Download - Predictive Control 2
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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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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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Trajectories, flatness,
and predictive control
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Trajectories, flatness,
and predictive control
PLANT OR
PROCESSPID
-yref
output
(online)
Trajectory
generator
+
This reminds command governorof Prof. Mosca & col. 1997, 1999
Jacobian linearization (around equilibrium points)
= Y
U
Fliess & Marquez,Int J Control, 73 (7): 606-623 (2000)
Again the problem is stability in the closed loop!
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Trajectories, flatness,
and predictive control
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
Fliess & Marquez,Int J Control, 73 (7): 606-623 (2000)
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Trajectories, flatness,
and predictive control
C(s) G(s)u y
-
u*
y* +uee
Feedforward + closed loop Horowitz (1963)
predicted input trajectorypredicted output trajectory
(reference trajectory)
Fliess & Marquez,Int J Control, 73 (7): 606-623 (2000)
FBPC
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Two simple illustrative examples
First
example:
DC motor
constraints
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Two simple illustrative examples
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Two simple illustrative examples
Fliess & Marquez,Int J Control, 73 (7): 606-623 (2000)
Agrawal & col. 1996, 1998, 2001
with
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Two simple illustrative examples
Second
example:
PI control
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Two simple illustrative examples
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Two simple illustrative examplesFlat output and its derivatives
Output and Input trajectories
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Two simple illustrative examples
Fliess & Marquez,Int J Control, 73 (7): 606-623 (2000)
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Two simple illustrative examples
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Nonlinearpredictive control
C(s) NPlantu y-
u*
y* +uee
predicted input trajectorypredicted output trajectory
(reference trajectory)
FBPC
Fliess & Marquez,Int J Control, 73 (7): 606-623 (2000)
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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
(reference 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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Thank you
very much foryour attention!
Danke