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MPC Design for Power Electronics:Perspectives and Challenges
Daniel E. Quevedo
Chair for Automatic ControlInstitute of Electrical Engineering (EIM-E)
Paderborn University, [email protected]
IIT Bombay, March 2017
D
x00 k
x( )-k x
±
a) b)
x1 x1
x2
x2
?
?
?
x( )-k x?
±
1 2 3 4 50
0.2
0.4
0.6
0.8
1
Prediction horizon of the MPC
Cost func.Complexity
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 1 / 42
Model Predictive Control
Model Predictive Control (MPC) is one of the key strategies incontemporary systems control.It has a long history1 and has had a major impact on industrial(process) control applications.An attractive feature of MPC lies in its unique capacity to tackleflexible problem formulations.MPC can handle general constrained nonlinear systems withmultiple inputs and outputs in a unified and clear manner.Concepts needed to implement MPC are intuitive and easy tounderstand→ “human based”.
1e.g., Dreyfus, The art and theory of dynamic programming, 1977.Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 2 / 42
MPC for Power Electronics
Due to their switching nature, power electronics circuits give rise to aunique set of control engineering challenges.
Various embodiments of MPC principles have emerged as apromising alternative for power converters and electrical drives.MPC can handle converters and drives with multiple switches andstates; e.g., current, voltage, power, torque, etc.It has the potential to replace involved control architectures, suchas cascaded loops, by a unique controller.MPC formulations can be extended to suit specific modes ofoperation, e.g., start-up procedures and fault accommodation.Successful designs however, require domain specific knowledge.
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 3 / 42
This talk1 revises basic concepts of MPC (apologies)2 presents some of our work on how to choose design
parameters in MPC for power converters3 points to research challenges
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 4 / 42
Outline
1 Background to MPC
2 Choice of Weighting Functions
3 Switching Constraint Sets
4 Reference Design
5 Challenges
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 5 / 42
Background to MPC
Basic Ingredients of MPC
1 A (discrete-time) system model to evaluate predictions:2
x(k + 1) = f (x(k),u(k)), k ∈ 0,1,2, . . . ,
whereI x(k) is the system state (capacitor voltages, inductor currents),I u(k) is the control input (e.g., switch positions)
The discrete-time model can be obtained from a continuous timemodel and take into account computational delays.
2 Constraints3 Cost function4 Moving horizon optimization
2Quevedo, Aguilera, Geyer, Advanced and Intelligent Control in Power Electronicsand Drives, Springer, 2014.
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 6 / 42
Background to MPC
System constraints
State and input constraints can be incorporated
x(k) ∈ X ⊆ Rn, k ∈ 0,1,2, . . . ,u(k) ∈ U ⊆ Rm, k ∈ 0,1,2, . . . .
State constraints: e.g., capacitor voltages or load currentsInput constraints
Input constraintsu(k) ∈ U describes switch positions during theinterval (kh, (k + 1)h].
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 7 / 42
Background to MPC
Input constraints
Continuous control set
ControllerModulation
PowerConverter
ElectricalLoad
MPCx?
x k( )
PowerSource
d k( )
S k( )
~
u(k) = d(k) ∈ U , [−1,1]m
Finite control setPower
Converter
Electrical
Load
Power
Source
~
FCS-MPC
Controller
x?
S k( )
x k( )
u(k) = S(k) ∈ U , 0,1m
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 8 / 42
Background to MPC
Cost functionA cost function over a finite horizon of length N is minimized at eachtime instant k and for a given (measured or estimated) plant state x(k).
Performance Measure
V (x(k), ~u′(k)) , F (x ′(k + N)) +k+N−1∑`=k
L(x ′(`),u′(`)).
The controller uses the current plant state x(k) to examinepredictions x ′(`), which would result if the inputs were set to
~u′(k) ,
u′(k),u′(k + 1), . . . ,u′(k + N − 1),
The weighting functions L(·, ·) and F (·) serve to trade quality ofcontrol for actuation effort (e.g., switching losses).
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 9 / 42
Background to MPC
Optimizing control sequenceConstrained minimization of V (·, ·) gives the optimizing controlsequence at time k and for state x(k):
~uopt(k) ,
uopt(k),uopt(k + 1; k), . . . ,uopt(k + N − 1; k).
In general, plant state predictions, x ′(`), will differ from actual plantstate trajectories, x(`). This is due to:
uncertainties in the parameter valuesuse of simplified modelsdisturbances
To address these issues, feedback is used!
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 10 / 42
Background to MPC
Moving Horizon Optimization
Optimizing control sequence
~uopt(k) ,
uopt(k),uopt(k + 1; k), . . . ,uopt(k + N − 1; k).
To obtain a closed loop control law, commonly only the firstelement is used:
u(k)←− uopt(k).
At the next sampling step, the current state x(k + 1) is measured(or estimated) and another optimization is carried out.This gives ~uopt(k + 1) and
u(k + 1) = uopt(k + 1) 6= uopt(k + 1; k).
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 11 / 42
Background to MPC
Moving Horizon Optimization
The constrained minimizationof the cost function is carriedout at every time step kThe optimization takes intoaccount the entire horizonOnly the first element of~uopt(k) is usedThe horizon slides forward ask increases
6 Daniel E. Quevedo, Ricardo P. Aguilera, and Tobias Geyer
(k +1)hkh (k +2)h (k +3)h (k +4)h (k +5)h (k +6)h
(k +1)hkh (k +2)h (k +3)h (k +4)h (k +5)h (k +6)h
(k +1)hkh (k +2)h (k +3)h (k +4)h (k +5)h (k +6)h
uopt(k +1)
uopt(k +2)
uopt(k)
uopt(k)
uopt(k +1)
uopt(k +2)
Fig. 3 Moving horizon principle with horizon N = 3.
The design of observers for the system state lies outside the scope of the presentchapter. The interested reader is referred to [2, 29, 41], which illustrate the use ofKalman filters for MPC formulations in power electronics.
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 12 / 42
Background to MPC
1 System model2 Constraints3 Cost function4 Moving horizon optimization
Choice of Cost FunctionIn addition to assigning the sampling interval (which, inter alia,determines the system model), the choice of cost function is key.
Design parametersweighting functions F (·) and L(·, ·),references,constraint set U,horizon length N.
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 13 / 42
Background to MPC
Cost Function Design
V (x(k), ~u′(k)) , F (x ′(k + N)) +k+N−1∑`=k
L(x ′(`),u′(`)), u′(`) ∈ U.
The weighting functions F (·) and L(·, ·) should take into accountthe actual control objectives and may also considerstability/performance issues.The choice of constraint set has an impact on hardware to beused and resulting performance.To design reference trajectories for the system state, one needs totake into account physical/electrical properties.The optimization horizon N allows the designer to trade-offperformance versus on-line computational effort.
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 14 / 42
Choice of Weighting Functions
Table of Contents
1 Background to MPC
2 Choice of Weighting Functions
3 Switching Constraint Sets
4 Reference Design
5 Challenges
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 15 / 42
Choice of Weighting Functions
Closed Loop Dynamics
Due to the switching nature of power converters, characterizingclosed loop performance is a highly non-trivial task.Lyapunov-stability ideas can be used to design the cost function toensure that the state trajectory remains bounded.3
D
x00 k
x( )-k x
±
a) b)
x1 x1
x2
x2
?
?
?
x( )-k x?
±
Convergence of the converterstate, x(k), to a neighbourhood ofthe reference x?:
1 Practical asymptotic stability2 x(k) will be confined in D
3Aguilera and Quevedo, IEEE Trans. Ind. Inf., Feb. 2015Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 16 / 42
Choice of Weighting Functions
Quadratic cost, horizon N = 1, finite U
V (x(k),u′(k)) = ‖x(k)− x?(k)‖2Q+ ‖u′(k)− u?(k)‖2R + ‖x ′(k + 1)− x?(k + 1)‖2P .
Constrained solution (also valid for larger horizons!)
uopt(k) = W−1/2qV
(W 1/2uopt
uc (k))∈ U,
uoptuc (k) is the unconstrained solution and qV is a vector quantizer.a
aQuevedo, Goodwin, De Dona, Int. J. Robust Nonlin. Contr., 2004
By denoting the quantization error via ηV(k), we obtain:
uopt(k) = uoptuc (k) + W−1/2ηV(k),
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 17 / 42
Choice of Weighting Functions
Performance GuaranteesUsing the cost as a candidate Lyapunov function and adapting robustcontrol (ISS) ideas, we obtain an
FCS-MPC design procedure1 Choose Q and R2 Calculate matrices P and W3 Assign the (circular) nominal
control region U.4 Check an inequality which
relates the maximumquantization error to systemparameters
5 Calculate regions Xf and Dδ.
u1
u0
u2u3
u4
u5 u6
u ´
UXf
u® d,
u¯ q, q
xd
umax
x
D
b
±
xd?
xq?
(a) (b)
(a) Finite control set U andnominal control region U.(b) Terminal region Xf and
bounded set Dδ.
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 18 / 42
Choice of Weighting Functions
Example: Two-Level Inverter
a
dcV
ia
ib
ic
L r
vib
via
vic
S bS cS
The switch position are restricted to belong to the finite set
S ,
[000
],
[001
],
[010
],
[011
],
[100
],
[101
],
[110
],
[111
].
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 19 / 42
Choice of Weighting Functions
State Space Descriptiona
dcV
ia
ib
ic
L r
vib
via
vic
S bS cS
Considering x = idq and u = sdq, a discrete-time model of the 2-levelinverter, in the rotating dq frame, is given by:
x(k + 1) = Ax(k) + Bu(k),
where
A =
[1− hr/L ωh−ωh 1− hr/L
], B =
[hVdc/L 0
0 hVdc/L
].
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 20 / 42
Choice of Weighting Functions
Experimental results; Vdc = 200V , r = 5Ω,L = 17mHR = 2I2×2
-1 0 1 2 3 4 5 6 7 8-3
-2
-1
0
1
2
3
id
i q
x0
D± Xf
=XXMPC
0 10 20 30 40 50 60
-5
0
5
i ab
c(t
) [A
]
0 10 20 30 40 50 60
0
100
200
va(t
) [V
]
0 10 20 30 40 50 60
-200
-100
0
100
200
va
b(t
) [V
]
Time [ms]
0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000
20
40
60
Frequency [Hz]
Va
[%]
R = 0.0001I2×2
-1 0 1 2 3 4 5 6 7 8-3
-2
-1
0
1
2
3
id
i q
x0
D±
=XXMPC
Xf
0 10 20 30 40 50 60
-5
0
5
i ab
c(t
) [A
]
0 10 20 30 40 50 60
0
100
200
va(t
) [V
]0 10 20 30 40 50 60
-200
-100
0
100
200
va
b(t
) [V
]Time [ms]
0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000
20
40
60
Frequency [Hz]
Va
[%]
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 21 / 42
Choice of Weighting Functions
Summary
When controlling solid-state power converters in discrete-time, ingeneral, voltages and currents will not converge to the desiredsteady-state values.
In some situations, the cost functionof Finite Control-Set MPC can bedesigned to guarantee
1 practical stability of the powerconverter
2 a desired performance level
D
x00 k
x( )-k x
±
a) b)
x1 x1
x2
x2
?
?
?
x( )-k x?
±
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 22 / 42
Switched MPC
Outline
1 Background to MPC
2 Choice of Weighting Functions
3 Switching Constraint Sets
4 Reference Design
5 Challenges
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 23 / 42
Switched MPC
Choice of Constraint Set
Continuous control set
ControllerModulation
PowerConverter
ElectricalLoad
MPCx?
x k( )
PowerSource
d k( )
S k( )
~
u(k) = d(k) ∈ U , [−1,1]m
Finite control setPower
Converter
Electrical
Load
Power
Source
~
FCS-MPC
Controller
x?
S k( )
x k( )
u(k) = S(k) ∈ U , 0,1m
Depending on the constraint set imposed, the resulting controllershave complementary properties.
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 24 / 42
Switched MPC
Finite Control-Set MPC
Finite control setPower
Converter
Electrical
Load
Power
Source
~
FCS-MPC
Controller
x?
S k( )
x k( )
u(k) = S(k) ∈ U , 0,1m
Advantagescan deal with non-linearconverter topologiesprovides fast transients
Limitationsoften gives steady stateerrors and wide-spreadspectra4
4cf., Cortes, Rodrıguez, Quevedo, Silva, IEEE Trans. Power Electron., Mar. 2008.Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 25 / 42
Switched MPC
Continuous Control-Set MPC
Continuous control set
ControllerModulation
PowerConverter
ElectricalLoad
MPCx?
x k( )
PowerSource
d k( )
S k( )
~
u(k) = d(k) ∈ U , [−1,1]m
Advantagessteady-state performancezero-average tracking errorconcentrated spectra
Limitation(tractable) convexformulations are limited tolinear(izable) models
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 26 / 42
Switched MPC
MPC with Switching Constraint Sets
An MPC formulation which combines the complementaryproperties of MPC with and without a modulator can beconceived.5
During transients, the proposed method uses horizon-onenon-linear Finite Control Set MPC to drive the system towards thedesired reference.When the system state is close to the reference, the controllerswitches to linear operation, i.e., a modulator is used.
5Aguilera, Lezana, Quevedo, IEEE Trans. Ind. Inf., Aug. 2015Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 27 / 42
Switched MPC
The constraint set chosen in MPC depends on the value taken bythe triggering function
J(k) , ‖x(k)− x?(k)‖2P ,
To avoid chattering, a hysteresis band is introduced:
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 28 / 42
Switched MPC
Example: Three-cell (four-level) single-phase FCC
States and Inputs
x(k) =
vc1(k)vc2(k)ia(k)
, u(k) =
S1(k)S2(k)S3(k)
Nonlinear Dynamics
x(k + 1) = Ax(k) + B(x(k))u(k)
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 29 / 42
Switched MPC
Experimental results: Start-up
Switched MPC
0
10
20
30
40
50
0
100
200
300
0
5
10
0 10 20 30 40 50
FCS-MPC LSF-PWM
JL
JH
J k[ ]
Syste
m d
evia
tion
Ouput curr
ent [A
]
(b)
(c)
(a)
Syste
m v
oltages [V
]
Vdc
vo
vc2
vc1
Time [ms]
Proposed Switching controller
15ms settling time
Linear State Feedbackcontroller
0
100
200
300
0
5
10
Ouput cu
rrent [A
]
( )b
( )a
Sys
tem
volta
ges
[V]
Vdc
vo
vc2
vc1
0
100
200
300
0
5
10
Ouput cu
rrent [A
]S
yste
m v
olta
ges
[V]
0
100
200
300
0
5
10
Ouput cu
rrent [A
]S
yste
m v
olta
ges
[V]
0 0.2 0.4 0.6 0.8 1 1.2 1.4Time [s]
Vdc
vo
vc2
vc1
Vdc
vo
vc1v
c2
io
io*
io
io*
Time [s]1.381.371.361.351.340 0.01 0.02 0.03 0.04
Time [s](c) ( )d
LSF controller
700ms settling time
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 30 / 42
Switched MPC
Steady-state Performance
Switched MPC Finite Constraint Set MPC
0
100
200
300
4
Ou
tpu
t cu
rre
nt
sp
ectr
[A
]u
mO
up
ut
cu
rre
nt
[A]
(b)
(c)
(a)
Inn
er
vo
lta
ge
s [
V]
Vdc
vo
vc2
vc1
Time [ms]
6
8
2
0 5 10 15 20 25 30 35 40
0.1
0.2
00 1 2 3 4 5 6 7 8 9 10
Frequency [kHz]
10
4.0 A@50 Hz
0
100
200
300
Ou
tpu
t cu
rre
nt
sp
ectr
[A
]u
mO
up
ut
cu
rre
nt
[A]
(e)
(f)
(d)
Inn
er
vo
lta
ge
s [
V]
Vdc
vo
vc2
Time [ms]0 5 10 15 20 25 30 35 40
0.1
0.2
00 1 2 3 4 5 6 7 8 9 10
Frequency [kHz]
vc1
3.9 A@50 Hz
4
6
8
2
10
FCS-MPCProposed Switching controller
Better steady-state response than Finite Constraint Set MPCDaniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 31 / 42
Switched MPC
Summary
In some instances, one may choose the input constraint set usedin the MPC formulation.The control algorithm described switches between non-linearFinite Control Set MPC and linear state-feedback control.This exploits the advantages of both basic control strategies.Experiments showed that fast dynamic response can be obtained,even when the system non-linearities are more evident.In steady state, the output current tracks the reference, and powersemiconductors operate at a constant switching frequency.
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 32 / 42
Reference Design
Outline
1 Background to MPC
2 Choice of Weighting Functions
3 Switching Constraint Sets
4 Reference Design
5 Challenges
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 33 / 42
Reference Design
Reference Design
MPC allows one to incorporate references in an explicit manner.
Especially when using short horizons, reference trajectories forthe entire state x(k) should be specified.This requires knowledge of possibilities and limitations of thesystem to be controlled:
1 For AFE converters, careful consideration of energy balancing anddynamic limitations can be used to design compatible referencesfor powers and capacitor voltages.6
2 For Modular Multilevel Converters, it is useful to understand therole of internal (circulating) currents.
6Quevedo, Aguilera, Perez, Cortes, Lizana, IEEE Trans. Power Electron., 2012.Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 34 / 42
Reference Design
Modular Multilevel Converters (MMCs)use a DC/AC topology capable to reach high voltages and power.
Control ChallengesMany input signals (one permodule).The output current ildepends on
1 the circulating current ic2 the capacitor voltages
Thus, a control is required foric and the capacitor voltages.
All variables are related; theirreferences have to be carefullydesigned.
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 35 / 42
Reference Design
FCS MPC with a quadratic cost and N = 1A reduced order model is used for the design of state references(MMC with M = 8 modules per arm).7
Simplified DC references(a) ic, Simplified DC reference for the circulating current ic. The dashedline represents the reference (i0 = 0.0014)
(b) ic , Proposed Reference for the circulating current. The dashed linerepresents the reference (i0 = 0.0014, i2 = −0.46, φ2 = 1.6) see (26)
0 0.005 0.01 0.015 0.02 0.025 0.03
0.215
0.22
0.225
0.23
0.235
time (s)
Cap
acito
r vol
tage
s (p
.u.)
vu vl
(c) vl and vu, Simplified DC reference for the voltages of the capacitors.The dashed line represents the reference (vu,l
DC = 0.224)
0 0.005 0.01 0.015 0.02 0.025 0.03
0.215
0.22
0.225
0.23
0.235
time (s)C
apac
itor v
olta
ges
(p.u
.)
vu vl
(d) vl and vu , Proposed reference for the voltages of the capacitors. Thedashed lines represent the references see (28) and (29)
(e) il, Reference for the load current. The dashed line represents thereference (il = 0.8, φ = 1.57) see (1)
(f) il, Reference for the load current. The dashed line represents thereference (il = 0.8, φ = 1.57) see (1)
Fig. 3. Response of the MPC to a set of simplified references (a), (c) and (d). And the proposed set of references (b), (d) and (e). Sampling frequency 5kHz,P = diag(1, 100, 100, . . . , 100)
bad reference trackinghigh voltage ripple
Designed references(a) ic, Simplified DC reference for the circulating current ic. The dashedline represents the reference (i0 = 0.0014)
(b) ic , Proposed Reference for the circulating current. The dashed linerepresents the reference (i0 = 0.0014, i2 = −0.46, φ2 = 1.6) see (26)
0 0.005 0.01 0.015 0.02 0.025 0.03
0.215
0.22
0.225
0.23
0.235
time (s)
Cap
acito
r vol
tage
s (p
.u.)
vu vl
(c) vl and vu, Simplified DC reference for the voltages of the capacitors.The dashed line represents the reference (vu,l
DC = 0.224)
0 0.005 0.01 0.015 0.02 0.025 0.03
0.215
0.22
0.225
0.23
0.235
time (s)
Cap
acito
r vol
tage
s (p
.u.)
vu vl
(d) vl and vu , Proposed reference for the voltages of the capacitors. Thedashed lines represent the references see (28) and (29)
(e) il, Reference for the load current. The dashed line represents thereference (il = 0.8, φ = 1.57) see (1)
(f) il, Reference for the load current. The dashed line represents thereference (il = 0.8, φ = 1.57) see (1)
Fig. 3. Response of the MPC to a set of simplified references (a), (c) and (d). And the proposed set of references (b), (d) and (e). Sampling frequency 5kHz,P = diag(1, 100, 100, . . . , 100)
accurate reference trackingoptimal voltage ripple
7Lopez, Quevedo, Aguilera, Geyer and Oikonomou, Australian Control Conf., 2014.Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 36 / 42
Reference Design
MPC with larger horizons
Given the large number of switches in MMCs, MPC with largehorizons and using explicit enumeration becomes infeasible.In fact, with M = 8 optimizing for N = 5 would require evaluating(216)5 ≈ 1.2× 1024 switching combinations!
Sphere decoding8 can beadapted to the presentsituation in order to find theoptimal solution with onlyfew computations.Larger horizons giveperformance gains.
1 2 3 4 50
0.2
0.4
0.6
0.8
1
Cost func.Complexity
8Geyer and Quevedo, IEEE Trans. Power Electron., 2014, 2015.Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 37 / 42
Challenges
Outline
1 Background to MPC
2 Choice of Weighting Functions
3 Switching Constraint Sets
4 Reference Design
5 Challenges
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 38 / 42
Challenges
Some research challenges1 developing methods to quantify stability and performance of more
general situationsI more general cost functionsI horizons larger than oneI bilinear systems
2 systematic design methods for referencesI Here domain specific knowledge is key!
3 further focus on computational issuesI larger horizons for bilinear systemsI sphere decoding is just one of the available methods (study signal
processing and information theory literature!)I suboptimal methods / early terminations?
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 39 / 42
Challenges
Some research challenges (I am interested in)More advanced computational methods
I distributed computations in multi-core systemsI time-varying processing resources, e.g., shared computingI non-periodic computations
Networked controlI wireless opens new possibilities!I hot topic in systems control theory and applications (process
control, Internet of Things, Industry 4.0, etc.)I shared communications lead to communication resource limitationsI control / communications co-design is difficult
Can (or should?) Model Predictive Control of power electronicsand drives benefit from these developments?
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 40 / 42
Challenges
Further Reading1 Quevedo, Aguilera, Geyer, “Predictive Control in Power
Electronics and Drives: basic concepts, theory and methods,” inAdvanced and Intelligent Control in Power Electronics and Drives,pp. 181–226, Springer, 2014.
2 Aguilera and Quevedo, “Predictive Control of Power Converters:Designs with Guaranteed Performance,” IEEE Transactions onIndustrial Informatics, vol. 11, no. 1, pp. 53–63, Feb. 2015.
3 Aguilera, Lezana, Quevedo, “Switched Model Predictive Controlfor Improved Transient and Steady-State Performance,” IEEETransactions on Industrial Informatics, pp. 968–977, Aug. 2015.
4 Lopez, Quevedo, Aguilera, Geyer and Oikonomou, “ReferenceDesign for Predictive Control of Modular Multilevel Converters,”Proceedings of the Australian Control Conference, 2014.
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 41 / 42
Challenges
Acknowledgements
Andres LopezPaderborn University, GermanyRicardo AguileraUniversity of Technology Sydney, AustraliaTobias GeyerABB Corporate Research, SwitzerlandPablo LezanaUniversidad Federico Santa Marıa, Chile
Thank you!
Daniel Quevedo ([email protected]) MPC Design for Power Electronics IIT Bombay, March 2017 42 / 42