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Technische Universität München
Predictive Control - A Simple and Powerful Method
to Control Power Converters and DrivesRalph M. Kennel, Technische Universitaet Muenchen,Germany
Marian Kazmierkowski, Technical University of Warsaw, Poland
José Rodríguez, Universidad Técnica Federico Santa María, Chile
Technische Universität München
Technische Universität München
Outline
Introduction
Predictive Control Methods
Predictive Control versus Cascaded Control
Conclusions/Discussion
Technische Universität München
Outline
Introduction
Predictive Control Methods
Predictive Control versus Cascaded Control
Conclusions/Discussion
Technische Universität München
State of the Art : Field Oriented Control
model
PWM
mainsstator coordinatesfield coordinates
currentcontrollers
fluxcontroller
speedcontroller
encoder
M3~
r
r
is
is
us
ej
e-j
us
6
Technische Universität München
Problems of Linear Algorithms
Linear control characteristics Drive systems characteristics
• Control unit and controlled unit
are assumed to be linear
• Drive systems are non-linear
• Control unit
are assumed to be time constant• Drive systems are time-variant
• Linear circuits
show identical reactions
in each operation range
under the same
reference commands
• The behavior of a drive system
is depending
on the operation range
Technische Universität München
Problems of Linear AlgorithmsFeedforward Control Feedback Control
Advantages• high dynamic behaviour
• no impact by sensor characteristics
• high accuracy
• high reliability
• high longterm stability
• simple optimization/adjustment procedure
• controlled quantities can be monitored
Disadvantages• models are not absolutely accurate
• high accuracy requires
knowledge of all quantuities
• temperature and drift behaviour
often cannot be described/modeled
• (re)action only,
when there is a control difference already
• sensors cause measuring errors
Technische Universität München
Problems of Linear Algorithms
• any controller optimization is a compromise
making the inverter unnecessarily slow
in many operation points
• controllers with parameter adaptation and/or structure adaptation
are very complex
they often have bad effects during the adaptation process itself
• converters cause harmonics
leading to offset effects
in combination with fast control loops
• the elimination of harmonics by filtering
causes a time delay in the feedback
and therefore leads to a less dynamic control
Technische Universität München
Problems of Linear Algorithms
• any controller optimization is a compromise
making the inverter unnecessarily slow
in many operation points
• controllers with parameter adaptation and/or structure adaptation
are very complex
they often have bad effects during the adaptation process itself
• converters cause harmonics
leading to offset effects
in combination with fast control loops
• the elimination of harmonics by filtering
causes a time delay in the feedback
and therefore leads to a less dynamic control
Technische Universität München
Typical Cascaded Structure of Drive Control
inertia gear etc.
I
current controller
speed controller
positioncontroller
– – –
motorwindings
powerelectronics
Technische Universität München
Typical Cascaded Structure of Drive Control
inertia gear etc.
I
current controller
speed controller
positioncontroller
– – –
motorwindings
powerelectronics
Technische Universität München
Problems of Linear Algorithms
• using cascaded PI(D) control
most problems (= differences between theory and practical results)
occur with the (inner) current control
• a linear controller tries to control an extremely non-linear inverter
whose behaviour is depending on the modultaion method
• most developments of converter control
deal with current control or flux control
because these elements are closest to the inverter itself
• the behaviour of any improved current control
is expected to be more linear than the inverter itself
speed and position controllers
can be designed as PI(D) controllers as before
Technische Universität München
in cascaded control structures
speed control must be much faster than position control
and current control must be much faster than speed control
current control must be very fast
to achieve position control with reasonable cycle times
in the controlled system (drive, converter, …)
however, there is no time constant justifying cycle times
of 100 µs or less
Problems of Linear Algorithms
Technische Universität München
Outline
Introduction
Predictive Control Methods
Predictive Control versus Cascaded Control
Conclusions/Discussion
Technische Universität München
General Structure of a Predictive Controller
inertia gear etc.
switchingstate
actual
machine state
I
prediction andcalculation
machine andpower electronics
model
motorwindings
powerelectronics
reminds slightly to state control
state control, however, is basically a linear control
predictive control is not !!!
Technische Universität München
Usual Structure of Drive Control
DC link
PI controller
Technische Universität München
Usual Structure of Drive Control
DC link
PI controller
why PWM ?
• linearization of the inverter
consequences ?
• very high switching frequency
Technische Universität München
Structure of a Direct Control
DC link
direct controller
Technische Universität München
Principle of Predictive Control
inverter
definite number of
switching elements
definite number of
switching states
definite number of
equivalent circuits
without switching
elements
precalculation of the
behaviour for each of
the switching states
next switching state
or switching time
can be fixed
comparison between
precalculation and
reference commands
reference
commands
Technische Universität München
direct controlof IM currents(Mayer/Pfaff)
direct digital predictivecurrent controller(Holmes/Martin)
digitalcurrent controller
(Betz/Cook/Henriksen)
current control(Choi/Sul)
direct torque control (DTC)(Takahashi/Nogushi)
(Tiitinen/Lalu)
multilevelhysteresis DTC
(Purcell/Acarnley)
direct torquecontrol (DTC)
(Chapuis, et.al.)
DTC with ORS(Moucary et.al.)
DTC-PPWC(Nillesen et.al.)
direct mean torquecontrol (DMTC)(Flach, et.al.)
new directtorque control
(Kang/Sul)
torque pulsationreduced DTC(Vas, et.al.)
DTC + dithering(Noguchi, et.al.)
DTC with reductionof torque ripple(La/Shin/Hyun)
DTDTC(Maes/Melkebeek)
DTC-SVM(Lascu et.al.)
DTC-DSVM(Casadei et.al)
adaptive switchingpattern (ASP)
(Nagy)
direct currentcontrol
(Pfaff/Wick)
current controlmethod
(Salama et.al)
adaptive andoptimized regulator
(Ackva, et.al.)
“space vector”control
(Wuest/Jenni)
“space vector”control
(Kazmierkowski, et.al.)
direct selfcontrol (DSC)(Depenbrock)
direct speedcontrol (DSPC)
(Mutschler)
integralspace-vector PWM
(Trzynadlowski, et.al.)
direct selfcontrol (DSC)
(Bonanno, et.al.)
predictive control(Kennel/Schröder)
fast-responsecurrent control(Holtz, et.al)
improvedpredictive control(Warmer et.al.)
new predictivecurrent control
(Hecht)
Family tree of predictive control algorithms
optimal on-line-tuningcurrent regulator
(du Toit Mouton/Enslin)
predictive current controlfor resonant link inverter
(Oh/Jung/Youn)
vectorial torque control(Attaianese, et.al.)
trajectorytracking control(Holtz/Beyer)
sliding mode control(Emeljanov)
trajectory based strategies
predictivecurrent control
(Holtz/Stadtfeld)
hysteresis control(bang bang)
PROMCvoltage control
(Hintze)
PROMCcurrent control
(Kohlmeier et.al.)
hysteresis based strategies
Technische Universität München
Family tree of predictive control algorithms
Part 2 MPC
Continuous-Set-Model based strategies Finite-Set-Model based strategies
DMC
(Cutler/Ramaker)
GPC
(Clarke)
Modular multilevel converter
(Perez/Rodriguez)
Direct matrix converter
(Vargas/Rodriguez)
Indirect matrix converter
(Correa/Rodriguez/Espinoza)
Fast online optimization
Fast gradient method for converter
control
(Richter/Morari)
LP solution for quadratic cost
(Stumper/Kennel)
Explicit MPC
(Bemporad)
MPC with MPT
(Kvasnica)
MPC for PMSM
(Kuehl/Bolognani/Kennel)
Dead beat control
(Lee)
dc-dc converter
(Geyer/Morari)
MPTC
(Rodriguez)
Predictive current control
(Rodriguez)
Predictive speed control
(Fuentes/Rodriguez/Kennel)
Heuristic direct MPC
(Stolze/Kennel)
Sensorless MPC
(Wojciechowski/Strzelecki)
Saliency based encoderless
PTC
(Landsmann/Kennel)
Observer-based sensorless
PTC
(Davari/Wang/Kennel)
Weighting factors design
(Cortes/Rodriguez)
Weighting factor optimization
(Davari/Kennel)
2-steps MPC of 3 phase UPS
inverter
(Cortes/Rodriguez)
FPGA-based PCC
(Naouar/Monmasson)
ac-ac converter
CRHPC
(Clarke/Scattolini)
GPC--PID
(Nakano)
GPC for motor control
(Linder/Kennel) dc-ac converter
2L-VSI
(Cortes/Rodriguez)
3L-NPC
(Geyer/Rodriguez)
CHB
(Perez/Rodriguez/Cortes)
Flying capacitor converter
(Lezana/Aguilera/Quevedo)
Current source rectifier
(Correa/Rodriguez)
ac-dc converter
Technische Universität München
Outline
Introduction
Predictive Control Methods (Kennel)
Trajectory Based Predictive Control
Hysteresis Based Predictive Control
Long-Range Predictive Control
Predictive Control with Heuristic Preselection
Technische Universität München
Outline
Introduction
Predictive Control Methods (Kennel)
Trajectory Based Predictive Control
Hysteresis Based Predictive Control
Long-Range Predictive Control
Predictive Control with Heuristic Preselection
Technische Universität München
Example : Trajectory Based Predictive Control
Predictive Current Control acc. to Kennel
DC drive supplied by a line commutated thyristor inverter
+ + +
grid
U0≈
- - -
=
Technische Universität München
Example : Trajectory Based Predictive Control
Predictive Current Control acc. to Kennel
Technische Universität München
Trajectory Based Predictive Control Strategies
system states are forced to follow
(pre-)defined natural reference trajectories
difference to sliding mode control
there the trajectories are not natural
Technische Universität München
Example : Trajectory Based Predictive Control
Direct Speed Control acc. to Mutschler
model andprediction
3~M
*
ud
uk
isus
=~
e
e = – ref
a =
e ak k/
e ak+3 k+3/
e ak+1 k+1/
e ak+2 k+2/
+Hy–Hy
Sk
Sk+1
Sk+2
Technische Universität München
Characteristicsof Trajectory Based Predictive Control
• system states are forced to follow (pre-)defined reference trajectories
• switching takes place at intersections
between different system-trajectories or at (pre-)defined instants
• switching frequency of the inverter can be fixed to a constant value
• control behaviour comparable to feedforward control
• exact knowledge of system parameters is required
• appropriate for realisation by digital circuits or controllers
Technische Universität München
Example : Trajectory Based Predictive ControlDirect Self Control (DSC) acc. to Depenbrock
Technische Universität München
Example : Hysteresis Based Predictive ControlDirect Self Control acc. to Takahashi
Technische Universität München
Outline
Introduction
Predictive Control Methods (Kennel)
Trajectory Based Predictive Control
Hysteresis Based Predictive Control
Long-Range Predictive Control
Predictive Control with Heuristic Preselection
Technische Universität München
Hysteresis Based Predictive Control Strategies
switching of inverter takes place
at the (multi-dimensional) border(s)
of a hysteresis area
Technische Universität München
Example : Hysteresis Based Predictive ControlPredictive Current Control acc. to Holtz
Technische Universität München
Example : Hysteresis Based Predictive ControlPredictive Current Control acc. to Holtz
Technische Universität München
Re
jIm
0
s
is
is*
din
dt
3~M
=predictis
model
uduk
usk
is
is
disk
is
*
dt us
~
Example : Hysteresis Based Predictive ControlPredictive Current Control acc. to Holtz
Technische Universität München
Characteristicsof Hysteresis Based Predictive Control
• switching takes place at borders of a hysteresis area
• a maximum error can be (pre-)defined
• switching frequency of the inverter is not constant
• control behaviour comparable to feedback control
• exact knowledge of system parameters is not required
• appropriate for realisation by analog circuits
Technische Universität München
Example : Hysteresis Based Predictive ControlPredictive Current Control acc. to Holtz
Technische Universität München
Comparison
of different
predictive control
schemes
Technische Universität München
Flux Trajectories10 Hz fundamental frequency
500 Hz switching frequency
standard PWM
DSC (Depenbrock)
bang-bang control
DSC (Takahashi)
7 % hysteresis
predictive control
(Holtz)DSC (Takahashi)
2 % hysteresis
source Andreas Haun, Vergleich von Steuerverfahren …, VDI-Fortschrittsbereichte, Reihe 21, Nr. 113, 1992:
Technische Universität München
Flux Trajectories40 Hz fundamental frequency
500 Hz switching frequency
standard PWM
DSC (Depenbrock)
bang-bang control
DSC (Takahashi)
7 % hysteresis
predictive control
(Holtz)DSC (Takahashi)
2 % hysteresis
source Andreas Haun, Vergleich von Steuerverfahren …, VDI-Fortschrittsbereichte, Reihe 21, Nr. 113, 1992:
Technische Universität München
standard PWM
DSC (Depenbrock)
bang-bang control
DSC (Takahashi)
7 % hysteresis
predictive control
(Holtz)DSC (Takahashi)
2 % hysteresis
Stator Current Trajectories40 Hz fundamental frequency
500 Hz switching frequency
source Andreas Haun, Vergleich von Steuerverfahren …, VDI-Fortschrittsbereichte, Reihe 21, Nr. 113, 1992:
Technische Universität München
source Andreas Haun, Vergleich von Steuerverfahren …, VDI-Fortschrittsbereichte, Reihe 21, Nr. 113, 1992:
Frequency Spectrum of Torque
a) 40 Hz fundamental frequency
250 Hz switching frequency
b) 45 Hz fundamental frequency
500 Hz switching frequency
1. standard PWM
2. bang-bang control
3. predictive control (Holtz)
4. DSC (Depenbrock)
5. DSC (Takahashi) with 7 % hysteresis
Technische Universität München
source Andreas Haun, Vergleich von Steuerverfahren …, VDI-Fortschrittsbereichte, Reihe 21, Nr. 113, 1992:
Additional Losses
under Inverter Supply
a) variable fundamental frequency
500 Hz switching frequency
b) 40 Hz fundamental frequency
variable switching frequency
1. standard PWM
2. bang-bang control
3. predictive control (Holtz)
4. DSC (Depenbrock)
5. DSC (Takahashi) with 7 % hysteresis
6. DSC (Takahashi) with 7 % hysteresis
Technische Universität München
Outline
Introduction
Predictive Control Methods (Kennel)
Trajectory Based Predictive Control
Hysteresis Based Predictive Control
Long-Range Predictive Control
Predictive Control with Heuristic Preselection
Technische Universität München
switching control
SVM(space vector modulation)
directly
steps of
prediction
(prediction
horizon)
1
>1
• DTC
• DSC
• DSPC
• direct control of
IM currents
• DFC
• DMC
• GPC
• DMPC
predictive control categoriesanother way of distinction
Technische Universität München
• the player calculates
in advance
all possible moves
until a „prediction horizon“
• the player chooses
the move with the best
expectations of success
• after each opponent‘s move
pre-calculation and
optimization is repeatedDMPC is like playing chess
The „Human Behaviour“ of DMPC
Technische Universität München Page 47
Model Predictive Control
History Future
Technische Universität München
Model Predictive Control
Overview
Page 48
Technische Universität München
Direct Model Predictive ControlSystem Model / Cost Function
Technische Universität München
Direct Model Predictive Control
System Model / Cost Function
Technische Universität München
Characteristicsof Model Based Predictive Control
• basic ideas are derived from state-space control
• the past is explicitely considered (mostly by the system state)
• future control values are pre-calculated and optimized
until a (pre-)defined „horizon“
• the first of the precalculated control values only
is transmitted to the controlled system
• model parameters can be estimated on-line
• extension to MIMO-control is possible with little additional effort
• use of non-linear model is possible for non-linear control systems
• a lot of calculation power is required
Technische Universität München
strategy Np max. calculation timecases
complete enumeration 2 35 µs64
online-optimization is not applicable for drive control
Calculation TimesDMPC - control, implicite solution
complete enumeration 3 > 500 µs512
branch and bound 2 27 µs 64
branch and bound 3 186 µs 512
processor:
900 MHz AMD Duron, 128 MB RAM
Linux 2.2.14 with RTAI 1.3
Technische Universität München
Model Based Predictive Current Control
there are
7 (or 8) possiblities
for “the following
switching state”
the respective
system behaviour (current)
can be calculated
in advance
complete enumeration extensive processing power needed
a chess player, however, does not really consider each possibility
Technische Universität München
Model Based Predictive Current Control
there are
7 (or 8) possiblities
for “the following
switching state”
the respective
system behaviour (current)
can be calculated
in advance
complete enumeration extensive processing power needed
… so why should we do that in predictive control ???
Technische Universität München
further prediction, however,
is only considered for
the candidate sequences
staying within
the permitted limits
Model Based Predictive Current Control
… so why should we do that in predictive control ???
Technische Universität München
… determine those switching possibilities only
that are either feasible or point in the proper direction
these are candidate sequences
feasible pointing in the proper direction
Model Based Predictive Current Control
Technische Universität München
not feasible not pointing in the proper direction
Model Based Predictive Current Control
… determine those switching possibilities only
that are either feasible or point in the proper direction
these are candidate sequences
Technische Universität München
Model Based Predictive Current Control
… for the candidate sequences, further prediction (e. g. by a reduced system model) is performed
example : the number of steps after which the first of the two variables the isa and iisb
leaves the feasible regionis the number h
Technische Universität München
h1 = 4
h1 = 4
Model Based Predictive Current Control
… for the candidate sequences, further prediction (e. g. by a reduced system model) is performed
example : the number of steps after which the first of the two variables the isa and iisb
leaves the feasible regionis the number h
Technische Universität München
h1 = 4 h2 = 10
Model Based Predictive Current Control
… for the candidate sequences, further prediction (e. g. by a reduced system model) is performed
example : the number of steps after which the first of the two variables the isa and iisb
leaves the feasible regionis the number h
Technische Universität München
Different Way of Thinkingin Model Based Predictive Control
1. model of the controlled system
this is no difference to conventional control
the better the model, the better the prediction
Page 61
2. cost function
the engineer has to learn to describe
what he wants the controlled system really to do !!!
3. stability
… that‘s a really good question … next question ?
Technische Universität München
Experimental Results (DMPC)current control
comparison : PI control model predictive control
Technische Universität München
Experimental Results (DMPC)current control
Low switching frequency high switching frequency
dynamic of step response is identical !
Technische Universität München
Experimental Results (DMPC)current control
a change of the cost function (nothing else !!!)
results in different behaviour !
Technische Universität München
Features of (Longe Range) Predictive Control
Advantages
• possibility to use foreknowledge about drive system (system model)
• inverter limitations and dynamic behaviours are taken into account
• improved representation of non-linear systems
• no need for time challenging cascade structure
• improved dynamic behaviour
Disadvantages
• high processing capability required
• for industrial use change in teaching engineers necessary
• stationary accuracy and dynamic behaviour
depend on accurracy of model parameters
Technische Universität München
Actual Situation
in cascaded control structures
speed control must be much faster than position control
and current control must be much faster than speed control
current control must be extremely fast
to achieve position control with reasonable cycle times
at the time most requirements in industrial applications are satisfied sufficiently
there is no strong need for improvement in industry
however – at a certain time there will be a demand for improvement
with respect to a future increase of requirements
more investigations should be done
Page 66
Technische Universität München
Discussion
• predictive control strategies
offer the possibility to use foreknowledge about the drive system
• physical limitations and dynamic behaviour of power electronics
are taken into account
• non-linear systems are represented better (by non-linear models)
• no need for time challenging cascaded structures
• the way of thinking is different
model of the controlled system cost function
with respect to a future increase of requirements
more investigations should be done
Technische Universität München
Outline
Introduction
Predictive Control Methods (Kennel)
Trajectory Based Predictive Control
Hysteresis Based Predictive Control
Long-Range Predictive Control
Predictive Control with Heuristic Preselection
Technische Universität München
Control task
Current control of a three-phase resistive-inductive-active load
Technische Universität München
Heuristic method
• Calculation effort rises exponentially with the prediction horizon
• Three or four prediction steps impossible in real-time
(online as well as offline)
• Cost function to describe the performance to be obtained
• Basic idea of Heuristic Method :
• Optimum integer solution of a linear program
is close to the continuous-valued solution of the integer problem
=> Important: Optimum integer solution is not necessarily
the integer solution which is closest to the continuous-valued optimum
=> Not all integer points have to be examined,
only the ones closest to the continuous-valued optimum
Peter Stolze
Technische Universität München
Heuristic method• Continuous-valued “switching states“ in the range [0; 1]
• Determination of the sector in which the
continuous-valued optimum lies (I to VI)
• For the first two prediction steps the three
closest integer solutions are used for
an exhaustive search
(corners of the triangle)
• For the 3rd and 4th prediction step only the
2 closest integer solutions are used
• 3 prediction steps: 18 possible combinations
4 prediction steps: 36 possible combinations
• In more than 95% of the cases the “real“ optimum is still found
Technische Universität München
Simulation Results
Sinusoidal references Back EMF voltages
R = 10Ω, L = 10mH, Vdc = 540V, T = 100μs
Technische Universität München
Peter Stolze
Finite-Set Model Predictive Control of a
Flying Capacitor Converter with Heuristic
Voltage Vector Preselection
Technische Universität München
Control task• Current control of a three-phase resistive-inductive-active load
• Hysteresis controller for voltage balancing
C1
i1
S11
S12
S13
S14
C2
i2
S21
S22
S23
S24
C3
i3
S31
S32
S33
S34
0.5Vdc
0.5Vdc
R
L
R
L
R
L
E1
E2
E3
Technische Universität München
General remarks
• Heuristic voltage vector
selection algorithm basically
the same as for two-level
inverters but now the
continuous-valued “switching
states“ can be
in the range [-1; 1]
• 24 possible sectors
Re
Im
++-
+0-
+--
+-0
+-+0-+--+
-0+
-++
-+0
-+- 0+-
0+0
-0-
++0
00-
+00
0--
+0+
0-0
00+
--0
0++
-00
+++
000
---
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Technische Universität München
Simulation Results
Sinusoidal references Flying capacitor voltages
R = 10Ω, L = 10mH, Vdc = 540V, T = 100μs, C = 480μF
Technische Universität München
• system states are
forced to follow
(pre-)defined reference
trajectories
• examples
– Direct Self Control
– Direct Speed Control
Predictive Control Strategies
trajectory basedhysteresis based model based
• switching of inverter
takes place at the
(multi-dimensional)
border(s) of a
hysteresis area
• examples
– hysteresis control
(bang-bang control)
– Direct
Torque Control (DTC)
• future control values
are pre-calculated
and optimized until a
(pre-)defined „horizon“
• examples
– Dynamic
Matrix Control
– Generalized
Predictive Control
– Predictive Control with
Heuristic Pre-Selection
Technische Universität München
Outline
Introduction
Predictive Control Methods
Predictive Control versus Cascaded Control
Conclusions/Discussion
Technische Universität München
State of the Art : Field Oriented Control
model
PWM
mainsstator coordinatesfield coordinates
currentcontrollers
fluxcontroller
speedcontroller
encoder
M3~
r
r
is
is
us
ej
e-j
us
6
Technische Universität München
Typical Cascaded Structure of Drive Control
inertia gear etc.
I
current controller
speed controller
positioncontroller
– – –
motorwindings
powerelectronics
Technische Universität München
in cascaded control structures
speed control must be much faster than position control
and current control must be much faster than speed control
current control must be very fast
to achieve position control with reasonable cycle times
in the controlled system (drive, converter, …)
however, there is no time constant justifying cycle times
of 100 µs or less
Problems of Linear Algorithms
Technische Universität München
General Structure of a Predictive Controller
inertia gear etc.
switchingstate
actual
machine state
I
prediction andcalculation
machine andpower electronics
model
motorwindings
powerelectronics
Technische Universität München
• control behaviour
comparable to
feedforward control
• exact knowledge of
system parameters is
required
• appropriate for
realisation by digital
circuits or controllers
Predictive Control Strategies
trajectory basedhysteresis based model based
• control behaviour
comparable to
feedback control
• exact knowledge of
system parameters is
not required
• a maximum error can
be (pre-)defined
• the past is explicitely
considered
• future control values are
pre-calculated and
optimized
until a (pre-)defined
„horizon“
• model parameters can be
estimated on-line
• use of non-linear model is
possible for non-linear
control systems
Technische Universität München
Outline
Introduction
Predictive Control Methods
Predictive Control versus Cascaded Control
Conclusions/Discussion
Technische Universität München
Actual Situation
in cascaded control structures
speed control must be much faster than position control
and current control must be much faster than speed control
current control must be extremely fast
to achieve position control with reasonable cycle times
at the time most requirements in industrial applications are satisfied sufficiently
there is no strong need for improvement in industry
however – at a certain time there will be a demand for improvement
with respect to a future increase of requirements
investigations should be done
Technische Universität München
Conclusions/Discussion
• predictive control strategies
offer the possibility to use foreknowledge about the drive system
• physical limitations and dynamic behaviour of power electronics
are taken into account
• non-linear systems are represented better (by non-linear models)
• no need for time challenging cascaded structures
• the way of thinking is different
model of the controlled system cost function
with respect to a future increase of requirements
investigations should be done
Technische Universität München
Thank you !