Outline MPC and Applications - IEEEsites.ieee.org/sb-us/files/2017/01/Camacho_MPC_Aplicaciones.pdf · MPC and Applications ... Caída de Presión: Ecuación de Hazen-Williams C: Coeficiente

E.F. Camacho Robust MPC design, Future and Practical Applications Rocond'2015

MPC and

Applications

Eduardo F. Camacho

Universidad de Sevilla

1E.F. Camacho Robust MPC design, Future and Practical Applications Rocond'2015

Outline

Model Predictive Control

Applications

Oil pipelines

UAV trajectories

Solar energy

2


Woody Allen:

“I took a speed reading course and read

'War and Peace' in twenty minutes. …

….. It involves Russia.”


MPC successful in industry.

Many and very diverse and successful

applications:

Petrochemical, polymers,

Semiconductor production,

Air traffic control

Clinical anesthesia,

….

Life Extending of Boiler-Turbine Systems via

Model Predictive Methods, Li et al (2004)

Many MPC vendors

4


MPC successful in Academia

Many MPC sessions in control conferences

(2/12 at this symposium) and control journals,

MPC workshops.

MPC in other research areas: industrial

electronics, chemical engineering, energy,

transport …

4/8 finalist papers for the IFAC journal CEP

best paper award were MPC papers (2/3

finally awarded were MPC papers)


IFAC Pilot Industry CommitteeChaired by Tariq Samad (Honeywell), 28 total: 15 industry, 12

academia, 1 gov’t;

Members asked to assess impact of several advanced control

technologies:

Q1 Responses [23 responses]

• PID control: 23 High-impact

• Model-predictive control: 18 High-impact; 2 No/Lo impact

• System identification: 14 High-impact; 2 No/Lo impact

• Process data analytics: 14 High-impact; 4 No/Lo impact

• Soft sensing: 12 High-impact; 5 No/Lo impact

• Fault detection and identification [22]: 11 High-impact; 4 No/Lo impact

• Decentralized and/or coordinated control: 11 High-impact; 7 No/Lo impact

• Intelligent control: 8 High-impact; 7 No/Lo impact

• Discrete-event systems [22]: 5 High-impact; 7 No/Lo impact

• Nonlinear control: 5 High-impact; 8 No/Lo impact

• Adaptive control: 4 High-impact; 10 No/Lo impact

• Hybrid dynamical systems: 3 High-impact; 10 No/Lo impact

• Robust control: 3 High-impact; 10 No/Lo impact

6


Why is MPC so successful ?

MPC is Most general way of posing the control problem in the time domain: Optimal control

Stochastic control

Known references

Measurable disturbances

Multivariable

Dead time

Constraints

Uncertainties


Real reason of success: Economics

MPC can be used to optimize operating points (economic objectives). Optimum usually at the intersection of a set of constraints.

Obtaining smaller variance and taking constraints into account allow to operate closer to constraints (and optimum).

Repsol reported 2-6 months payback periods for new MPC applications.

P1 P2

Tmax

8


Flash

Línea 2

Línea 1Lavado

Contacto 1

Contacto 3

Contacto 2

EXHAUST GAS PIPING


10


-5

-4

-3

-2

-1

0

1

2

1 100 199 298 397 496 595 694 793 892

Serie1


12


Benefits

Yearly saving of more that 1900 MWh

Standard deviation of the mixing chamber

pressure reduced from 0.94 to 0.66

Operator’s supervisory effort: percentage

of time operating in auto mode raised

from 27% to 84%.


14

MPC strategy

At sampling time t the future control sequence is compute so that the future sequence of predicted output y(t+k/t) along a horizon N follows the future references as best as possible.

The first control signal is used and the rest disregarded.

The process is repeated at the next sampling instant t+1

t t+1 t+2 t+N

Control actions

Setpoint

E.F. Camacho Robust MPC design, Future and Practical Applications Rocond'2015 15

tt+1t+2

t+N t t+1 t+2 …….. t+N

u(t)

Only the first

control move is

applied

Errors minimized over

a finite horizon

Constraints

taken into

account

Model of

process used

for predicting


t+2 t+1

t+N

t+N+1

t t+1 t+2 …….. t+N t+N+1

u(t)

Only the first

control move is

applied again


PID: u(t)=u(t-1)+g0 e(t) + g1 e(t-1) + g2 e(t-2)

MPC vs. PID


MPC strategy

Consider a nonlinear invariant discrete time system:

x+=f(x,u), x Rn, u Rm

The system is subject to hard constraints

x X, u U

Let u={u(0),...,u(N-1) } be a sequence of N control inputsapplied at x(0)=x,

the predicted state at i is

x(i)=(i;x, u)=f(x(i-1), u(i-1) )

18


MPC strategy

1. Optimization problem PN(x,):

u*= arg minu (i=0,...,N-1) l(x(i),u(i)) + F(x(N))

Operating constaints .

x(i) X, u(i) U, i=0,...,N-1

Terminal constraint (stability): x(N)

2. Apply the receding horizon control law: KN(x)=u*(0).


Linear MPC

f(x,u) is an affine function (model)

X,U, are polyhedra (constraints)

l and F are quadratic functions (or 1-norm

or -norm functions)

QP or LP

20


Otherwise

If f(x,u) is not an affine function

Or any of X,U, are not polyhedra

Or any of l and F are not quadratic functions

(or 1-norm or -norm functions)

Non linear MPC (NMPC)

Non linear (non necessarily convex) optimization problem much more difficult to solve.


Outline


Applications

Oil pipelines

UAV trajectories

Solar energy

22


Redes de oleoductos

Varios

Orígenes


Redes de oleoductos

Varios

Terminales


Redes de oleoductos

Topologías

Activas

Líneas

Dobles


Oleoductos Simples (Topología)

Origen

Terminal

Estación

Bombeo

Bifurcación


Estaciones de Bombeo


Piezométrica


Terminales

• Depósitos para distintos tipos de productos

• Volúmenes operativos máximos y mínimos

• ConsumosE.F. Camacho Robust MPC design, Future and Practical Applications Rocond'2015

Descripción del problema

Problema Global

Conocidos:

Periodo de tiempo

Capacidad de producción de origenes

Necesidades en los terminales (consumo)

Obtener:

Secuencia de bombeo en cada origen

Distribución origen-terminal

Obtención de las secuencias de bombeo

Operación óptima del oleoducto

Operación de las estaciones de bombeo

Ajuste de válvulas en terminales o bifurcaciones


Simulación de Oleoductos

Modelo (I)

Estaciones de Bombeo

Configuraciones programables

Curvas características

Válvulas

Terminales

Capacidades

Consumo variable

Válvulas de regulación de caudal

Tubería

Diámetro

Rugosidad

Longitud

Head Power

Flow

Bifurcaciones

– Válvulas de regulación


Modo Automático

Modo Stripping (I)

Caudal de entrada en cada terminal proporcional al volumen del

paquete destinado a dicho terminal

BATCH 1

TERM1 : 30%

OTROS: 70 %

Q=100

TERM1

Qi=30

Qs=70



Modelo (II)

Caída de Presión: Ecuación de Hazen-Williams

C : Coeficiente de Hazen-Williams

J : Caida de presión en metros por kilómetro

D : Diámetro interior en milímetros

f : Viscosidad del producto en centistokes

Q : Caudal en metros cúbicos por hora



Modelo (III)

Perfil Topográfico

Agentes externos

– Tarifas Eléctricas (Tres tarifas dependiendo del

día de la semana y de la hora del día)

– Paradas para mantenimiento

Paquetes

– Identificación

– Tipo de Producto

– Volumen total

– Destinos



Tipos de Eventos

Llegada de interfases a un componente (estación de

bombeo, terminal,...)

Nivel de un depósito en valor extremo (desbordamiento

o desabastacimiento)

Cambio de tarifa eléctrica (para calcular el coste de

operación)

Parada del sistema

Arranque del oleoducto

Evento periódico (para prevenir tiempos entre eventos

demasiado largos)


Modo Automático

Restricción del Espacio V-T

Curva Superior: Bombeo utilizando la capacidad máxima del sistema

Curva inferior: Cantidad mínima bombeada que permite que cubre las

necesidades y el tiempo prefijado de bombeo

Curva Superior

Curva Inferior


Proyecto ASSESSMENT OF ENERGY

SAVING IN OIL PIPELINES (AESOP)

Redes de oleoductos casi saturadas. Necesidad de

incrementar las capacidades de transporte en los

oleoductos

Uso de aditivos poliméricos (flow improvers)

Experiencias previas muestran que reducen drásticamente las

Caídas de Presión

Muchas cuestiones abiertas para grandes instalaciones

industriales

Socios: CLH, SMPR, LICENERGY,CRF, CSL, USE


Proyecto AESOP (EU)

38

DRA

Energy Saving

Transport capabilities

increasing

Truck fleet

reduction

CO2 emission

reduction

Road and railways

traffic reduction

FuelSpillage risk

reduction


Friction Reduction from the injection point

Pipeline diameter: 12"

0,0

10,0

20,0

30,0

40,0

50,0

60,0

70,0

80,0

0,0 20,0 40,0 60,0 80,0 100,0 120,0 140,0 160,0 180,0 200,0

Km from origin

FR

%

AG-RO (5 ppm) AG-RO (10 ppm) AG-RO (15 ppm) AG-RO (20 ppm) PO-LO (10 ppm)



0,0

10,0

20,0

30,0

40,0

50,0

60,0

70,0

80,0

0,000 20,000 40,000 60,000 80,000 100,000 120,000

Km from origin

FR

(%

)

AD-PO (5 ppm) AD-PO (10 ppm) AD-PO (15 ppm) MA-LE (10 ppm) HU-SE (5 ppm) HU-SE (10 ppm)



0,00

10,00

20,00

30,00

40,00

50,00

60,00

70,00

76,00 78,00 80,00 82,00 84,00 86,00 88,00 90,00 92,00 94,00

Km from origin

FR

(%

)

SO-MI (5ppm) SO-MI (10 ppm) SO-MI (15 ppm)

USE

1. Modelo de la efectividad y

degradación de los polímeros

2. Simulación oleoductos con

inyección de polímeros

3. Optimización de la operación


Resultados europeos

40

ADDITIVE

CONCENTRATION

(ppm)

AVERAGE

FUEL FLOW

INCREASING

(%)

TRAFFIC

INCREASING

(millions of ton

km)

ENERGY SAVING

(GW h)

5 26,8 28.676 6.046

10 40,4 43.228 9.114

15 44,4 47.508 10.016

20 52,4 56.068 11.821

ADDITIVE

CONCENTRATION

(ppm)

AVERAGE

ENERGY

SAVING

(kWh/ton

km)

AVERAGE

ENERGY

SAVING

(%)

AVERAGE

ENERGY

SAVING

(GWh)

PRIMARY

ENERGY

SAVING

(GWh)

5 0,0096 19 1027 3094

10 0,0134 26,5 1434 4319

15 0,0155 30,7 1659 4995

20 0,0182 36 1947 5866

Escenario 1: Oleoductos con capacidad suficiente

Escenario 2: Oleoductos saturados. El aumento se transporta

por camiones y trenes


Outline


Applications

Oil pipelines

UAV trajectories

Solar energy


AIRPORTS-MPC(Project funded by Boeing)

42

Project GoalsMinimize control error with respect to guidance indications

• Flight guidance shall be provided in the form of AIDL (Aircraft Intent

Description Language)

• MPC is expected to increase performance, in particular, during

transitory maneuvers in comparison with conventional flight

controllers

• Actual flight tests imply that considerations for real-time, embedded

execution and uncertainties in the flight dynamics need to be taken


Sample AIDL trajectory model

Vertical profile

O… PP

cL1

cL1

PP ORTO PP PP

cL1

cL1

cL1

cL1

cL1

cL1

cWP7WP1

cWP0:L1

WP0

WP1

WP4

WP5

WP6

WP7

iM.78

cV0

cAT1000

STHS MACH HS CAS

HSB

HLGSLG

cHIDL

x

HS CAS

iCAS 280

iCAS180

x x xc30%

c60%

c90%

x

HSB

HHL SHL HHL SHL HHL

LG DWNc

CAS>250x

SHL

iAT6000

WP4

x

C… OO

HA

C… OO

HS MACH

HT

HLG

HSB

HAR HAR

HT

HHL

MACH/CAS transition altitude

TOD

ST

cLIDL

WP5 WP6

CAS250 CAS220

WP4 WP5 WP6

WP7

RWY

Lateral profile

1 2 3 4 5 6 7 8 9 10 11 12 13 .. 15 .. 17 18 .. 20 21 .... 24

ORTO PP

FL240

3000 AGL

AT 1000 AGL

cAT3000:V1

cV0

CIRC OOCIRC PP

AR

LG

SB

HL

LAT

LON

PROP

Ops

Point Orto Circle

LL PP PR

OO PC OO

CP

CC

PS

PP

Helix

HELIX PSHELIX PS HELIX PP

WP2

WP3

CIRC OOORTO PPCIRC OOORTO PP

cWP3:L1cWP2:L1cWP1:L1c WP0

0.40.30.20.1

WP0

WP2

WP3

WP4

WP5

WP1

AOB 3000 AGL

ATA FL240

WP0

WP6WP7

AT 1000 AGL

Hippodrome Eight

OR

OC

PPR

PBR

PBP

c

WP1 WP2 WP0WP3 WP1

At (altitude) wih path angle

At (altitude)

At (altitude) or below (AOB)

At (altitude) or above (AOA)

Waypoint with bearing

Distance/time signaled waypoint

L2/V2 continuity symbol


Reference fix/point

Waypoint (L0 continuity)

Waypoint with L1 continuity

Waypoint with L2 continuity


Begin of AI instance

End of AI instance

Constraint trigger

i Inspective trigger

x Explicit trigger

Milestone

Diverter

Simultaneity link

Diversion link

AIDL – Abstract view

Latitude

Longitude

Altitude

Distance


Mugin


Outline


Applications

Oil pipelines

UAV trajectories

Solar energy


46

•Accounts for about 98.6% of the Solar System's mass.

•The mean distance from the Earth is approximately 149,600,000 kilometres

•Its light travels this distance in 8 minutes and 19 seconds.

•Consists of hydrogen (74% of its mass, or 92% of its volume), helium (24% of

mass, 7% of volume),

Here comes the Sun


47

Solar radiation


48


Available Power


50

The cosine factor


51

Extraterrestial daily solar radiation and

latitude


Source INM

Average daily solar energy in Spain


Solar power systems covering the dark disks could

provide more than the world's total primary energy

demand (assuming a conversion efficiency of 8%)


Use of solar energy


Concentrating solar power:

Parabolic trough collectors


Solar towers

Abengoa solar PS20 tower

•1,255 mirrored heliostats

•531 feet-high tower


57

Six dish stirling systems,

in operation at the PSA


Control problems in solar

systems

Collectors movement (sun tracking)

Slow

Open loop (almost)

Temperature and pressure control

Rich dynamics (PDEs, deadtimes, nonlinear, …)

High disturbances

Closed loop (almost)


PS 10 (Abengoa)


Heliostat normal

60


Celestial North PoleSpring/Summer

Φ

Northen Hemisfere

observer

Φ

Sun vectorZenit

S N

E

W

Ψ

δ

α

θz

θz Zenital angle

α Solar elevation

Ψ Acimut

δ declination

Φ latitude

ω

ω Hourly angle

15º/hour


Parabolic trough collectors


Parabolic trough fine tracking


Solar platform of Almeria (PSA)

(desert of Tabernas)


Solar platform of Almeria (PSA)

(desert of Tabernas)


66

PSA


67

GRAAL project:

Gamma ray observatory


68

• Heliostats direct the Cherenkov light generated by air-showers

arriving in the direction of the cosmic source

•(R. Plaga et al, 1999)


69

Heliostat normal


70


71

Some feedback in heliostat solar tracking


72

Receiver feedback: uniform heating


73

Uniform receiver heating


74

Uniform receiver heating


75

Max temperature deviation

(manual operation)


76

Max temperature deviation

(automatic mode)


77

Heliostat calibration


78

Heliostat calibration


79

Blob centroid computation


Plantas cilindro parabólicas

80


81

Acurex plant diagram


Metal: ρm Cm Am ∂Tm / ∂t = ηo I G – G Hl (Tm-Ta) – LHt (Tm-Tf)

Fluid: ρf Cf Af ∂Tf / ∂t + ρf Cf q ∂Tf / ∂x = LHt (Tm-Tf)

Process model

Simulink model can be downloaded from:

E.F. Camacho, et al. Advanced Control of Solar Power Plants, Springer, 1997

http://www.esi2.us.es/~eduardo/libro-s/libro.html

82


Solar field

Parabolic trough

Outlet temp.Oil flow

Solar

radiation

Air

Temp.

Inlet oil

Temp.


84

Why controlling the solar plants is a challenge ?

The energy source is not a manipulated variable but a

perturbation !

Complex dynamics: Non linear, PDE, dead time, never at a

steady state

Constraints (operating closed to constraints)

Deciding the operating mode is part of the control strategy.


MPC and solar power plants


Level 1: Planning (Power tracking)

86

maxmax

max

24

0

)(,)(

)(,0)(,0)(,0)(

)()()1)(()1(

)()()()(

)24()24()()()()(

ccdd

ststststst

stststststst

ststststdsun

stst

tt

pdccd

PtPPtP

PtPtPtptp

dtpdtptPtP

ctpctptPtP

ePtePtPtetPJ

•Given Psun(t) and Pc(t) compute Pd(t) which maximize J

•Every hour and decreasing control horizon


Level 2:

Optimal operating points

Solar

radiation

Reflectivity

Solar

power

Day, hour

Thermal

losses

Net

thermal

power

Outlet oil

temperature

Inlet oil

temperature

Air

temperature,

…

Oil flow

Pumps

power

Generated

electrical

power

Net

electrical

power

x

x

xStored

Energy

Dynamical problem


Level 2 PSA

Optimal electricity production (black) vs FixedTemp. 300ºC.

Increase of 200 KWh/day

Extrapolating to a 50MWe >>> 20 MWh/day >>> 6000 euros/day

88

E.F. Camacho, A.J. Gallego. Optimal operation in solar trough plants, Solar Energy, 2013.5


89

Level 3: Regulation.Many contributors and many control techniques !

R. Carmona (1985)

F.R. Rubio (1985)

J.A. Gutierrez (1987)

M. Hughes (1992)

M. Berenguel (1995)

J. Normey (1997)

M. R. Arahal (1997)

L. Valenzuela (2005)

E. Zarza (2005)

C. M. Cirre (2006)

M.P. Parte (2005)

I. Alvarado (2008)

….

• J. M. Lemos (1997)• E. Mosca (1998)• R.N. Silva (1997)• L.M. Rato (1997)• A.L. Cardoso (1999)• A. Dourado (1999)• T.A. Jonahansen (2000)• M. Brao (2000)• E. Juuso (2000)• I. Farkas (2002)• I. Vajk (2002)• L. Yebra (2005)• ….…


90

Feedforward compensation

Camacho, Rubio and Hughes. IEEE CSM, 1992


91

Why MPC in Solar ?


92

NMPC computation


93

Plant results: a clear day

Very fast setpoint tracking, little overshoot


94

Plant results: a cloudy day


Unscented Kalman Filter

MPC

Control Predictivo de Sistemas de Energ´ıa Solar Distribuidos 80 / 81

Conclusiones y trabajos futuros

Lista de Publicaciones

1 A.J.Gallego, E.F. Camacho (2012,2013)


PSA Acurex


Spain (650 MWe)• Solucar (3x50MWe)

• Helioenergy (2x50MWe)

• Solacor (2x50MWe)

• Helios (2x50MWe)

• Solaben (4x50MWe)

USA (560 MWe)• Solana (280 MWe)

• Mojave (2x140 MWe)

South Africa (100 Mwe)• Kaxu (100 MWe)

Arabs Emirates• Sham1 (100 MWe)

Argelia• Hassi R'Mel (20MW)

Abengoa trough plants


Solucar (3x50MWe)


Solucar (3x50MWe)



Parabolic trough plants


2011-2013 Modelling and simulation studies

2013 Plant tests (July-Aug)

Commissioning on first plant (Sept)

2013 Controller design, programming and commissioning on theremaining 12 plants including operator courses (Oct – Dec)

2015-2016 USA and South Africa plants

2014 Analysis of results and incidences (Jan-June)

Design of versión 2 and commissioning on 13 plants (July-Dec)

Development and commissioning

E.F. Camacho Robust MPC design, Future and Practical Applications Rocond'2015 E.F. Camacho Robust MPC design, Future and Practical Applications Rocond'2015

Conclusions

• MPC is being succesfully applied in many

fields

• Solar energy is looking bright

• But … needs to reduce costs and increase

availability.

• MPC helps to enable solar technolgy


Thanks !

Some references:

E.F. Camacho and C. Bordons, Model Predictive Control,

Springer Verlag (1997, second edition 2004)

E.F. Camacho, M Berenguel, F.R. Rubio and D. Martinez,

Control of Solar Energy Systems, Springer, 2012. (2015 China

mainland)

E.F. Camacho, M Berenguel and F.R. Rubio. Advanced Control

of Solar Power Plants, Springer, 1977

[email protected]

Documents

Outline MPC and Applications - IEEEsites.ieee.org/sb-us/files/2017/01/Camacho_MPC_Aplicaciones.pdf · MPC and Applications ... Caída de Presión: Ecuación de Hazen-Williams C: Coeficiente