Model Predictive Control: an MPC successful in Introductory …chemori/Temp/Predictive/MPC_course1/MPC... · 2010-04-07 · Paris'2010 Eduardo F. Camacho MPC:An Introductory Survey

Eduardo F. Camacho MPC:An Introductory Survey 1 Paris'2010

Model Predictive Control: an Introductory Survey

Eduardo F. Camacho Universidad de Sevilla

Paris, 2009


MPC successful in industry.

Many and very diverse and successful applications: Refining, petrochemical, polymers, Semiconductor production scheduling, Air traffic control Clinical anesthesia, …. Life Extending of Boiler-Turbine Systems via Model

Predictive Methods, Li et al (2004) Many MPC vendors.


MPC successful in Academia

Many MPC sessions in control conferences and control journals, MPC workshops.

4/8 finalist papers for the CEP best paper award were MPC papers (2/3 finally awarded were MPC papers)


Análisis de las distintas técnicas

Informe de Takatsu et al. (1998) para la Society of Instrumentation and Control Engineering Principales problemas de control que se encuentran en la industria de procesos Estado de aplicación de la técnicas avanzadas Grado de satisfacción de los usuarios con cada técnica Expectativas Indicativo de las necesidades futuras de la industria en el ámbito del control


Principales problemas de control


Grado de satisfacción de las distintas técnicas


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

Pmax


Flash

Línea 2

Línea 1 Lavado

Contacto 1

Contacto 3

Contacto 2

ESQUEMA GENERAL CIRCUITO DE GASES


Eduardo F. Camacho MPC:An Introductory Survey 11 Paris'2010 Eduardo F. Camacho MPC:An Introductory Survey 12 Paris'2010


Benefits

Yearly saving of more that 1900 MWh Standard deviation of the mixing chamber

pressure reduced from 0.94 to 0.66 mm water column.

Operator’s supervisory effort: percentage of time operating in auto mode raised from 27% to 84%.


Outline A little bit of history Model Predictive Control concepts Linear MPC Multivariable Constraints Nonlinear MPC Stability and robustness Hybrid systems Implementation Some applications Conclusions


Bibliografía

R. Bitmead, Gevers M. and Werts W. “Adaptive Optimal Control: The Thinking man GPC”, Prentice Hall, 1990

R. Soeteboek, Predictive Control: A Unified Approach, Prentice Hall, 1991.

E.F. Camacho and C. Bordons, “Model Predictive Control in the Process Industry”, Springer-Verlag, 1995.

J. Maciejowski, “Predictive Control with constraints”, Prentice Hall, 2002.

A. Rossiter, “Model-Based Predictive Control: A Practical Approach”, CRC Press, 2003

E.F. Camacho and C. Bordons, “Model Predictive Control”, Springer-Verlag, 1999 (Second edition coming soon: 2004)


A little bit of history: the beginning

Kalman, LQG (1960) Propoi, “Use of LP methods ...” (1963)

Richalet et al, Model Predictive Heuristic Control (MPHC) IDCOM (1976, 1978) (150.000 $/year benefits because of increased flowrate in the fractionator application)

Cutler & Ramaker, DMC (1979,1980)

Cutler et al QDMC (QP+DMC) (1983)

Clarke et al GPC (1987)

First book: Bitmead et al, (1990)


The impulse of the 90s. A renewed interest from Academia (stability)

Stability was difficult to prove because of the finite horizon and the presence of constraints (non linear controller, no explicit solution, …)

A breakthrough produced in the field. As pointed out by Morari: ”the recent work has removed this technical and to some extent psychological barrier (people did not even try) and started wide spread efforts to tackle extensions of this basic problem with the new tools”. (Rawlings & Muske, 1993)

Many contributions to stability and robustness of MPC: Allgower, Campo, Chen, Jaddbabaie, Kothare, Limon, Magni, Mayne, Michalska, Morari, Mosca, de Nicolao, de Olivera, Scattolini, Scokaert…


The new millenium

Linear MPC is a mature discipline. More than 4500 industrial applications (not counting licensed technology companies app.) Qin and Badgwell’03.

The number of applications seems to duplicate every 4 years. Some vendors have NMPC products: Adersa (PFC), Aspen Tech

(Aspen Target), Continental Control (MVC), DOT Products (NOVA-NLC), Pavilon Tech. (Process Perfecter)

Efforts to developed MPC for more difficult situations: Multiple and logical objectives (Morari, Floudas) Hybrid processes (Morari, Bemporad, Borrelli, De Schutter, van den

Boom …) Nonlinear (Alamir, Alamo, Allgower, Biegler, Bock, Bravo, Chen, De

Nicolao, Findeisen, Jadbadbadie, Limon, Magni, …)


MPC Objetive

Compute at each time instant the sequence of future control moves that will make the future predicted controlled variables to best follow the reference over a finite horizon and taking into account the control effort.

Only the first element of the sequence is used and the computation is done again at the next sampling time.


MPC basic concepts

Common ideas: Explicit use of a model to predict output.

Compute the control moves minimizing an objective fuction.

Receding horizon strategy. Estrategia deslizante (el horizonte se desplaza hacia el futuro).

The algorithms mainly differ in the type of model and objective function used.


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

Acciones de control

Setpoint


t t+1 t+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


MPC

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

vs. PID


Estructura básica de MPC

Restricciones Función de coste

Optimizador

Trayectoria de Referencia

Errores Futuros

-

Controles Futuros

Entradas y salidas pasadas Modelo

Salidas Futuras


GPC

CARIMA model

Cost function


GPC

Control moves

with




U1

U2

Un

Y2

Yn

Y1

Proceso ...

...


Gd G

(Proc.)

U

Y

+R1 Gc1 -

+R2 Gc2 -

+Rn Gcn -


Multivariable MPC

Direct extension But …

Dead times, control horizon, ... Unstable transmission zeros


Multivariable MPC


Multivariable MPC




Constraints in process control

All process are constrained Actuators have a limited range and slew

rate Safety limits: maximun pressure or

temperature Tecnological or quality requirements Enviromental legislation


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

Pmax


Work close to the optimal but not violating it

120

Fine

400 Euros

3 points


MPC: constraints IV

umin<u(t)< umax Umin<U(t)< Umax ymin (t)<y(t)< ymax(t)

Minu J(u,x(t))

s.t.: R u < r +S x(t)


Usual way of dealing with constraints

Señal óptima

J (curvas de nivel)

Señal de control sin saturar

u(t)

u(t+1)

Solución sin restricciones

Señal de control saturada

u(t)

u(t+1)

Señal óptima


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 inputs applied at x(0)=x,

the predicted state at i is x(i)=Φ(i;x, u)=f(x(i-1), u(i-1) )


MPC strategy

1. Optimization problem PN(x,Ω):

u*= arg minu Σ(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) ∈ Ω

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


Linear MPC

f(x,u) is an affine function (model) X,U,Ω are polyhedra (constraints) l and F are quadratic functions (or 1-norm

or ∞-norm functions)

⇓ QP or LP


Control predictivo lineal


Otherwise

If f(x,u) is not an affine function Or any of X,U,Ω 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.


MPC and nonlinear processes

Most processes are non-linear, Linear approximations works for small perturbations

around the operating point (well in most cases) There are processes with

continuous transitions (startups, shutdowns, etc.) and spend a great deal of time away from a steady-state operating region or

never in steady-state operation (i.e. batch processes, solar plants), where the whole operation is carried out in transient mode.

severe nonlinearities (even in the vicinity of steady states) hybrid


NMPC vs. LMPC

Consider the nonlinear system y(t+1)= 0.9 y(t) + u(t)1/4

with 0<u(t)< 1.

Linear model: y(t+1)= 0.9 y(t) + u(t)

Applying a L-MPC and a NL-MPC with N=10, λ=0

0 20 40 60 80 100 120 140 1600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100 120 140 1600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


NMPC vs. LMPC

Better predictions should be obtained from more accurate models.

Better predictive control should be obtain with better predictions.

Is that so ?


MPC turns out to be a linear controller with a feedback of the prediction of y(t+D)

H C Process

Predictor y(t+D) ^

u(t) y(t)

R


Falatious congeture

An optimal predictor plus an optimal controller is going to produce the “best” closed loop behaviour.

J. Normey showed that Smith predictor (and other DTC structures) produce “better” (more robust) controllers than optimal predictor.

Optimal state estimator + optimal controller (LQG/LTR) Optimal identifier + optimal controller does not produce

the optimal adaptive control (identification for control) A fundamental issue: The best model is the one that

produces the “best” close loop control not necessarily best predictions..


Nonlinear Identification is more difficult

Lack of a superposition principle A high number of plant tests required

tests with many different size steps Multivariable processes the difference in the number

of tests required is even greater.

Optimization problem for parameter estimation is more difficult (offline)


Modeling: Empirical Models

Fixed structure, parameters determined from data State space x(t+1)=f(x(t),u(t)), y(t)=g(x(t))

Input-output (NARMAX) y(t+)= Φ(y(t), ..., y(t-ny), u(t),...,u(t-nu),e(t),...,e(t-ne+1))

Volterra (FIR, bilineal) y(t+1)= y0+Σ {i=0..N}h1(i) u(k-i)+ Σ {i=0..M} Σ {i=0..M} h2(i,j)u(t-i)u(t-j)

Hammerstein Wiener NN

(t) y(t)u(t)

g(.)H(z)

Linear dynamic

!

a) b)

g(.) H(z)

" (t)

Linear dynamic

y(t)u(t)

Nonlinear static Nonlinear static


Neural Networks Multilayer Perceptron: a nonlinear function with good approximation

properties and “backpropagation”. Input-output with NN: y(t)= NN(y(t-1), ..., y(t-ny), u(t-1),...,u(t-nu))

State space with NN x(t+1)=NNf(x(t),u(t)), y(t)=NNg(x(t))

. . . .

. . . .

!"!(k)

V(k). . . .

. . . .

. . . .

(k)"

(k)d

S0 (k)

S5 (k)

S6 (k)

V(k-1)

(k-1).

(k).

#

#

z-1


Local Model Networks

A set of models to accommodate local operating regimes The output of each submodel is passed through a

processing function that generates a window of validity. y(t+1)=F(Ψ(t), Φ(t)) = Σ {i=1.M}fi(Ψ(t), Φ(t)), ρi (Φ(t))

local models are usually linear multiplied by basis functions ρi (Φ(t)) chosen to have a value close to 1 in regimes where is a good approximation and a value close to 0 in other cases.

Piece Wise Affine (PWA) systems


PWA. (Sontag, 1981)

Nonlinear System:

PWA Approx.

Some hybrid processes can be modeled by PWA system

x(t+1)=f(x(t),u(t))

y(t)=g(x(t))


Function


PWA Approximation


Approximation error




MPC: constraints II

Difference in input and output constraints: manipulated variables can always be kept in

bound by the controller by clipping the control action or by the actuator.

Output constraints are mainly due to safety reasons, and must be controlled in advance because output variables are affected by process dynamics.


MPC: constraints III

Not considering constraints on manipulated variables may result in higher values of the objective function. But this is not the main problem.

Violating the limits on the controlled variables may be more costly and dangerous as it could cause damage to equipment and losses in production.

Not considering input contraints may lead to unstability


Stability

Optimal controllers with infinite horizon guaranty stability.

Optimal finite horizon and the presence of constraints make it very difficult to prove stability (non linear controller, no explicit solution)

A breakthrough has been made in the last few years in this field. As pointed out by Morari , ”the recent work has removed this technical and to some extent psychological barrier (people did not even try) and started wide spread efforts to tackle extensions of thisbasic problem with the new tools”.



Stability and constraints y(t+1)=1.2 y(t)+0.2 u(t-2) with -4 < u(t) < 4, N=5


MPC stability

Infinite horizon, the objective function can be considered a Lyapunov function, providing nominal stability. Cannot be implemented: an infinite set of decision variables.

Terminal cost. Bitmead et al’90 (linear uncostrained), Rawling & Muske’93 (linear contrained).

Terminal state equality constraint. Kwon & Pearson’77 (LQR constraints), Keerthi and Gilbert’88, x(k+N)= xS

xS

x(t)

x(t+1) x(t+2)

x(t+N)


MPC stability: terminal region

Dual control. Michalska and Mayne (1993) x(N) ∈ Ω

Once the state enters Ω the controller switches to a previously computed stable linear strategy.

Quasi-infinite horizon. Chen and Allgower (1998). Terminal region and stabilizing control, but only for the computation of the terminal cost. The control action is determined by solving a finite horizon problem without switching to the linear controller even inside the terminal region. The term (|| x(t+N)||P)2 added to the cost function and approximates the infinite- horizon cost to go.

x(t)

x(t+1) x(t+2)

x(t+N) Ω


MPC and sliding mode control

Robust controllers Impose surface S as

terminal constraints


NMPC stability: all ingredients

Asymptotic stability theorem (Mayne 2001) The terminal set Ω is a control invariant set. The terminal cost F(x) is an associated Control

Lyapunov function such that min{u ∈ U} {F(f(x,u))-F(x) + l(x,u) | f(x,u)∈Ω} ≤0 ∀ x∈Ω Then the closed loop system is asymptotically

stable in XN(Ω )


Removing the terminal constraint maintaining stability

The optimization problem is simplified (especially when the state is not constrained)

u*= arg minu Σ(i=0,...,N-1) l(x(i),u(i)) + F(x(N)) s.t. x(i) ∈ X, u(i) ∈ U, i=0,...,N-1 and to the terminal constraint: x(N) ∈ Ω

There is a strong interplay between infinite horizon-terminal cost and terminal regions : A prediction horizon N and a quadratic terminal cost stabilizes the system in a

neighborhood of the origin. (Parisini and Zoppoli’95)

The unconstrained (no terminal constraints) MPC satisfies the terminal constraint in a neighborhood of the origin. (Jadbabaie et al’01)

Given a terminal cost F(x) that is a CLF in Ω , define Fs(x)= F(x) if x ∈ Ω and Fs(x)= α if x ∉ Ω where Ω = {x ∈ Rn: F(x) ≤ α}. The MPC with Fs(x) as terminal cost is stabilizing for all initial state in the region where the optimal solution to PN(x,X) reaches the terminal region. (Hu and Linnemann’02)

Procedure for removing the terminal constraint while maintaining asymptotic stability and computing the domain of attraction. (Limon et al’03). Suboptimality


Robustness Nonlinear uncertain system: x+=f(x,u, θ ), x ∈ Rn, u ∈ Rm θ ∈ Rp

With bounded uncertainties θ∈Θ and subject to hard constraints x ∈ X, u ∈ U

The uncertain evolution sets: X(i)=Γ(i;x, u)= {z ∈ Rn | ∃ θ∈Θ , y ∈ X(i-1), z=f(y, u(i-1), θ)}

and X(0)=x

t t+1 t+2 … t+N

y(t)

u(t)


Robustness (2) The stability conditions has to be

satisfied for all possible values of the uncertainties.

The terminal set Ω is a robust control invariant set. (i.e. ∀ x∈Ω, ∀ θ∈Θ ∃ u ∈ U | f(x,u, θ)∈Ω)

The terminal cost F(x) is an associated Control Lyapunov function such that

min{u ∈ U} {F(f(x,u,θ))-F(x) + l(x,u) | f(x,u,θ)∈Ω} ≤0 ∀ x∈Ω, ∀ θ∈Θ


Computation of regions in robust NMPC

Invariant regions, domain of attraction, uncertain evolution sets bounding sets (state estimation) bounding sets (identification) …

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Continuous stirred tank reactor (CSTR)

• Relatively easy if regions are polyhedron and linear transformations (f(x,u, θ) ), Kerrigan’00

• NMPC more complex and approximations are normally used.


Example: continuos stirred tank reactor (CSTR) Zonotopes: (Bravo et al’03)

Sampling period 0.03.

A normalized additive uncertainty is added. It is bounded by w1=(-6.5*10-3, 6.5*10-3) and w2=(-1.2*10-3, 1.2*10-3).

A terminal robust positively invariant set is calculated.

A prediction horizon of N = 11 is used.


Example

Some of these methods are too conservative: Pure interval arithmetic: boxes


State estimation

The observer error must be small to guarantee stability of the closed-loop and in general little can be said about the necessary degree of smallness.

No general valid separation principle for nonlinear systems exists.

Nevertheless observers are applied successfully in many NMPC applications.

Extended Kalman Filter (EKF), High gain estimators.


State estimation (2)

Moving Horizon Estimation (MHE). Moving window looking backward A dual problem to MPC: Control moves: known, process state:

unknown, horizon: backwards. (Kwon et al’83), (Zimmer’94), (Mishalska and Mayne’95) ..

IDCOM (Richalet’76) was developed as the dual to identification !!!

Set-membership estimation Compute a set of all states consistent with the measured output

and the given noise parameters. Ellipsoidal bounding (Schweppe’68), (Kurzhanski and Valyi’96) Polyhedron bounding (Kuntsevich and Lychak’85) Interval arithmetics, zonotopes (Kieffer et al’01), (Alamo et al’03)




MPC and polytopes

MPC with linear constraints is a MultiParametric-QP o LP (Bemporad y Morari, 2000)

The solution of an mp_QP o mp_Lp is a PWA function of state.

Min-max quadratic is PWA (Ramirez y Camacho, 2001).


Min-Max MPC with bounded global uncertainties

Process: y(t+1)=g(y(t),u(t),...) Model:

z(t+1)=f(y(t),u(t),...,θ ) si ∃ θ∈Θ | z(t+1)=y(t+1)


Properties of J and J*

• The set of j-ahead optimal predictions for j=1,...,N2 can be written as:

where:

• Mθ θ is positive definite.

• Also, Muu is positive definite for positive values of λ


Properties of J and J*

• Due to convexity of J and compactness of Θ, the maximum will be reached at one of the vertexes of the polytope Θ . J* can be expressed as a convex function of u (if Muu is positive definite) :

• Due to its convexity, J* has a unique minimizer, thus the min-max problem has a unique solution.


Piecewise Linearity of the Control Law

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• This situation can be generalized to N quadratic functions, thus it can be stated that the solution will be attained on either a minimizer of one of them or on an intersection point of two or more of them.


An illustrative example

• Consider the following first order integrated uncertainties prediction model:

• Let Nu=2, N2=2, λ=1.0 and -0.1 ≤ θk ≤ 0.1 then the following output predictions can be formulated:



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• The control law has been calculated numerically for (only Δuk shown):

• The lower region is due to the minimizer of J1.The upper region is due to the minimizer of J4. Between them there is another region due to the intersection of J1 and J4.


An illustrative example • Boundary regions can be computed:

• J4 - J41: • J41 - J1:

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• An explicit form of the control law can be found:

• The output under the MMMPC control law versus an unconstrained GPC:


Min-max MPC: open-close loop predictions

Minu(k),u(k+1),.. Max w(k),w(k+1) … J(u,w)

Minu(k) Max w(k) Minu(k+1) Max w(k+1) … J(u,w) Minu(k)c(x(k+1)),c(x(k+2)) .. Max w(k) w(k+1) … J(u,w)

Control laws


Min-max MPC: bucle abierto-bucle cerrado (2)

x(k+1)=x(k)+u(k)+w(k) with -2 < x(k) < 2 -2 < u(k) < 2 -1 < w(k) < 1 Qith horizon 3 there is no u(1),u(2), u(3) which

keeps -2 < x(k) < 2 dor all w(k) If u(k)= - x(k) then -2 < x(k) < 2 for all w(k) Game theory: available information by each

player


NMPC implementation

Solving a Nonlinear (non QP), possibly nonconvex.

Real time and no convexity >>> suboptimal solutions Sequential Quadratic Programming (SQP) Simultaneous approach (Findeisen and Allgower’02) Using a sequential approach with successive

linearization around the previous trajectory. PWA >>>> Mixed Integer Programming Problem.


Hybrid System

Computer

Science

Discrete Events

X={1,2,3,4,5}

U={A,B,C}

1 3

4 5

2 C

A B

B B

C

C C A

Control

Theory

Dynamical

systems


Hybrid System 1

Computer

Science

Control

Theory

Dynamical Systems - Physical processes in control system e.g. robots, aircraft, ...

Discrete Events

- Collisions - Decision logic - Discrete communication


Hybrid System 2

Computer

Science

Control

Theory

Model: - Differential equations - Algebraic equations - Invariant constraints

Model: Automata, Petri nets, statecharts, etc.

1 3

4 5

2 C

A B

B B

C

C C

A


Hybrid System 3

Computer

Science

Control

Theory

Analytical Tools:

Lyapunov functions, eigenvalue analysis, etc.

Analytical Tools:

Boolean algebra, formal logics, recursion, etc.


Hybrid System 4

Computer

Science

Control

Theory

Software Tools:

MATLAB, MatrixX, VisSim, etc.,

Software Tools:

Statemate, Design CPN, Slam II, SMV, etc.


PWA systems

x

u

x(k+1) = A1 x(k) + B1 u(t) + f1

x(k+1) = A2 x(k) + B2 u(t) + f2

x(k+1) = A3 x(k) + B3 u(t) + f3


PWA approximations

X k y k =C k x k +g k

x k+1 =A k x k +B k u k +f k ?

X k+1 y k+1 =C k+1 x k+1 +g k+1

x k+2 =A k+1 x k+1 +B k+1 u k+1 +f k+1 ?

X k+2 y k+2 =C k+2 x k+2 +g k+2

x k+3 =A k+2 x k+2 +B k+2 u k+2 +f k+2

The resulting optimization problem

U = {u(k), u(k+1), u(k+2), …,u (k+N-1)} real I = {I(k), I(k+1), I(k+2),…, I(k+N-1)} Integer

Mixed Integer-Real

Optimization Problem


NMPC implementation (2)

Although there are many clever tricks to alleviate the situation, these algorithms take time. This is a major obstacle. Only slow or small processes.

Approximations and simplifications Using short horizons Precomputation of solution over a grid in the state

space (only small systems)




Application of NMPC to a mobile robot: Path tracking in an unstructured environment

Problem Future trajectory known (computed by planner) Unexpected obstacles Control signals and state are constrained System model is highly nonlinear The objective function: position error, the acceleration, robot

angular velocity and the proximity between the robot and the obstacles (detected with an ultrasound proximity system)

Unexpected obstacles makes the objective function more complex.

(Gómez & Camacho, 1994)


Mobile robot avoiding obstacles

0.0 2.0 4.0 6.0

-1.0

0.0

1.0

2.0

3.0

X (m)b )

Y (

m)


Mobile robot NMPC

-2.0 0.0 2.0 4.0 6.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

Y (

m)

X ( ))


NMPC at a Solar plant Almeria


NMPC application at the Solar plant in Almeria (PSA)


Distributed collectors


Plant diagram


Nonlinear disturbances prediction: Solar radiation

400

500

600

700

800

900

1000

9 10 11 12 13 14 15 16

direct sola

r ra

dia

tion (

W/m

2)

local time (hours)

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43/5410,:.17<3=-2;


Plant results: a clear day

9.5 10.5 11.5 12.5 13.5 14.5 15.5

local time (hours)

20.0

50.0

80.0

110.0

140.0

170.0

200.0

230.0

tem

pe

ratu

re (

C)

inlet oil temperature

outlet oil temperature

set point temperature

9.5 10.5 11.5 12.5 13.5 14.5 15.5

local time (hours)

800.0

850.0

900.0

950.0

1000.0

direct sola

r ra

dia

tion (

W/m

2)

real direct solar radiation

predicted direct solar radiation

Very fast setpoint tracking, little overshoot


Plant results: a cloudy day

12.4 12.9 13.4 13.9 14.4 14.9 15.4 15.9

local time (hours)

90.0

110.0

130.0

150.0

170.0

190.0

210.0

tem

pera

ture

(C

)

inlet oil temperature

outlet oil temperature

set point temperature

12.4 12.9 13.4 13.9 14.4 14.9 15.4 15.9

local time (hours)

100.0

200.0

300.0

400.0

500.0

600.0

700.0

800.0

900.0

1000.0

dire

ct so

lar

radia

tion

(W

/m2

)

real direct solar radiation

predicted direct solar radiation


Conclusions

Well established in industry and academia

Great expectations for MPC Many contribution from the research

community but … Many open issues Good hunting ground for PhD

students.


Documents

Model Predictive Control: an MPC successful in Introductory …chemori/Temp/Predictive/MPC_course1/MPC... · 2010-04-07 · Paris'2010 Eduardo F. Camacho MPC:An Introductory Survey