = r + (1-D)2 R LG (R + ro)

(5)

(6)

(7)

G [r (R + re) + (1 -D)2 Rre] � = (8)

2J LG (R + re) [r + (1 -D)2 R] where r is an equivalent resistance. The resistance r depends

of the inductor resistance, the switch on-resistance RDS and

the capacitor equivalent series resistance re. The value of r is given by [5] :

DR D (1 -D) Rre

r = rL + DS + R ' +re

(9)

1038

•

o ( �� ) = ( -1/C(R + ro) o -(rL + RDS)/L ) ( �� ) + ( I�L ) E (10)

•

( �� ) = ( -1/C(R + ro) R/C(R + ro) ) ( �� ) + ( o I/L (11) -R/L(ro +R) - [R(ro + rL) + rO + rL) /L(R + ro)

Input Voltage E Inductor L Switch S Diode

Capacitor C Resistor R

TABLE I

Circuit parameters

Switch resistance RDS Capacitor resistance ro Inductor resistance r L Switching frequency

12 V 1.7mH

IRF740

MUR860

44f.£F

480

0.550

0.850 0.3 0

20kHz

The implemented circuit parameters are presented in the Ta­ble I.

With the values from Table I, the average transfer function

of the boost converter is given by:

G(8) = -0.802482 - 1.592xl048 + 1.479xl08

82 + 10318 + 3.492xl04

B. Instrumentation Circuit

(12)

The instrumentation circuit comprises the voltage divider,

which reduces the voltage converter output tenfold, the sec­ond order lowpass filter which function is to filter the ripple of

boost converter output voltage and the zener diode 5 V which function is protect the microcontroller if the filter output sig­

nal exceeds 5 V. In order to increase input impedance of the instrumentation circuit the buffer is used between the resistive

divider and the low pass filter. A pull down resistor is used in the circuit output. The filtered signal is then converted to

digital by the microcontroller. A second order lowpass filter can be implemented using the

circuit shown in Fig. 5, which employs an opamp in an ar­

rangement of a VCV S with gain G. Its transfer voltage ratio, obtained by analyzing the circuit, is shown in (13).

where:

G=I+Rb Ra

(14)

The complete instrumentation circuit is shown in Fig. 6. The filter cutoff frequency of Fig. 6 is 2 kHz, a decade be­

low the switching frequency of the boost converter. In order to achieve unity gain in the circuit, is used Rb = 00. The

v.

Fig. 5. : A second order lowpass circuit.

10 k!l 1 k!l 1 k!l

5 V

20nF

4.7 ill

Fig. 6. : Diagram of instrumentation circuit.

equation of lowpass filter is shown in (15).

lOill

H(8) - 1. 579x108

(15) - 82 + 1.776xl048 + 1.579xl08

C. Microcontroller Used and PI Discrete Time Controller

The microcontrollers are programmable devices composed

of a processing unit that includes some peripherals use in in­ternal structure. The micro controllers have peripherals such

as memory read and write, analog to digital converter, PWM

generators and other devices that vary depending on the model used. The bits of the micro controller also varies depending on

the model used, where as higher the number of microcontroller

bits, greater will be the numerical accuracy. The DSP devices have a processing speed much higher com­

paring to the microcontrollers. Moreover, the DSP devices utilize the digital representation for floating point, which pro­

vides greater accuracy for numerical representation. The most micro controllers advantage is their low cost compared to DSP.

The digital controllers have some advantages compared to

analog controllers. One of the advantages of digital controllers is the design flexibility, where the poles and zeros allocation

is done by changing only one value in the control equation implemented in the microcontroller.

1039

'" ·x cd

� .S 00 cd

,§

Fig. 7. : Block diagram of control loop.

x10' 1.5

0.5 r 0

-0.5

-1

-1.5_4 -3 -2 -1 o

Real axis

Fig. 8. : Roots locus graphic.

2 x10'

This paper proposes a PI discrete-time classic controller. This controller was chosen because it is easily implemented,

and presents wide use in industrial control systems. The

discrete-time PI controller is obtained by discretization of a continuous-time controller. From the discretized PI is found

the control action implemented in a micro controller. The continuous-time PI controller is shown in (16):

(16)

where K represents the proportional gain and I/Ti the integral

gain [6] . The block diagram of the control loop is shown in Fig. 6.

The discrete-time controller is represented by C(z), the blocks G(s) and H(s) are defined by (12) and (15), respectively. The control action u[k] determines the boost converter switch con­

duction time ton, calculated by [7] :

(17)

where E is the converter input voltage and T the switching period. To calculate the conduction time should be make the

acquisition of the boost converter input voltage.

The Ziegler-Nichols method is used to tune the continuous­time controller. In this kind of tuning is necessary be found the value of the gain Ker which makes the system critically stable using an integral gain equal to zero (Ti = 00) . With the value

of Ken the parameters in (16) are calculated as K = 0.45Ker and Ti = Per/1.2, where Per is the system critical oscillation period with gain Ker [6] .

The critical gain can be determined by many ways, this pa­per used the roots locus graphic, using MATLAB as a tool for

finding the critical gain. In Fig. 8 is shown the roots locus. The critical gain is Ker = 0.031. The critical period is

Per = 2.2. This results to a controller given by:

( ) 7.1

C s = 0.0135 + -s

(18)

The discretization of the compensator C ( s) is made by the Euler method. Making s � (1 -z)/T, with a discretization

interval of 1 ms, is determined the discrete time compensator C(z):

0.0071 C(z) = 0.0135 + -1 ' l-z

(19)

therefore, the control action u[k] can be implemented by the

difference equation:

k u[k] = 0.0135e[k] + 0.0071 L eli] , (20)

i=l

the control action u[k] sets the boost converter switch conduc­

tion time, defined in (17). The adder in (20) can be imple­mented using a variable that accumulates the error sum for

each sample. In (21) the variable S is used to accumulate the

error sum.

S = S+e[k] (21)

Ill. RESULTS

The performance verification of the discrete-time PI con­

troller to control the boost converter was performed using the

modeling presented in (10) an (11), and discretized by the Eu­

ler method with time discretization Ts = 50 f-Ls. To verification the behavior of the output voltage during a switching interval,

the system was again discretized using a simulation step of 0.5 f-Ls.

The proposed controller is implemented in a MC9S08AW60

microcontroller. This micro controller has 8-bit and an 20 MHz clock. The main peripherals used for the project implementa­

tion are a PWM generator and an AID converter. Due to the calculations required for the control action, the acquisition rate

was limited to 1 kHz. The prototype is implemented using a micro controlled board developed during the Microcontrollers

Systems course. This board includes AID and PWM separated

connectors, which becomes easier to interface with instrumen­tation circuit and PWM drive. Moreover, power and program­

ing connectors are included in this board to allow control flex­ibility through reprogramming. The Fig. 9 shows a picture

detailing the micro controlled board.

A. Open Loop Convener

The Fig. 10 shows the simulated output with a 0.5 duty cy­cle using the state space equations. Still in Fig. 10 is shown

the graph relating to the converter average transfer function response. The software used for simulation is MATLAB.

In Fig. II(a) is shown the detail of simulated output volt­age ripple and in the Fig. 11 (b) is shown the same detailing obtained experimentally. The output voltage oscillations sim­

ulated and experimental behave similarly.

Finally, the Fig. 12(a) shows the simulated PWM and the output voltage, the Fig. 12(b) shows the same waveforms for

the circuit implemented.

1040

Fig. 9. : Microcontroller board and its main connections.

30

� 20

- State space equations _. _ .. Transfer function

r -- ·!----- �--------:----�---t--------!-------r------­� 10 - t-----.;------�---�---t---------_:_-------�---------. , ___ -' ________ '-_______ 1... _________ ..... ________ ..: ________ _

0 .. .i�-----�---------l--------� -------+ ------� --------

o 2 4 6 8

Time (ms)

10 12

Fig. 10. : Simulated system response with a 0.5 duty cycle.

24

>' � 23

E - 22 � 21

Time (20 Ils/div)

(a) Simulated

Time (20 Ils/div)

(b) Experimental

'0111.2010 " ':0'

Fig. 11. : Detail of the output voltage: (a) simulated (b) exper­imental.

I , I , I --- --r - --�- ---;----1------; ----:- ----;-----1--- -�-----····r ... ...... �.::::L .... _· .... ····· .. r-· : .. ..

-----i- -- -t � ---I- ----1' ---- ,------ r----

, , , __ --'------.. --- --_0. ------1- ----,- ---.... - ----�---

� � ---i---�-i- ----� ----�- �-�---� ..... �. ..� ..... ' .... E ... : ... � .. . . .. '. I ,......... -----f - ---�------�- I -----T ----r-- --1--� ---I ----�------�

I

-----+ -- -�--... �.� ... � .... �, ... + ---,-- � .... -;---I , , , ,

Time (20 Ils/div)

(a) Simulated

--=. .-

I

....J.. -J.. -t -- --:--"1 r--- '- lJl I I I I L • i'"'"'"-' ;-- .--

'M" ,�, 20.� 1',"0000"'

(b) Experimental

m:ir.·��" U • J 2.I0v

�

Fig. 12. : Detail of PWM and output voltage: (a) simulated (b) experimental

L D

Fig. 13. : Block diagram of the implemented circuit.

B. Closed Loop Converter

The diagram of the implemented system is shown in Fig. 13.

The converter input voltage was measured to calculate the

switch conduction time. The two signals (output and input voltage) goes to micro controller, which makes the AID con­

version, calculating the switch conduction time. The PWM signal generated by the microcontroller is sent to a driver.

The system simulation using MATLAB is shown in

Fig. 14(a). The reference voltage is 24 V. The circuit values

and other parameters are the same presented in Table I. The Fig. 14(b) shows the system experimental response. When connected to the input source, the converter output stands at

12 V for 150 ms until the control begins to operate, nullifying the error at 700 ms. The initial time interval is due to u[k]

1041

>' '-' Q) 01) o:s -�

45

40

35

30

25

20

15 10

5

0

o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Time (s)

(a) Simulated

,I l / t

.J I '"' ,-Time (100 ms/div)

- Vo - E (b) Experimental

..I. .... I 'I r

It::t�' I u r '.1ev

�. ":)001:15

Fig. 14. : System response with PI control: (a) simulated (b) experimental.

have initial value equal to zero, causing a negative te, accord­

ing to (17). A negative te causes the switch remains open, and the output voltage of the circuit will be equal to input voltage.

The controller will act only when the value of te is greater than

zero, which happens some time after the error have been ac­

cumulated, increasing the value of u[k]. This initial interval can be avoided using u[k] = 12 as initial value. The behav­

iors of the experimental and simulated system shows similar

responses. We performed variations in converter input voltage. The re­

sult for an input voltage of 8 V is shown in Fig. 15 and Fig. 16

shows the result when the input voltage is 16 V. The Fig. 15

and Fig. 16 show the command pulse and the input and output voltage of converter. In the presented cases, control acted on

the switch conduction time to maintain output voltage constant at 24 V.

IV. CONCLUSION

With the proposed experiment, the student will be able to analyze, design and implement static converters using digi­

tal control systems. To perform this experiment, the students should have background knowledge on power electronics, ana-

.-' -�C"'"'II

I

'"'

.

t ! J l

I � I I I I t � �r .IIIIY

-

1 � I I � '--i

N...... II�HM"'" I e J " .,V lM'9o(t<!OfGI , .... ..

� n.n:2'

Time (20 �s/div)

-E

- PWM

Fig. 15. : Output voltage, input voltage and PWM for E = 8 V.

- h- I -

I

� n n ilL 1 ) 1 � • . '-----i __ I . 'Ii 011 V :'OIlY

f N...... U� .. M...", B _ J " .tV _J .··GOf�'H ..... .

� n:ll: oH

Time (20 �s/div)

-E

-PWM

Fig. 16. : Output voltage, input voltage and PWM for E = 16 V.

log and digital electronics and programming techniques of mi­crocontrollers. The student could observe, from the experi­

mental results, the validity of theoretical models. In this ex­

periment we used a boost converter and a discrete-time PI controller, but other converters, e.g., buck and buck-boost,

and other controllers can be used without the need for major

changes to the proposed experiment. It is suggest that when applied to a class of undergraduate students, more kind of con­

verters can be analyzed. The class can be divide in groups,

when each group should investigate a different converter or

digital controller.

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