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Tampere University of Technology —DEE-34106 Converter dynamies and EMC 9.5.2017
Electrical Engineering

Teuvo Suntio

Ouestion 1.

Ouestion 2.

Ouestion 3.

Programmable calculator allowed 5 guestions/ 6 pts

The transfer function of the typical PI controller (Type 2) in power electronics is given in Eg.
(1). Sketch its magnitude and phase behavior (i.e., Bode plot) in logarithmic x-scale by using
the asymptotic behavior of its magnitude and phase according to the zeros and poles as they
are typically placed in power electronics.

K. ((l+5/0)
GET ia (1 )
s(l+5/0)
Correct magnitude and phase behavior will yield 3 pts each.
Two different control-to-output-voltage transfer functions are of the form
G) =kK 1-s/o, 2)

(1+5/0,)J1+5/0,)
and

1+s/w

Gliss =. -
(15/0, A+5/0,,)

(3)

rad 407 13d
s

where &, =27-10 =, 0, =27 » 0, =27-105 A and K =10.
s s

a) Which one of G;, indicates unstable system and why? (2 pts)

b) Can you stabilize the unstable system by control design and how? (2 pts)
c) Does the stable system contain any control design limitation? Justify your answer (2 pts).

Fig. 1 shows G,,, of a certain switched-mode converter at the minimum and maximum input
voltages. Each of the subguestions gives 2 points.

a) Which of the transfer function shall be used as the base for the control design and why?
b) What kind of controller type you have to use and why (P, I, PI, PID)?
€) What is the theoretical factor limiting the achievable control bandwidth?

a
v
S
2

 

10! 10? 10 10*
Freguency (Hz)

Fig. 1 Control-to-output transfer function at the input voltage of 20 V (solid line) and 50 V (dashed line).

10)
Tampere University of Technology —DEF-34106 Converter dynamics and EMC 9.5. 2017
Electrical Engineering
Teuvo Suntio Programmable calculator allowed 5 guestions/ 6 pts

Ouestion 4. — If we know that the set of transfer functions (i.e., G parameters) of the converter in Fig. 2a

can be given by
; ys 76 Go]
ll 5a G 4
v, Gi 2 G

io o

»

a,

then compute the corresponding set of transfer functions (i.e., Y parameters) representing the
dynamics of the converter in Fig. 2b according to

i] [x mo e];
kehä 5 G] &

The power stage of the converter is the same all the time.

 

Fig.2 — VF-converter (a) voltage-output mode, and (b) current-output mode.

Each correct transfer function will give 1 pt.

23)
Tampere University of Technology —DEF-34106 Converter dynamics and EMC 9.5. 2017
Electrical Engineering

Teuvo Suntio Programmable calculator allowed 5 guestions/ ä 6 pts

Ouestion 5. — Fig. 3 shows the Bode plot of an impedance composing of L and C and their internal ohmic
loss components (i.e., x; and 7, ). The characteristic impedance of the circuit eguals 0.58 2.
a) What is the name of the circuit?, b) What is the approximate value of the corresponding
inductance?, c) What is the approximate value of corresponding capacitance, d) What is the
approximate value of n; +r.?, e) What is the approximate value of 1/VLC /27?, f) What is

the value of the phase of the circuit at 1/VLC/27? Each subguestion gives 1 pt.

 

Magnitude (dB)
S

 

 

Phase (deg)
o

 

 

 

10 10? 10? 10 10
Freguency (Hz)

Fig.3 — The freguency response of a specific impedance circuit.

3(3)