Fuzzy modeling and model based control

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Fuzzy modeling and model based control

• with the use of a priori knowledge

J. Abonyi, R. Babuka, L.F.A. Wessels,H.B.
Verbruggen, F. Szeifert
Control Engineering Laboratory Faculty of
Information Technology and SystemsDelft
University of TechnologyDelft, the
Netherlandse-mail J.Abonyi_at_ITS.TUDelft.NL
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Outline

• Problem formulation
• Proposed modeling framework
• Constrained parameter estimation and adaptation
  of fuzzy models
• Formulation of a priori knowledge in inequality
  constraints
• Application to adaptive control
• Example Adaptive predictive control of a liquid
  level process
• Conclusions

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Control design strategies
without model
with model
Modeling and Identification
Controller tuning
Process Analysis
Control Specification
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Conventional approach
Knowledge-based (Fuzzy) models
Black-box models
Expert knowledge
Measured data
Mechanistic knowledge
White-box models
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Problem formulation

• The bottleneck of model based control is the
  modeling step
• The applied information determines the structure
  of the model

• There is a need for a framework that can handle
  different type of information
• and it can be easily applied in model based
  control

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The proposed approach
Expert knowledge
Measured data
Mechanistic knowledge
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The TS fuzzy model
Antecedent part
Consequent part
Divide and conquer
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TS fuzzy model as an LPV model
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The constrained parameter estimation method

• Rule-consequents define a convex region
  (polytope).
• This polytope can be constrained by global linear
  constraints.
• The individual rule-consequents can be
  constrained separately local linear constraints.

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Graphical representation
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Quadratic programming

• H and d contain the measured input-output data
• ? and ? represents the a priori knowledge based
  constraints

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Types of prior knowledge

• Sampling (global)
• Stability (global)
• Stationary gain (global or local)
• Open-loop settling time (global or local)

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Example Stationary gain

• Upper and lower bounds

• Inequality constraints for QP

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Example Liquid level process

• Process input Flow rate (0-100)
• Process outputLiquid level in the bottom tank
  (0-100)

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Model predictive control
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Indirect adaptive control
Adaptive IMC scheme
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Control result

• Unconstrained adaptation
• MSE 0.8
• CE 0.3

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Prior knowledge

• Open-loop stability
• Kmin 0, Kmax 2.5
• Settling-time of the local models

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Control results

• Constrained adaptation
• MSE 0.6 (0.8)
• CE 0.1 (0.3)

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Conclusions

• Transform a priori knowledge into constraints on
  model parameters.
• Limited data prior knowledge ?good control
  relevant model
• Application to indirect adaptive control
• Useful for control based on LPV model
• Detailed prior knowledge is neededFuture
  research MIMO systems

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Conclusions
Expert knowledge
Measured data
Mechanistic knowledge
Dynamic data and (local) model
Optimization