Cybernetic Model Predictive Control for poly3hydroxybutyrate Production

1
Cybernetic Model Predictive Control for
poly-3-hydroxybutyrate Production

• Timothy J. Crowley, Francis J. Doyle III
• University of Delaware, Newark, DE 19716
• Jeffrey Varner
• University of Minnesota, Minneapolis, MN 55455

2
Outline

• Background motivation
• Case study
• cybernetic storage synthesis model
• linear model predictive control (MPC) with state
  estimation
• poly-?-hydroxybutyrate (PHB) productivity control
  results
• Summary

3
Background

• Synthesis of PHB in Alcaligenes eutrophus
• polymer biodegradable, thermoplastic
• process green synthesis route for polyesters
• Potential applications
• medical (implants, drug delivery)
• film, packaging
• Focus PHB productivity control in continuous
  culture
• potentially higher productivity than fed-batch
  operation

4
Past Work

• Control of PHB in fed-batch cultures
• glucose concentration control (Kim et al., 1993)
• inferential control (Cornet et al., 1993)
• on-line optimal control (Lee et al., 1997)
• Control using cybernetic models
• data generator to identify model for MPC of a
  bioreactor (Parker and Doyle, 1998)

5
Motivation

• Cybernetic modeling
• captures complex cell regulatory mechanisms
  (diauxic growth, storage synthesis)
• model parameters identified from easily measured
  quantities (substrate, biomass, etc.)
• MPC with state estimation
• cannot measure PHB concentration on-line
• infer PHB from secondary measurements
• constraint handling
• multivariable structure

6
Continuous Culture with Biomass Recycle
biomass recycle
dilution rate (glucose and ammonium feed)
PHB productivity
ideal separator (microfiltration)
reactor
glucose measurement
7
Cybernetic Model Development(Varner, 1999)

• Lumped metabolic pathway
• S1, S2 glucose, ammonium sulfate
• ej enzymes
• p1, p2 metabolic precursors
• p3 storage polymer
• cr residual biomass

storage pathway model
p3
e5
e6
e3
e4
e2
e1
p2
p1
S2
S1
eg
cr
8
Model Equations
Cybernetic variable regulating rate of p3
synthesis
9
MPC Concept

• MPC prediction equation
• Calculation of control moves

past future
prediction horizon
10
Inferential Linear MPC Algorithm(Lee et al.,
1992 Wisnewski and Doyle, 1999)

• Dual-rate state estimation

States disturbance states infrequent PHB
measurement frequent glucose measurement
11
Simulation Case Study

• PHB productivity control
• process model/controller model mismatch
• unmeasured recycle drift, d
• measured glucose feed disturbance, ?

d
Process model
?
measurements
u
MPC with linearized controller model
PHB setpoint
12
Process/Controller Model Mismatch

• Inhibition of biomass growth rate at high biomass
  concentrations in process model

13
Steady-state Operating Locus

• Controller model linearized at point on locus
• dilution rate 0.25 hr-1

linearization point
minimum phase
non-minimum phase
14
Disturbances

• Step disturbance in glucose feed concentration
• Drift in recycle biomass concentration

15
Disturbance Rejection and Reference Tracking with
Ideal Measurement Set

• Measurement of PHB every 2 hr with 1 hr delay
• Measurement of glucose and ammonium sulfate every
  30 minutes

16
Inferential Disturbance Rejection and Reference
Tracking with Glucose Measurement

• Measurement of glucose every 30 minutes

17
Disturbance Rejection and Reference Tracking with
Off-line PHB measurement

• Measurement of glucose every 30 minutes
• Measurement of PHB off-line every 24 hours

18
Wash-out Due to Persistent Recycle Drift
Disturbance
19
Cybernetic Variable Profiles

• Cybernetic variables governing synthesis of
  enzymes for PHB storage and biomass growth

20
Cybernetic Variables Governing Enzyme Activity in
Batch Culture

• Cybernetic variables are non-smooth functions
• cybernetic variable modulating activity of
  storage enzyme
• Batch culture profile for v3
• Gradient based optimization?

21
Open-Loop Batch PHB Production Optimal Ammonium
Initial Condition

• Optimization
• Optimization fails in 2-D search

22
Summary

• Cybernetic model interfaced to dual-rate MPC
  controller for PHB control in continuous culture
• Steady-state offset observed for inferential
  control case
• Offset eliminated with one off-line PHB
  measurement every 24 hours
• Non-smooth cybernetic potentially problematic for
  gradient based optimization

23
Acknowledgments

• National Science Foundation (BES 9896061)
• Doyle group members