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An overview of the active constraint methodology for flexibility analysis. Kedar Kulkarni Advisor: Prof. Andreas A. Linninger Laboratory for Product and Process Design, Department of Bioengineering, University of Illinois, Chicago, IL 60607, U.S.A. Motivation.

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An overview of the active constraint methodology for flexibility analysis

Kedar Kulkarni

Advisor: Prof. Andreas A. Linninger

Laboratory for Product and Process Design,

Department of Bioengineering, University of Illinois,

Chicago, IL 60607, U.S.A.

motivation
Motivation
  • To really understand various approaches of uncertainty analysis as employed by Grossmann et al. (1980-87) and apply them to design of distributed systems under uncertainty

Outline of the talk

  • The active constraint methodology for flexibility analysis
  • A note on Lagrangian Multipliers
flexibility analysis

Process adjustments

Control variables, z

Specifications

Changing

constraints

Fixed

conditions

Design

£

Uncertain

f (d,z,q)

0

d

q

parameters,

FEASIBLE

OPERATION???

Flexibility Analysis
mathematical background
Mathematical background

Chemical process:

System equations:h(d,z,x,q) = 0 (Mass or energy balances)

Constraints:g(d,z,x,q)  0 (For feasible operation)

Feasibility condition (Semantic):

{ q  T { z {s.t.  j  J, hj(d,z,x,q)  0}}}

Design ‘just’ feasible

feasibility test the formulation
Feasibility test: the formulation

Feasibility condition (Mathematical):

Calculate

  • x(d) could be regarded as a feasibility measure for a given
  • design d
  • * x(d)  0 => feasibility ensured q  T
  • * x(d) > 0 => design infeasible for at least one value of q

Rewrite:

the formulation1
The formulation

KKT:

Single level optimization problem solvable by available methods

flexibility index the formulation
Flexibility index: the formulation

Observing that to calculate the flexibility index we need to enforce that the feasibility test condition holds as an equality

Thus