Predictive Control 2

8/11/2019 Predictive Control 2

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04/07/05 Workshop on Identification, StateReconstruction and GPI Control, July 2005.University of the Bundeswehr Munich

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Richard MrquezDepartamento de Sistemas de Control

UNIVERSIDAD DE LOS ANDES

Mrida, Venezuela


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This presentation is notabout

New modelingtechniques

New optimizationalgorithms or procedures

New stabilityor robustnessresults onreceding horizon control

but

Is there any chance to viewpredictive control from a flatness

viewpoint?


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Outline

Model-based predictive control

Trajectories, flatness, and predictive

control: the linear case

Two illustrative examples

Non-linear case: Hagenmeyer-Delaleau

Final remarks to go further


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Predictive control

Beginning at 70s Like ubiquitous PID controller,

a standard approach in industry(for Advanced Control)

Performanceis an essentialrequirement (good tracking)

Physical insight (the model)

I/O constraints handling

Online computationis a deal(more than PI controllers!)

Question:How many strategies under same name?


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Predictive Control

Camacho and Bordons 1998:

+ 15different strategiesare named this

way

Today there exist hundred of techniques

referred to as predict ive con tro l

MBPC

strateg

ies


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How to recognize predictive control

(Richalet 1993, Camacho and

Bordons 1998)?

Explicit use of a modelto predict the

process output

Control is computed by minimizing an

objective function

Receding strategy:the horizon is

displaced towards the future


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How predictive control

works (theory)?

Where is Feedback on MBPC?

It is based on thereceding horizon algorithm!

(predicted) output signal

(predicted) input sequence

or input trajectory

prediction horizon

desired value

Controllability a la Wil lems (Willems 1991, Fliess 1992)

constraints

Fliess & Marquez,Int J Control, 73 (7): 606-623 (2000)


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How predictive control

works (practice)?

In practice:PI controllers are fed

with reference (set-point) signals provided

by MBPC algorithm! (Qin & Badgwell 1996)

MBCP (with RHC) turns out

to be an on l ine trajecto ry generator

MBPC

Optimizer PI controller

Set points

measured

output


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How predictive control works?

PLANT OR

PROCESS-PIDyref

output

MBPC RH

(+ model)

This works with appropriate (high) gains in the PI

+MBPC RH

(+ model)

Stability and computation of receding horizon algorithm

(Clarke, Richalet, Muske & Rawlings, etc.)

Online

optimizer

Flat systems (Van Niewstadt and Murray 1998)


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Essential features of predictive

control

The modelPerformance index

Costs, constraints, etc.

Input and output trajectories

preciseknowledge of model

good trajectories

a key feature: feed-forward


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Essential features of predictive

control

This means:Obtain good trajectories

bu t the quest ion is:

Can feedbackbe based on (robust) classical

control (PI control or the like) instead of RHC?

YES!

Explicit use of a modelto predict the

process output

Control is computed by minimizing an

objective function

Remember:


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04/07/05Workshop on Identification, State

Reconstruction and GPI Control, July 2005.

University of the Bundeswehr Munich

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Trajectories, flatness,

and predictive control

In the linear case: flatness = controllability

All variables can be written in terms of flat

outputs of their derivatives. For example:

Brunovsky canonical form


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University of the Bundeswehr Munich13




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PLANT OR

PROCESSPID

-yref

output

(online)

Trajectory

generator

+

This reminds command governorof Prof. Mosca & col. 1997, 1999

Jacobian linearization (around equilibrium points)

= Y

U


Again the problem is stability in the closed loop!


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PLANT OR

PROCESSPID

-State

or output

transferbetween two

equilibrium

points

output

Flat system

trajectory

+

Fliess, Levine, Martin, Rouchon (1991-)

Fliess, Sira-Ramirez, Marquez (1998)

input trajectory

output trajectory



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C(s) G(s)u y

-

u*

y* +uee

Feedforward + closed loop Horowitz (1963)

predicted input trajectorypredicted output trajectory

(reference trajectory)


FBPC


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Two simple illustrative examples

First

example:

DC motor

constraints


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Agrawal & col. 1996, 1998, 2001

with


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Second

example:

PI control


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Two simple illustrative examplesFlat output and its derivatives

Output and Input trajectories


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Nonlinearpredictive control

C(s) NPlantu y-

u*

y* +uee

predicted input trajectorypredicted output trajectory


FBPC



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Nonlinear predictive control

Hagenmeyer-Delaleau 2003

u*(z,sz,,z(n))predicted input trajectory

C(s) Plantu y

-

y*(z,sz,, z(w))

e

predicted output trajectory


NFBPC

u(z,,ue)ue

Exact feed-forward linearization

z(t)


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Nonlinear predictive control

Hagenmeyer-Delaleau 2003

Hagenmeyer, Kohlrausch, Delaleau

(2000): Separately excited DC motor

Hagenmeyer, Ranftl, Delaleau (2002):

Induction drive

Magnetic levitation system in Hagenmeyer

(2003)


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Nonlinear Flatness-based

predictive control principles

A good first-principlesmodel is necessary:Know your system!!

Consider online (slow, MBPC type) or off-line(fast) calculations: it depends on the process

Is there a PI (or the like) control working?Adapt the strategy to your problem or definea new control algorithm: create useful

KNOW-HOW Regulation and performance are almost

independent


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To go further

V. Hagenmeyer, PhD Thesis (Fortschritt-

Berichte VDI Nr. 978)

Sunil Agrawal works (Euler-Lagrange

optimization with constraints) Sira-Ramirez and Agrawal, Differentially flat

systems, 2004

Delaleau, Hagenmeyer, Marquez (2005)

References at (book in german by J. Rudolph):

www.ing.ula.ve/~marquez


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Reconstruction and GPI Control, July 2005. 31

Thank you

very much foryour attention!

Danke

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Predictive Control 2