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Bangbang controller Design for EAST
Vertical Instability
YUEHANG WANG, BINGJIA XIAO,
LEI LIU, QIPING YUAN
OUTLINE
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Motivation
Bangbang controller Design for EAST Vertical Instabiliy
• plasma model
• time optimal controller design
• optimal controller with time delay
EAST VDE Experiment by Bangbang Controller
Summary
OUTLINE
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Motivation
Bangbang controller Design for EAST Vertical Instabiliy
• plasma model
• time optimal controller design
• optimal controller with time delay
EAST VDE Experiment by Bangbang Controller
Summary
Motivation-EAST Vertical Instability
Some advanced plasma
configurations have been
used in EAST which have
high vertical instability
growth rate
The older vertical
displacement control
system is required to be
upgraded for safe control
and rubust control
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Summary of EAST experiment
measuring dZmax in 2012
shows that the dZmax is about
2cm for 150s-1 growth rate and
1.2cm for 200s-1 growth rate
Motivation-Voltage mode IC power supply
Voltage mode of IC power
supply has been available
and assure a faster active
than current mode
• current mode current
rising time:0>5.1KA~1ms
• voltage mode current
rising time:0>5.4KA~0.6ms
• communication
time~550μs
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OUTLINE
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Motivation
Bangbang controller Design for EAST Vertical Instabiliy
• linearized plasma model
• time optimal controller design
• optimal controller with time delay
EAST VDE Experiment by Bangbang Controller
Summary
Linearized plasma model
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Using the RZIP rigid current displacement model to
design the controller
The RZIP plasma model can be cast in the standard
state-space model form:
 x  Ax  Bu

 y  Cx  Du
mostly Du<<Cx, the D matrix has
always been ignored
Linearized plasma model
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When we consider the vertical displacement, the
model can be change to:
y  CAC 1 y  CBuic
For this system, the gorwth rate of the vertical
displacement mode is much more higher than other
modes.Thus:y   y  CBu
z
z z
ic
γz is the maxmum eigenvalue
of the matrix CAC-1
The vertical displacement can be given by:
z   z z  CBuic
OUTLINE
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Motivation
Bangbang controller Design for EAST Vertical Instabiliy
• plasma model
• time optimal controller design
• optimal controller with time delay
EAST VDE Experiment by Bangbang Controller
Summary
Time Optimal controller Design
The linearized plasma model has been given as:
z   z z  CBuic
It's initial status:
z（t0 )  z0
Let the time cost as the performence function:
tf
J  t f  t0   dt
t0
Using the minimum principle, thus the optimal
control law is:
u * (t )  Vmax sgn{ b * (t )}  Vmax sgn{ bke at }
k is given by the hamilton canonical
equation of the system
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system root locus in ( z,dz/dt)space
Compair Bangbang with PID
Bangbang is faster
than PID control, but
will shock around the
target position.
PID control is slower
than Bangbang
control, but more
stable
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OUTLINE
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Motivation
Bangbang controller Design for EAST Vertical Instabiliy
• plasma model
• time optimal controller design
• optimal controller with time delay
EAST VDE Experiment by Bangbang Controller
Summary
Optimal controller with time delay
Simply using Bangbang control will cause the
plasma shocked around the target position when
the time delay of the power supply cannot be
ignored
Using two method to optimise it:
– consider the dz/dt parameter to optimise the overshoot
– combine with the PID controller, using PID controller for
smaller dz drift
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Optimal controller with time delay
The Bangbang control command can be
optimised as：
uic  Vmax sgn( Z  Kdz / dt )
Combine with the linearized plasma model:
z   z z  CBuic
The vertical position's general solution is:
z  Me
 zt

C z Bic
z
uic
the parameter M depends
on the initial condition
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Optimal controller with time delay
When the Bangbang command changed, the vertical position
should be controlled into the range for PID control, thus:
z  Kz  0
 zTps
 Z lim  Me

Cz Bic
z
uic  Z lim
The parameter K should be confined:
Cz Bic
Cz Bic
 zTps
 Zlim 
uic (1  e )
Zlim 
uic (1  e zTps )
z
z
K
  z Z limCz Bicuic
 z Z limCz Bicuic
Especially, when Zlim=0
K  1 e
 zTps
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Bangbang+PID control
BangBang
control for
larger dz drift
PID control for smaller dz drfit
Details of BangBang control “sgn” block
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Simulation result
τps=0.2ms,Tps=0.2ms，Vmax=1000V
compair BangBang+PID control withPID control
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Optimal controller with time delay
 The simulation result without
optimal the controller for
time delay(K=0)
 Plasma will shocked around
the stable position
 The simulation result with
optimal the controller for
time delay(K=1-exp(γTps))
 Plasma comes stability in
stable position
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OUTLINE
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Motivation
Bangbang controller Design for EAST Vertical Instabiliy
• plasma model
• time optimal controller design
• optimal controller with time delay
EAST VDE Experiment by Bangbang Controller
Summary
Bangbang+PID control vs. PID control
Bang
bang
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I
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Max IC current
4.6cm
Trigger
Bangbang+PID voltage mode
 dz>=1cm，bangbang control, max ±voltage
output
 dz<1cm ，PID control:
PID voltage mode
The same discharge setup， 4.4s
trigger VDE，lost z control
U=Gp*zerror+Gd*dZerror/dt
 Bangbang and PID switch control works
 dz~ 4.6cm
Time ：4.4s , Ip：250KA， elongation : 1.72, li: 1.55 , ne: 1.0 ，VDE growth rate : ~530/s
OUTLINE
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Motivation
Bangbang controller Design for EAST Vertical Instabiliy
• plasma model
• time optimal controller design
• optimal controller with time delay
EAST VDE Experiment by Bangbang Controller
Summary
SUMMARY
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The experiment shows the Bangbang+PID controller
has increase the control ability than PID controller
Sometimes IC overcurrent would have happend
when the Bangbang controller worked. Further
optimization should consider IC current saturation
The noise of dz/dt cannot be ignored in this
campaign. In the incoming campaign, dz/dt from
loop voltage signals will try to be used
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THANKS FOR YOU ATTENTION!