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Optimal Control of Product Quality for Batch Nylon 6,6 Autoclaves Sachin Kansal Computer Process Control Group Chemical & Materials Engineering University of Alberta, Edmonton Nylon 6,6 - Process Description Common Industrial Control Practices Motivation for an Advanced Control Scheme

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optimal control of product quality for batch nylon 6 6 autoclaves
Optimal Control of Product Quality for Batch Nylon 6,6 Autoclaves

Sachin Kansal

Computer Process Control Group

Chemical & Materials Engineering

University of Alberta, Edmonton

Department Seminar, April 1999

presentation outline
Nylon 6,6 - Process Description

Common Industrial Control Practices

Motivation for an Advanced Control Scheme

The On-line Trajectory Generation Problem

Discussion and Future Work

Presentation Outline

Department Seminar, April 1999

nylon 6 6 market trends
Nylon 6,6 - Market Trends
  • Remains number one engineering thermoplastic despite the introduction of other resins with competitive features
  • Bulk of U.S. polyamide production (over three-fourths) is Nylon 6,6
  • Market Demand expected to grow by 6-10% over the next few years

Department Seminar, April 1999

nylon 6 6 autoclave

vent

steam

P

Q

heat

T

condensate

Nylon 6,6 Autoclave

PolyamidationA + C  L + W

DegradationC  SE + W

L  SE + A

A - amine end groups (2 per HMD)

C - carboxyl end groups (2 per adipic acid)

L - polymer link

W - water

SE - stabilized end group

What are we trying to control?

The Quality Variables.

No. Average Molecular Weight*

13,000<MW<14,000

Concentration of NH2 End Groups*

50< NH2-ends<60

(gram-equivalents of amine ends/million grams of polymer)

* These will be used as representative polymer

characteristics for evaluating controller performance

Department Seminar, April 1999

common industrial control practices
Common Industrial Control Practices
  • Control Objective - achieving the target molecular weight and concentration of amine end groups
  • Regulation of temperature or other secondary process variables is employed
  • Track nominal T & P trajectories from acceptable runs as setpoints (Russell et al., 1998)

Department Seminar, April 1999

implementation of trajectory tracking pid

vent

PC

steam

PT

P

Q

heat

T

TT

TC

Implementation of Trajectory Tracking PID

Control scheme based on tracking nominal reactor temperature and pressure profiles

  • Pressure profile control approach attractive - ready availability of pressure measurements
  • Final polymer properties - strong function of temperature history
  • Consistent quality development possible - feedback of temperature measurements

Control Scheme is simulated for

the following disturbances:

  • baseline - no disturbance
  • 10% decrease in U
  • 5% increase in CWo
  • 10 Kdecrease in To

Department Seminar, April 1999

pid control simulation results

550

500

Temperature

450

400

0

20

40

60

80

100

120

140

160

180

200

Time

PID Control/Simulation Results
  • Target values - those generated by the model following the nominal trajectories
  • Case 2 demonstrates the heat transfer disturbances
  • Cases 3 and 4 demonstrate the disturbance in feed conditions
  • Variations in the initial water content -considerable variations in polymer properties

Base(blue); U:-10%(red);

Wo:+5%(black); To:-10K(magenta)

Department Seminar, April 1999

what do these results mean
What Do These Results Mean?
  • Tracking pre-determined Nominal Trajectories is insufficient to guarantee Quality Product
  • Motivation to seek a more flexible control strategy capable of on-line changes to the nominal trajectories

Department Seminar, April 1999

optimal trajectory generation
Optimal Trajectory Generation

Objectives

  • Generate new reactor temperature and pressure trajectories on-line so that the final quality targets are met in the presence of disturbances
  • Generate the above trajectories in an optimal way, such that some production cost (e.g., heating costs) of the polymer is minimized
  • Keep the trajectory generation problem simple enough to be solvable in real-time

Department Seminar, April 1999

optimal trajectory generation steps

Mass and Energy Balances

  • Identify Process Variables
  • Differentially Flat System
  • Identify Flat Outputs
  • Identify the Control Objective
  • Setup the “Pseudo” Problem
  • Identify RTO Issues
  • Develop Solution Algorithm
Optimal Trajectory Generation - Steps

Department Seminar, April 1999

mathematical model development
Mathematical Model Development

Mass and energy balances

States, Inputs and Outputs

End Use Quality Variables

Department Seminar, April 1999

typical simulation results

Concentrations in the Reactor

10

550

300

5

Conc. A

500

200

T K

P, Pvap (red) psi

0

450

100

0

20

40

60

80

100

120

140

160

180

200

10

400

0

5

Conc. C

0

50

100

150

200

0

50

100

150

200

4

x 10

3

1500

0

0

20

40

60

80

100

120

140

160

180

200

10

2

5

1000

Pj mm Hg

Conc. L

Vent g/min

1

0

0

20

40

60

80

100

120

140

160

180

200

20

0

500

0

50

100

150

200

0

50

100

150

200

10

Conc. W

15000

6000

0

10000

4000

0

20

40

60

80

100

120

140

160

180

200

0.1

MW

Amine Ends

5000

2000

0.05

0

0

0

0

20

40

60

80

100

120

140

160

180

200

0

50

100

150

200

0

50

100

150

200

Time (minutes)

Typical Simulation Results

Conc. SE

Department Seminar, April 1999

model transformation differentially flat systems

.

=

x

f(x,

u)

Î

Â

Î

Â

x

,

u

n

m

Î

Â

y,

y

m

=

=

(1)

y

P

(x,

u,...

,

u

),

i

1,...

,

m

α

i

i

.

=

(2)

Q(y,

y

,...

,

y

)

0

β

.

=

=

(3)

z

[x

u

x

u

]

R(y,

y

,...

,

y

g

a

b

)

Model TransformationDifferentially Flat Systems

What does Differential Flatness Mean?

Original Nonlinear System

There exist so-called flat(or linearizing) outputs

such that:

y can be calculated from x, u and a finite number of time derivatives of u

y’s are differentially independent

Any x, u, their time derivatives and functions of them can be calculated from y and its time derivatives

Department Seminar, April 1999

chemical reactor examples

u1, Tin, cAin, cBin

u2, TJ

u2, TJin

u1, T, cA, cB

Extending the system with:

Differentially Flat system with:

as outputs

Chemical Reactor Examples

2 Chemical Species Example

(Guay, 1998)

Department Seminar, April 1999

slide15

Extending the system with:

u1, Tin, cAin, cBin cCin

u2, TJ

Differentially Flat system with:

as outputs

u2, TJin

Chemical Reactor Examples

3 Chemical Species Example

u1, T, cA, cB, cC

(Guay, 1998)

Department Seminar, April 1999

from flatness to trajectories

Flatness Reduces the

Dimensionality of the Problem

Makes Real-Time Implementation Possible

From Flatness to Trajectories

Behavior of Flat Systems is

determined by the Flat Outputs

Higher Dimensional

State Space

Lower Dimensional Flat Output Space

Transfer

Functions

Department Seminar, April 1999

slide17

Full-State

Feedback Linearizability

YES

NO

Approximate Trajectory

Generation Methods

Partially State

Feedback Linearizable

Stable: r dimensional

problem is solved

Zero Dynamics

of the System

Unstable: stabilized and

the resulting problem

is solved

r specifies the dimension of the differentially flat system

What if System is not Flat?

Differentially

Flat System

Department Seminar, April 1999

problem definition
Problem Definition

Statement of the Real-Time Optimal

Trajectory Generation Problem

Department Seminar, April 1999

slide19

Generates nominal state-space

trajectory and nominal inputs

Desired destination

in tracking space

Trajectory Generation?

Two Degree of Freedom Approach (Nieuwstadt et al.)

Error dynamics can be

written as e=x-xd

system is linearized

around e=0 and the

e=0 state is stabilized

Corrects for any errors

due to noise or plant

uncertainty

Trajectory Generation Block

Feedback Compensation Block

Department Seminar, April 1999

trajectory generation applications
Trajectory Generation - Applications
  • Control of Chemical Reactors
    • Guay, 1998
    • Rothfuss et al., 1996
  • Guidance of Aerospace Vehicles(Betts, 1990)
    • when a vehicle actually flies a trajectory, it is subjected to random perturbations that cannot be predicted preflight
    • role of trajectory generation is to maintain control of a vehicle and, when possible, optimize the trajectory
  • Control of an Autonomous Aircraft Following a Moving Target(Nieuwstadt and Murray, 1995)

Department Seminar, April 1999

discussion and future work
Discussion and Future Work
  • Present Control Schemes not Robust to Disturbances
  • Trajectory Generation Control Schemes:
    • Transformation of the Process Model to the Normal Form
    • Real-Time Implementation Issues
    • Increased Instrumentation and Computational Cost
  • Application to other Nonlinear Systems
    • Approximations for Systems which are not Differentially Flat

Department Seminar, April 1999

acknowledgements
Acknowledgements
  • Research Supervisors:
    • Dr. J. Fraser Forbes
    • Dr. Martin Guay
  • Computer Process Control Group
    • http://www.ualberta.ca/chemeng/groups/control/

Department Seminar, April 1999

slide23

Questions?

Department Seminar, April 1999