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NEW PARADIGMS FOR CONTROL THEORY

• Romeo Ortega
• LSS-CNRS-SUPELEC
• Gif-sur-Yvette, France

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Content

• Background
• Proposal
• Examples

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Facts

• Modern (model-based) control theory is not
  providing solutions to new practical control
  problems
• Prevailing trend in applications data-based
   solutions 
• Neural networks, fuzzy controllers, etc
• They might work but we will not understand
  why/when
• New applications are truly multidomain
• There is some structure hidden in complex
  systems 
• Revealed through physical laws
• Pattern of interconnection is more important than
  detail

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Why?

• Signal processing viewpoint is not adequate
• Input-Output-Reference-Disturbance.
• Classical assumptions not valid
• linear small  nonlinearities
• interconnections with large impedances
• time-scale separations
• lumped effects
• Methods focus on stability (of a set of given
  ODEs)
• no consideration of the physical nature of the
  model.

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Proposal

• Reconcile modelling with, and incorporate energy
  information into, control design.
• How?
• Propose models that capture main physical
  ingredients
• energy, dissipation, interconnection
• Attain classical control objectives (stability,
  performance) as by-products of
• Energy-shaping, interconnection and damping
  assignment.
• Confront, via experimentation, the proposal with
  current practice.

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Prevailing paradigm
Signal procesing viewpoint
Models
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Drawbacks!!!
Class of admissible systems TOO LARGE !!

• Conservativeness (min max designs)
• High gain (sliding modes, backstepping)
• Complexity

Practically useless
Intrinsic to signal-processing viewpoint
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Proposed alternative
(Energy-based) Control by interconnection
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Models

• PLANT
• H(x) energy function, x state,
• (v,i) conjugated port variables,
• Geometric (Dirac) structure capturing
  energy exchange
• Dissipation

• ENVIRONMENT
• Passive port
• Flexibility and dissipation effects
• Parasitic dynamics

Control objectives
Controller

• Focus on energy and dissipation
• Shape and exchange pattern

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IDA-PBC of mechanical systems

• To stabilize some underactuated mechanical
  devices it is necessary to modify the total
  energy function. In open loop

Where qÎRn, pÎRn are the generalized position and
momenta, respectively, M(q)MT(q)gt0 is the
inertia matrix, and V(q) is the potential energy

• MODEL

Control uÎRm, and assume rank(G)m lt n Convenient
to decompose uues(q,p)udi(q,p)
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• TARGET DYNAMICS

Desired (closed loop) energy function
where MdMdTgt0 and Vd(q)
with port controlled Hamiltonian dynamics
where
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All assignable energy functions are
characterized by a PDE!!
The PDE is parameterized by two free
matrices (related to physics)
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Examples
BALL AND BEAM
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Ball and Beam
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Ball and Beam
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Vertical take-off and landing aircraft
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Cart with inverted pendulum
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Examples
(PASSIVE) WALKING
Model

• Plant double pendulum
• Environement
• elastic (stiff)

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(Passive) walking
Control objetive
Shape energy
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(Passive) walking
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(Passive) walking
other mechatronic systems teleoperators,
robots in interaction (with environement)
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Piezoelectric actuators

• control objective shape energy

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Control through long cables
E.g., overvoltage in drives

• model

• control objective change interconnection to
  suppress waves

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Dual to teleoperators
Many examples in power electronics and power
systems
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Thank you!!