predictive control of complex systems - uiam.skklauco/files/presentations/...thermal comfort:...

Predictive Control of Complex Systems

Martin Klaučo

Slovak University of Technology in Bratislava, Slovakia

Complex Systems

Thermal Comfort Vehicle Routing

Predictive Control

Martin Klaučo February 27th, 2015 2 / 19

Thermal Comfort

Thermal Comfort: Motivation

Indoor Temperature


Thermal Comfort: Motivation

Indoor Temperature

Clothing

HumidityRadiant Temperature

Metabolic Rate Air Speed


Thermal Comfort: Predicted Mean Vote Index

PMV

Indoor Temperature

Clothing

HumidityRadiant Temperature

Metabolic Rate Air Speed



0 1 2 3-1-2-3

?EN ISO 7730:2006 Ergonomics of Thermal Environment



−3 −2 −1 0 1 2 3

0

20

40

60

80

100

PMV Index

PPS[%

]


Thermal Comfort: Control Objective

Maintain PMV index within -0.2 to 0.2?

?EN ISO 7730:2006 Ergonomics of Thermal Environment


Thermal Comfort: Closed-Loop System

ControlledProcess

Building

Disturbances

d



OnlineComputations

ControlledProcess

Building

Disturbances

x

u

d



OfflineComputations

OnlineComputations

ControlledProcess

Building

Disturbances

xx

u

dd

Explicit MPCConstruction


Thermal Comfort: MPC Implementation

minN−1∑k=0

quu2k + qpp2

k

s.t. xk+1 = Axk + Buk + Ed0

umin ≤ uk ≤ umax

pk = PMV(xk)

pmin ≤ pk ≤ pmax

x0 = x(t), d0 = d(t)

Online MPC Explicit MPC

u?(θ) =

F1θ + g1 if θ ∈ R1

...FLθ + gL if θ ∈ RM


MPC with PMV Index

PMV =(0.303e−0.036M + 0.028

)· L

L =(M −W )− 3.05 · 10−3(5733− 6.99(M −W )− pa)−

− 0.42((M −W )− 58.15

)− 1.7 · 10−5M(5867− pa)−

− 0.0014M(34− Tin)− 3.96 · 10−8fcl(Ktcl − Ktr

)−

− fclhc(Tcl − Tin)

Tcl =− 0.028(M −W )− Icl(3.96 · 10−8(fclKtcl − Ktr

)+

+ fclhc(Tcl − Tin))

+ 35.7

Ktcl = (Tcl + 273.16)4

Ktr = (Tr + 273.16)4



minN−1∑k=0

quu2k + qpp2

k



pk = PMV(xk)


x0 = x(t), d0 = d(t)


u?(θ) =

F1θ + g1 if θ ∈ R1


Klaučo M., Kvasnica M., Explicit MPC Approach to PMV-Based Thermal Comfort Control, IEEE CDC 2014 in Los Angeles,

CaliforniaMartin Klaučo February 27th, 2015 7 / 19


minN−1∑k=0

quu2k + qpp2

k



pk = `T1 a(x0) + `T2 xk−1 + `T3 uk−1 + `4 b(x0)


x0 = x(t), d0 = d(t)


u?(θ) =

F1θ + g1 if θ ∈ R1


Klaučo M., Kvasnica M., Explicit MPC Approach to PMV-Based Thermal Comfort Control, IEEE CDC 2014 in Los Angeles,

CaliforniaMartin Klaučo February 27th, 2015 7 / 19

Thermal Comfort: Simulation Test Scenarios

1

2

Temperature-based control

PMV-based control



0 2 4 6 8 10 12 14 16 18 20 22 240.00

0.05

0.10

0.15

0.20

AirSp

eed[m

/s]

0 2 4 6 8 10 12 14 16 18 20 22 240

100200300400500

Occup

ancy

[W]

0 2 4 6 8 10 12 14 16 18 20 22 240

150300450600750900

Time [h]

SolarRa

diation[W

]



0 2 4 6 8 10 12 14 16 18 20 22 240.00

0.05

0.10

0.15

0.20

AirSp

eed[m

/s]

0 2 4 6 8 10 12 14 16 18 20 22 240

100200300400500

Occup

ancy

[W]

0 2 4 6 8 10 12 14 16 18 20 22 2420

20.521

21.522

22.523

Int.

Temp[C]

0 2 4 6 8 10 12 14 16 18 20 22 240

150300450600750900

Time [h]

SolarRa

diation[W

]

0 2 4 6 8 10 12 14 16 18 20 22 24

−5−3−1135

Time [h]

HeatFlow

[kW/s]



0 2 4 6 8 10 12 14 16 18 20 22 240.00

0.05

0.10

0.15

0.20

AirSp

eed[m

/s]

0 2 4 6 8 10 12 14 16 18 20 22 24

−0.3−0.2−0.1

00.10.20.3

PMV

0 2 4 6 8 10 12 14 16 18 20 22 240

100200300400500

Occup

ancy

[W]

0 2 4 6 8 10 12 14 16 18 20 22 2420

20.521

21.522

22.523

Int.

Temp[C]

0 2 4 6 8 10 12 14 16 18 20 22 240

150300450600750900

Time [h]

SolarRa

diation[W

]

0 2 4 6 8 10 12 14 16 18 20 22 24

−5−3−1135

Time [h]

HeatFlow

[kW/s]


Thermal Comfort: Key Points

1

2

3

Thermal comfort model (PMV index)

Explicit MPC implementable on thermostat-like device

Mathematical framework for eMPC with quadratic constraints


Vehicle Routing

Vehicle Routing: Heterogeneous Multi-Vehicle Systems


Vehicle Routing: Heterogeneous Multi-Vehicle Systems

Operation range: ∞Maximum velocity: vc

Operation range: tmaxMaximum velocity: vh > vc

Operation range: ∞Maximum velocity: vc


Vehicle Routing: Motivation


Vehicle Routing: Single Vehicle

START STOP

q1 q2q3

q4

qi point to be visited

0.0 10.0 20.0 30.0 40.0 50.0

0.0

10.0

20.0

30.0

40.0

50.0

[km]

[km]


Vehicle Routing: Multi-vehicle System

START STOP

q1 q2q3

q4

qi point to be visited

0.0 10.0 20.0 30.0 40.0 50.0

0.0

10.0

20.0

30.0

40.0

50.0

[km]

[km]



START STOP

q1 q2q3

q4

τ1

qi point to be visitedτi take-off point

0.0 10.0 20.0 30.0 40.0 50.0

0.0

10.0

20.0

30.0

40.0

50.0

[km]

[km]



START STOP

q1 q2q3

q4

τ1`1

qi point to be visitedτi take-off point`i landing point

0.0 10.0 20.0 30.0 40.0 50.0

0.0

10.0

20.0

30.0

40.0

50.0

[km]

[km]



START STOP

q1 q2q3

q4

τ1τ2`1

`3


0.0 10.0 20.0 30.0 40.0 50.0

0.0

10.0

20.0

30.0

40.0

50.0

[km]

[km]



START STOP

q1 q2q3

q4

≈ 30%

τ1τ2

τ4

`1`3

`4


0.0 10.0 20.0 30.0 40.0 50.0

0.0

10.0

20.0

30.0

40.0

50.0

[km]

[km]


Vehicle Routing: Control Objective

Calculate coordinates of take-off and landing points

minimize mission time

visit all way-pointsbounded helicopter flyovervisit multiple way-points during one flyover


Vehicle Routing: Solution

MI-NLP reformulation

Garone, Determe, Naldi, CDC 2012



5 10 20 30 40 50 60 70 80 90 100100

101

102

103

104

105

Number of points qi to visit

Compu

tatio

ntim

e[sec]

MI-NLP



MI-NLP MI-SOCPreformulationequivalent

Garone, Determe, Naldi, CDC 2012 Klaučo, Blažek, Kvasnica, ECC 2014



5 10 20 30 40 50 60 70 80 90 100100

101

102

103

104

105

Number of points qi to visit

Compu

tatio

ntim

e[sec]

MI-NLPMI-SOCP


Vehicle Routing: Key Points

1

2

3

Optimal path planing for multi-vehicle systems

Mixed-integer SOCP formulation

Applicable to larger number of waypoints


Conclusions



Conclusions


Predictive Control


Conclusions


Predictive Control

Efficient problem formulations


Aims of Thesis

1

2

3

Development of computationally efficient optimal controlalgorithmsVerification and implementation of optimal control algorithmson laboratory devicesApplication of optimization and optimal control to path plan-ning problems


Publications

Publications - A-class

1 Klaučo, Drgoňa, Kvasnica, Cairano. Building Temperature Con-trol by Simple MPC-like Feedback Laws Learned from Closed-Loop Data. IFAC World Congress 2014


Publications - IEEE Conferences

2

3

4

5

Klaučo, Kvasnica. Explicit MPC Approach to PMV-BasedThermal Comfort Control. CDC 2014

Klaučo, Blažek, Kvasnica, Fikar. Mixed-Integer SOCP Formula-tion of the Path Planning Problem for Heterogeneous Multi-Vehicle Systems. ECC 2014

Drgoňa, Kvasnica, Klaučo, Fikar. Explicit Stochastic MPC Ap-proach to Building Temperature Control. CDC 2013

Klaučo, Poulsen, Mirzaei, Niemann. Frequency Weighted ModelPredictive Control of Wind Turbine. Process Control 2013


Publications - In Progress

Accepted:6 Oravec, Klaučo, Kvasnica, Löfberg. Vehicle Routing with Inter-

ception of Targets’ Neighbourhoods. ECC 2015

In preparation:7

8

9

Drgoňa, Klaučo, Fikar. Model Identification and Predic-tive Control of a Laboratory Binary Distillation Column.Process Control 2015

Kalúz, Klaučo, Kvasnica. Explicit MPC-based Reference Gov-ernor Control of Magnetic Levitation via Arduino Microcon-troller. Process Control 2015

Klaučo, Blažek, Kvasnica. Optimal Path Planning Problem forHeterogeneous Multi-Vehicle System. CC Journal


Opponents Questions

Question 1

Ako súvisí linearita so zhodou modelu a riadeného procesu? (str. 17)

minN−1∑k=0

(xk − x s)T Qx(xk − x s) +N−1∑k=0

(uk − us)T Qu(uk − us),

s.t. xk+1 = Axk + Buk k = 0, . . . ,N − 1,x0 = x(t)xk ∈ X k = 1, . . . ,N − 1uk ∈ U k = 1, . . . ,N − 1


Question 2

Je vektor X v (2.19) uvedený správne? (str. 21)

X =

x0x1...

xN−1

−→ X =

x0x1...

xN


Question 3

Čo musia spĺňať východiskové podmienky pre (3.9), aby bol problémriešiteľný? (str. 35)

minN−1∑k=0

qu(uk − us)2 + qpp2k+qssk

s.t. xk+1 = Axk + Buk + Ed0pk = PMV(xk)

− 5000 ≤ uk ≤ 5000− 0.2 ≤ pk ≤ 0.2

x0 = x(t), d0 = d(t)


Question 3

Čo musia spĺňať východiskové podmienky pre (3.9), aby bol problémriešiteľný? (str. 35)

minN−1∑k=0

qu(uk − us)2 + qpp2k+qssk

s.t. xk+1 = Axk + Buk + Ed0pk = PMV(xk)

− 5000 ≤ uk ≤ 5000−sk − 0.2 ≤ pk ≤ 0.2 + sk

x0 = x(t), d0 = d(t)


Question 4

Aký je vzťah medzi „k“ a „t“ pri riešení (3.11)? Aká je realistickáperióda vzorkovania pre ktorú možno očakávať riešiteľnosť problému(zaručiť PMV v predpísaných hraniciach)? (str. 36)

minN−1∑k=0

qu(ut+k − us)2 + qpp2t+k

s.t. xk+t+1 = Axt+k + But+k + Ed0pt+k = aT xt+k + b

− 5000 ≤ ut+k ≤ 5000− 0.2 ≤ pt+k ≤ 0.2

x0 = x(t), d0 = d(t)


Question 5

Prečo sa robila lineárna interpolácia PMV z kvadratickejaproximácie a nie z pôvodnej funkcie? (str. 40)

PMV =(0.303e−0.036M + 0.028

)· L

L =(M − W ) − 3.05 · 10−3(5733 − 6.99(M − W ) − pa

)−

− 0.42(

(M − W ) − 58.15)

− 1.7 · 10−5M(5867 − pa)−

− 0.0014M(34 − Tin) − 3.96 · 10−8fcl(

Ktcl − Ktr)

−

− fclhc(Tcl − Tin)

Tcl = − 0.028(M − W ) − Icl(3.96 · 10−8

(fclKtcl − Ktr

)+

+ fclhc(Tcl − Tin))

+ 35.7

Ktcl = (Tcl + 273.16)4

Ktr = (Tr + 273.16)4


Question 5

Prečo sa robila lineárna interpolácia PMV z kvadratickejaproximácie a nie z pôvodnej funkcie? (str. 40)

T1 T0 T2

−0.12

0.025

0.05

Temperature [◦C]

PMV


Question 6

Testovali ste riešenie problému (3.19) aj pre počiatočné podmienkys nerovnakými teplotami? Aký majú počiatočné podmienky vplyvna riešenie/riešiteľnosť problému? (str. 38)

minN−1∑k=0

qu(uk − us)2 + qpp2k

s.t. xk+1 = Axk + Buk + Ed0pk = θT Mkθ + θT KkUol + mT θ

− 5000 ≤ uk ≤ 5000− 0.2 ≤ pk ≤ 0.2x0 = x(t), d0 = d(t)


Question 7

Je interpretácia m vo formulácii problému (str.47) správna? (Vďalšom riešení sa uvažuje m=n.)

m = n


Question 8

Ako si navrhnuté prístupy riešenia poradia s neurčitosťami modelov?(Stačí na to pri riadení tepelného komfortu spätná väzba?)

trvalá regulačná odchýlkapoužitie "disturbance modelling"pri SISO zaviesť integrátor pred akčný zásah


Discussion - Backup Slides

Quadratic constraints

minN−1∑k=0

quu2k + qpp2

k



pk = PMV(xk)


x0 = x(t), d0 = d(t)

Online MPC

convex quadratic

linear

linear

linear



minN−1∑k=0

quu2k + qpp2

k



pk = a(x0)T xk + b(x0)


x0 = x(t), d0 = d(t)

Online MPC

convex quadratic

linear

linear

linear



minN−1∑k=0

quu2k + qpp2

k



pk = a(x0)T (Axk−1 + Buk−1) + b(x0)


x0 = x(t), d0 = d(t)

Online MPC

convex quadratic

linear

non-linear

linear

linear



minN−1∑k=0

quu2k + qpp2

k



pk = `T1 a(x0) + `T2 xk−1 + `T3 uk−1 + `4 b(x0)


x0 = x(t), d0 = d(t)

Online MPC

convex quadratic

linear

linear

linear

linear



minN−1∑k=0

quu2k + qpp2

k



pk = θT Mkθ + θT KkUol + mT


x0 = x(t), d0 = d(t)

Online MPC

convex quadratic

linear

linear

linear

linear


predictive control of complex systems - uiam.skklauco/files/presentations/...thermal comfort:...

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