1. Utilizing DeltaV to Perform
PAT Calculations Real Time
Real-Time Non-Linear Regression
Chromatography Endpoint Detection

2. Photography & Video Recording Policy
Photography and audio/video recording is not permitted in any sessions or in the
exhibition areas without press credentials or written permission from the Emerson
Exchange Board of Directors. Inquiries should be directed to:
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Thank you.

3. Presenters
 Michael Hausladen
Director of Manufacturing
Technology, BMS
 Paul Brodbeck
Engineering Manager,
Control Associates, LBP

4. Introduction
 Chromatography Project
 Functional Requirements
 Chromatography Elution
 Modeling
 Prototyping
 Implementation
 Results
 Summary

5. Chromatography Project
 BMS Syracuse
 Scientist: Mike Hausladen
 Pilot Plant Chromatography Skid Modification
 Purpose:
– Scale-up laboratory endpoint detection
– Ensure process robustness
• Minimize incorrectly determined collection end-point
– Pilot scale model of full scale production system
– Demonstrate capability for full scale production
 Focus of this presentation: Robust chromatography
elution end-point determination

6. Chromatography Basics
The basics of bind and elute chromatography:
– Modify the conditions of the mobile phase to cause binding
or elution of the product (protein)
– Aqueous systems: pH and conductivity
Stationary
Phase
Mobile phase:
1. Flush and prep column
2. Load protein on column
3. Wash
4. Elute protein
5. Clean and sanitize column
6. Store column
Monitor elution for product fraction
• UV adsorbance @ 280nm
• Collect the desired portion
of the elution peak

7. Elution Curve
0
10
20
30
40
50
60
70
80
90
100
mAU
Worse case chromatography
generated in the lab. Data is
not smooth., has multiple peaks.
z
w
h
The whole point – determine h (peak height) real time – to
calculate percent of peak maximum collection end-point
Percent of peak max (h)
stop collecting product

8. BMS Requirements
 Robust endpoint of Elution Determination - real time
 Peak Maximum Calculation
– Endpoint = Percent of Peak Maximum
• Model Predict Peak Max. of absolute optical density.
• Percent of Peak Max lookup table of Sialic Acid vs. load material.
 3 Models – in DeltaV Controller
– Smoothing (1st Order Filter) Model
– Linear Regression Algorithm - Polynomial Fit
– Non-Linear Model
• Extreme Value Function fit with Real-time Data
– Column Volume (mobile phase volume) vs. UV absorbance
 Alarming/Auto-Switching
– Limits to ensure that the Peak Maximum is not determined early.
– Ensure data is fitting the model with a sufficient level of accuracy.
– Limits end Model if the algorithm is not converging.
 Focus of this presentation is on the non-linear model real-time fit of the Extreme
Value Function

9. Implemented
 3 Models
– Smoothing Model
– Polynomial Fit
– Non-Linear Model
 1 Algorithm
– Newton-Raphson

10. System Integrator Process
 Select Model Equation
 Basic Curve Fitting
– Least Squares Error (LSE)
 Select Numerical Method Algorithm
– Gradient Descent
– Newton Raphson
– Levenberg-Marquardt
 Machine Learning Parallel
 Grey Box Modeling
 Math
– Linear Algebra
– Vector Based Programming Languages
(MATLAB)
– Solving of Partial Differential Equations
 Research
– Internet Literature
– Example Programs
– Textbook – Numerical Methods by Dahlquest &
Bjorck
 Program Construction
– Flowchart
 DeltaV CALC Block Limitation
– 2000 lines per scan
– 64 If-Then loops per block
– 256 field arrays
– Dynamic Reference delays
 Excel Solver
– Troubleshooting
– Math Checking
– Convergence Issues
 Switch Gradient to Newton
– Bad Hardware
– Convergence Issues
 Final Program
 Model Statistics
 IQ/OQ
 Levenberg-Marquart Future
 Numerical Integration
 Non-linear Models
 Controller vs. Application Station
 Other Approaches
– synTQ, MATLAB, SoftPhase
 Summary

11. Non-Linear Model
 Extreme Value Function: is an equation that
approximates a chromatography peak
 Using a dataset of x’s (volume of mobile phase) and y’s
(elution response – UV adsorbance )
– Determine h, w, and z that give the best approximation of the peak
– From h, determine endpoint
 There are many mathematical functions for the representation
of chromatographic peaks, extreme value function chosen for
simplicity (Journal of Chromatography)

12. Elution Curve Fitted
0
10
20
30
40
50
60
70
80
90
100
mAU
fit
z
w
h
The whole point – determine h (peak height) real time – to
calculate percent of peak maximum collection end-point
Percent of peak max –
stop collecting product

13. Numerical Method – Basic Curve Fitting
 Minimize the Squares of the Error
– Least Squares Error
 Curve fitting, minimizing error, finding best solution/ best fit
 Analytical solutions for simple fit
 Iterative numerical solution required for complex equations
– Initial guess required
– Convergence satisfied?
 Solving in multidimensional space

14. Numerical Methods – Solving Least Squares
 Gradient Descent
– Make Initial Guess Xi-1
– New Guess: Xi = Xi-1 – e * F’(Xi-1)
– e is tuning constant
• Too low = slow convergence, Too high = unstable
 Newton - Raphson
– Make Initial Guess Xi-1
– New Guess: Xi = Xi-1 - F’(xi-1)/2*(F’’(xi-1))
– Can be unstable with a poor initial guess
 Levenberg-Marquardt
– Start with Gradient, end with Newton
 Iteratively repeat, check for
convergence
SquareofError

15. Math
 In order to mathematically determine the slopes of a
multi-parameter system need to calculate the partial
differentials.
– Partials are slopes in n-dimensional space
 Linear Algebra
– When solving multivariate we need vectors, arrays or
matrices.
– Solutions become complex when dividing matrices
 Vector Based Programming
– Matlab, Python, Octave, …

16. Partial Differentials – 3D Slopes

17. Solving the Extreme Value Function
 Need to solve for h, z, w.
– h = maximum peak height.
– w = peak width.
– z = retention time of column.
 Vectorization Required
 Challenge here is dividing by a
Matrix
 Complex Linear Algebra
 Determinants
 Easy in Matlab
 Not so Easy Otherwise

18. Research
 Internet Literature
– Methods for Non-Linear Least Squares Problems1
• Nomenclature difficult
• Theoretical
– Wikipedia
– Dr. Math
• Least Squares Regression for Quadratic Curve Fitting2
– Example Programs
• L-A Algorithm by Pradit Mittrapiyanuruck
– MATLAB
• L-M Method for Non-Linear Least Squares by Henri Gavin
– MATLAB, extra code… weighting, CHI, R^2, lamda
 Textbook – Numerical Methods by Dahlquist & Bjorck
– 5.2.1 Numerical Linear Algebra
– 5.6 Iterative Methods
– 6.9.2 Newton-Raphson’s Method…
– 10.5.1 Non-Linear Optimization Problems (Hessian)

19. Project Challenges
DeltaV Limitations Other Obstacles
 No matrix math functions
 2000 lines per scan
 64 loops per scan
 Dynamic reference time
delay
 256 cell arrays max
 Hardware problem
 Literature for Matlab
 Solving Diff. Eq.’s
 Notation theory
 Matrix Algebra
 Numerical Methods
 Least Squared Error

20. Program Flowchart

21. Program – DeltaV CALC Block

22. Math – Solving PDE’s
 Solving PDE’s

23. Prototyping in MS Excel
h = 15
z = 0.24
w = 270

24. Model Performance
 Trust Zone
 5 Second scan time
 1000 pts each scan
 Model converges to solution each scan
 40% MX Controller Usage @ 5 sec scan
 90% MX Controller Usage @ 1 sec scan

25. IQ/OQ Validation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
6 6.5 7 7.5 8 8.5 9 9.5 10
Raw Data
Excel Prediction
DeltaV NonLinear
DeltaV Linear

26. Levenberg-Marqaudt Future Enhancement
 Prototyped in Matlab
 Tested in DeltaV
 Ready to be upgraded
 Faster, more robust

27. Implemented Models
 All 3 running simultaneously
 Auto Switch to best Model
 Non-Linear Model is primary
 Polynomial Model is secondary
 Smoothing Model last
 All 3 models tested within X% of each
 Monitor all 3 and Alarm if > X% Error

28. Other Options for Future
 MATLAB
– OPC communication
– Runs in App station
 synTQ
– $$$
– MATLAB or other math package
 Soft Phase
– Requires C, C++, C#, or VB
 Controller vs. Application Station
– Controller slightly more robust
• If App Station goes down Model still runs in controller
– Application Station
• Run at higher speeds
• Reduced controller memory & capacity

29. Summary DeltaV
 Non-linear was successfully implemented to predict
elution endpoint
 Model updates 1000pt every 5 seconds
 Model is capable of handling model non-convergence
 Model passed IQ/OQ

30. Thank You for Attending!
Enjoy the rest of the conference.