Modeling and Control of Roller Compaction for Pharmaceutical Manufacturing. Part I: Process Dynamics and Control Framework

  • Shuo-Huan Hsu
  • Gintaras V. Reklaitis
  • Venkat Venkatasubramanian
Research Article

Abstract

We derive a dynamic model for roller compaction process based on Johanson’s rolling theory, which is used to predict the stress and density profiles during the compaction and the material balance equation which describes the roll gap change. The proposed model considers the relationship between the input parameters (roll pressure, roll speed, and feed speed) and output parameters (ribbon density and thickness), so it becomes possible to design, optimize, and control the process using the model-based approach. Currently, the operating conditions are mostly found by trial and error. The simulation case studies show the model can predict the ribbon density and gap width while varying roll pressure, feed speed, and roll speed. The roll pressure influences the ribbon density much more than roll speed and feed speed, and the roll gap is affected by all three input parameters. Both output variables are very insensitive to the fluctuation of inlet bulk density. If the ratio of feed speed to roll speed is kept constant, neither ribbon density nor gap width change, but the production rate changes proportionally with feed speed. Based on observations from simulations, a control scheme is proposed. Furthermore, Quality by Design of the roller compactor can be achieved by combining this model and optimization procedure.

Keywords

Dry granulation Roller compaction Dynamic modeling Johanson’s rolling theory Process control Process design and optimization Quality by Design (QbD) 

Notes

Acknowledgment

The authors would like to acknowledge the research funding source from the NSF Engineering Research Center for Structured Organic Particulate Systems (ERC-SOPS).

Glossary

A

Compact surface area

B

\(\frac{1}{2}{\left( {\frac{\pi }{2} + \theta + \nu } \right)}\), a function of θ

C1

Pre-exponential coefficient in the model of material compression

dV

Differential volume

F

Roll-separating force per unit roll width

h0

Half of roll gap width

hmin, hmax

Minimum and maximum allowable values of h 0

K

Compressibility factor

Pd

Hydraulic pressure (set point)

Ph

Hydraulic pressure (actual value)

Pmin, Pmax

Minimum and maximum allowable values of P h

\( {\mathop m\limits^ \cdot } \)

Production rate

N(a, b)

Normal distribution with mean a and variance b

R

Radius of the rollers

s

Complex argument in Laplace domain

sin

standard deviation of inlet powder density

t

time

ud

Feed speed (set point)

uin

Feed speed (actual value)

umin, umax

Minimum and maximum allowable values of u in

W

Roll width

xin

Rsin θin

α

Nip angle

Δ

Effective angle of friction

θ

Angular position

θin

π/2 − ν

μ

\( \frac{\pi }{4} - \frac{\delta }{2}\)

v

\(\frac{1}{2}{\left( {\pi - \sin ^{{ - 1}} \frac{{\sin \phi }}{{\sin \delta }} - \phi } \right)}\)

ρ

Compact density

ρexit

Compact density at exit point

\(\rho ^{*}_{{{\text{exit}}}} \)

Desired ribbon density

ρin

Inlet powder density

\( \overline{\rho } _{{{\text{in}}}} \)

Average of inlet powder density

σ

Material stress, a function of θ

σexit

σ(θ = 0), material stress at exit point

τp

Time constant of the roll force response due to the change of hydraulic pressure

τu

Time constant of the feed speed response

τω

Time constant of the roll speed response

Φ

Cost function

ϕ

Angle of wall friction

ω

Angular velocity of the rolls (actual value)

ωd

Angular velocity of the rolls (set point)

ωmin, ωmax

Minimum and maximum allowable values of roll speed

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Copyright information

© International Society for Pharmaceutical Engineering 2010

Authors and Affiliations

  • Shuo-Huan Hsu
    • 1
  • Gintaras V. Reklaitis
    • 2
  • Venkat Venkatasubramanian
    • 2
  1. 1.OSIsoft LLCSan LeandroUSA
  2. 2.School of Chemical EngineeringPurdue UniversityWest LafayetteUSA

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