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:
EmersonExchange@Emerson.com
Thank you.
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)
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, …
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
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.