CONTENTS
1. Introduction 2. Modeling of CCM DC/DC Converter 3. Modeling of DCM DC/DC Converter 4. Current Programmed Control 5. Feedback Control Design 6. Modeling and Control of Single Phase Inverter
1 1.6kHz
2 LC
Given reference momentary value vmpulse width t2 is
1
Go
s
Vo Vi
s s
s2
LC 1 s
1
s2
n2 2n s
n2
RC LC
where， n
1 LC
Is
dampless
oscillation
angular
frequency
n
，1
LC ； 1 L Is damp ratio.
2R C
Which is typical second order oscillation system, frequency
CHAPTER 5 MODELING AND CONTROL OF SINGLE PHASE INVERTER
5.1 Modeling of inverter
Structure:
Structure of tri-phase half-bridge inverter
By average method, transfer function of G(s) is gained from Vi (s) to V0(s)
1 L
s
1
R
By bi-polar SPWM modulation，vi can be shown as
vi E(2S 1)
Where S is switch function
When S1(VD1) is on，then S=1；when S2(VD2) is on, then S=0. obviously, vi is un-continuous for S switch function. By average method, we have
fn n 2
Generally speaking, corner frequency of LC filter for SPWM converter ƒn文is chosed as one-tenth of switch frequency ƒs
11
fn
10
fs
16kz 10
1.6kz
That is
1
vm Vtri
Where vmis reference sine signal, Vtri is peak value of triangle carrier, then
vi
Ts
E vm Vtri
therefore
vi Ts E
vm
Vtri
and transfer function from modulation input to output of inverter
Go
s
Vo Vm
s s
Vo Vi
s s
Vi s Vm s
LCs2
L R
1 rC
s
1
r R
E Vtri
By Go(s), equivalent block diagram is shown as follow
Equivalent block diagram of One-phase halfbridge inverter
5.2 design of filter
Function of LC filter output for inverter
Omitting resistences of inductance and line, transfer function of filter output voltage to inverter bridge output voltage
1 L 0
1 22 L 40lg
1 1
0.707
Then the Bode diagram of this LC filter is shown as follows
Main parameters of filter：ωn and ξ。
corner frequency of LC filter for SPWM converter ƒn should far less than switch frequency ƒs, where
1
G
s
Vo Vi
s s
1
1 Cs R 1 Ls r
Cs
1
LCs2
L R
rC
s
1
r R
R
One-phase half-bridge inverter
SPWM modulation
when equivalent cascade r is omitted, then we have
G
s
CLs 2
character
G
j
n2
n2 2
j2n
1
1
n
2
j2 n
A e j
where
Then, log magnitude-frequency characteristics is
L 20 lg 20 lg
1
n
2
2
2
n
2
low-frequency stage high-frequency stage Cross frequency Peak value
vi
Ts
E
2
S
1
Ts
Where (vi)TS denotes switch period average value of vi, and where switch period average value S is
S Dt Ts
Where D(t) is duty ratio.
Then
D
1 2
bridge is
K pwm
Vi s Vm s
E Vtri
In SPWM, if carrier/switch frequency is far more higher than output frequency, inverter bridge can be looked as proportional component, proportional ratio is KPWM. Then transfer function will be