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Modeling and Control of Roller Compaction for Pharmaceutical Manufacturing

Part II: Control System Design

  • Research Article
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Abstract

Roller compaction is the major process of dry granulation which is attractive to heat or moisture-sensitive pharmaceutical products. Currently, the product quality of roller compaction is analyzed off-line in the quality control lab. In this work, we demonstrate how online process control can be applied on roller compaction using the simulator built in Part I of this paper. Different control strategies are discussed: multi-loop proportional–integral–derivative, linear model predictive control (MPC), and nonlinear MPC. The MPC strategy provides a systematic approach to design the multivariable control system. The simulation results show that the linear MPC can serve as a high-performance control strategy for roller compaction with the trade-off between the control performance and computational complexity. Such enhanced process control facilitates the FDA’s process analysis technology initiative.

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Abbreviations

e(s):

Error vector in Laplace domain

F :

BLT detune factor

f i (t):

Free response at time t

G(s):

Process transfer function matrix

Gc(s):

PI controller transfer function matrix

g i,mn :

Process parameters in step response model

h :

Roll gap size (mm)

h(t + i|t):

Predicted roll gap size at time t + i, given measurement at t

h*(t + i):

Desired roll gap size at time t + i

hm(t):

Measured roll gap sized at time t

i :

Dummy index

j :

Dummy index or imaginary unit

\( Jp(t + i) \) :

MPC performance index at time t + i × T s

Jc(t + i):

MPC control cost at time t + i × T s

K :

Process gain matrix

k :

Dummy index

K c :

PI controller gain

\( K_c^{ZN} \) :

PI controller gain, tuned by Ziegler–Nichols method

k ij :

Process gain

L c :

Maximum closed-loop log modulus

M :

Dummy index

N :

Number of terms of finite step response model

n :

Dummy index

N c :

Control horizon

n i (t):

Measurement noise

N p :

Prediction horizon

P :

Roll pressure change in future

P d :

Roll pressure (MPa)

[P d,min, P d,max]:

Operating range of P d

q i :

MPC tuning parameters for control performance

r j :

MPC tuning parameters for control cost

s :

Variable in Laplace domain

t :

Time (min)

T s :

Sampling time (min)

u :

Feed speed change in future

u(s):

Input vector in Laplace domain

u d :

Feed speed (cm/s)

[u d,min, u d,max]:

Operating range of u in

y(s):

Output vector in Laplace domain

α i :

Move suppression coefficient

Γ i :

Process parameter matrices in step response model

ΔP d(t + i|t):

Control action of roll pressure (MPa) at time t + i obtained at time t

[ΔP d,min, ΔP d,max]:

Lower and upper limits of roll pressure control action

Δu(t + i|t):

\( \left[ {\Delta {P_{\rm {d}}}\left( {t + i|t} \right)\;\Delta {u_{\rm {d}}}\left( {t + i|t} \right)} \right] \)

Δu 0 :

Initial guess of control action

Δu d(t + i|t):

Control action of feed speed (cm/s) at time t + i obtained at time t

[Δu d,min, Δu d,max]:

Lower and upper limits of feed speed control action

Λ :

Relative gain array

λ :

Relative gain

ρ*(t + i):

Desired ribbon density at time t + i

ρ exit :

Ribbon density (g/cm3)

ρexit(t + i|t):

Predicted ribbon density at time t + i, given measurement at t

ρ in :

Inlet bulk density (g/cm3)

ρm(t):

Measured ribbon density at time t

τ I :

Integral constant of PI controllers

\( \tau_I^{ZN} \) :

Integral constant of PI controllers, tuned by Ziegler–Nichols method

ω :

Frequency

References

  1. Shlieout G, Lammens RF, Kleinebudde P, Bultmann M. Dry granulation with a roller compactor. Part II: evaluating the operation modes. Pharm Technol Eur. 2002;14(9):32–9.

    CAS  Google Scholar 

  2. Inghelbrecht S, Remon JP. The roller compaction of different types of lactose. Int J Pharm. 1998;166(2):135–44.

    Article  CAS  Google Scholar 

  3. Inghelbrecht S, Remon J-P, de Aguiar PF, Walczak B, Massart DL, Van De Velde F, et al. Instrumentation of a roller compactor and the evaluation of the parameter settings by neural networks. Int J Pharm. 1997;148:103–15.

    Article  CAS  Google Scholar 

  4. Gupta A, Peck GE, Miller RW, Morris KR. Real-time near-infrared monitoring of content uniformity, moisture content, compact density, tensile strength, and Young’s molulus of roller compacted powder blends. J Pharm Sci. 2005;94(7):1589–97.

    Article  CAS  PubMed  Google Scholar 

  5. O’Dwyer A, editor. PI and PID controller tuning rules for time delay processes: a summary. Part 1: PI controller tuning rules. The Irish Signals and Systems Conference. Ireland: Galway; 1999.

  6. Seborg DE, Edgar TF, Mellichamp DA. Process dynamics and control. 2nd ed. New York: Wiley; 2003.

    Google Scholar 

  7. Deshpande PB. Multivariable process control. Research Triangle Park: Instrument Society of America; 1989.

    Google Scholar 

  8. Qin SJ, Badgwell TA. An overview of nonlinear model predictive control applications. In: Allgower F, Zheng A, editors. Nonlinear model predictive control. Boston: Birkhauser; 2000.

    Google Scholar 

  9. Qin SJ, Badgwell TA. A survey of industrial model predictive control technology. Control Eng Pract. 2003;11:733–64.

    Article  Google Scholar 

  10. Camacho EF, Bordons C. Model predictive control. London: Springer; 2004.

    Google Scholar 

  11. Lundstrom P, Lee JH, Morari M, Skogestad S. Limitations of dynamic matrix control. Comput Chem Eng. 1995;19(4):409–21.

    Article  CAS  Google Scholar 

  12. Biegler LT. Efficient solution of dynamic optimization and NMPC problems. In: Allgower F, Zheng A, editors. Nonlinear model predictive control. Basel: Birkhauser; 2000. p. 219–44.

    Google Scholar 

  13. Bock HG, Diehl M, Leineweber DB, Schloder JP. A direct multiple shooting method for real-time optimization of nonlinear DAE processes. In: Allgower F, Zheng A, editors. Nonlinear model predictive control. Basel: Birkhauser; 2000.

    Google Scholar 

  14. Diehl M, Bock HG, Schloder JP, Findeisen R, Nagy ZK, Allgower F. Real-time optimization and nonlinear model predictive control of processes governed by differential–algebraic equations. J Process Control. 2002;12:577–85.

    Article  CAS  Google Scholar 

  15. Mahadevan R, Doyle III FJ. Efficient optimization approaches to nonlinear model predictive control. Int J Robust Nonlinear Control. 2003;13:309–29.

    Article  Google Scholar 

  16. Zheng A, editor. A computationally efficient nonlinear MPC algorithm. The American Control Conference. Albuquerque: NM; 1997.

  17. Martinsen F, Biegler LT, Foss BA. A new optimization algorithm with application to nonlinear MPC. J Process Control. 2004;14:853–65.

    Article  CAS  Google Scholar 

  18. Leineweber DB, Bauer I, Bock HG, Schloder JP. An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization. Part 1: theoretical aspects. Comput Chem Eng. 2003;27:157–66.

    Article  CAS  Google Scholar 

  19. Ohtsuka T. A continuation/GMRES method for fast computation of nonlinear receding horizon control. Automatica. 2004;40:563–74.

    Article  Google Scholar 

  20. Findeisen R, Diehl M, Burner T, Allgower F, Bock HG, Schloder JP. Efficient output feedback nonlinear model predictive control. American Control Conference, May 8–10, Anchorage, AK2002. p. 4752–7.

  21. Bemporad A, Borrelli F, Morari M. Model predictive control based on linear programming—the explicit solution. IEEE Trans Autom Control. 2002;47(12):1974–85.

    Article  Google Scholar 

  22. Bemporad A, Morari M, Dua V, Pistikopoulos EN. The explicit linear quadratic regulator for constrained systems. Automatica. 2002;38:3–20.

    Article  Google Scholar 

  23. Tondel P, Johansen TA, Bemporad A. An algorithm for multi-parametric quadratic programming and explicit MPC solutions. Automatica. 2003;39:489–97.

    Article  Google Scholar 

  24. Johansen TA. Approximate explicit receding horizon control of contrained nonlinear systems. Automatica. 2004;40:293–300.

    Article  Google Scholar 

  25. Akesson BM, Toivonen HT. A neural network model predictive controller. J Process Control. 2006;16:937–46.

    Article  CAS  Google Scholar 

  26. Parisini T, Zoppoli R. A receding-horizon regulator for nonlinear systems and a neural approximation. Automatica. 1995;31(10):1443–51.

    Article  Google Scholar 

  27. Gupta A, Peck GE, Miller RW, Morris KR. Effect of the variation in the ambient moisture on the compaction behavior of powder undergoing roller-compaction and on the characteristics of tablets produced from the post-milled granules. J Pharm Sci. 2005;94(10):2314–26.

    Article  CAS  PubMed  Google Scholar 

  28. Luyben WL. A simple method for tuning SISO controllers in multivariable system. Ind Eng Chem Proc Des Dev. 1986;25(3):654–60.

    Article  CAS  Google Scholar 

  29. Bristol E. On a new measure of interaction for multivariable process control. IEEE Trans Autom Control. 1966;11(1):133–4.

    Article  Google Scholar 

  30. Lee JH, Morari M, Garcia CE. State-space interpretation of model predictive control. Automatica. 1994;30(4):707–17.

    Article  Google Scholar 

  31. Cutler CR, Ramaker BL. Model predictive control—a computer control algorithm. San Francisco: Automatic Control Conference; 1980.

    Google Scholar 

  32. Papadimitriou C. Computational complexity. Reading: Addison Wesley; 1994.

    Google Scholar 

  33. Garcia CE, Prett DM, Morari M. Model predictive control: theory and practice—a survey. Automatica. 1989;25(3):335–48.

    Article  Google Scholar 

  34. Rawlings JB, Muske KR. The stability of constrained receding horizon control. IEEE Trans Autom Control. 1993;38(10):1512–6.

    Article  Google Scholar 

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Acknowledgment

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

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Authors and Affiliations

  1. OSIsoft LLC, 777 Davis Street, Suite 250, San Leandro, CA, 94577, USA

    Shuo-Huan Hsu

  2. School of Chemical Engineering, Purdue University, 480 Stadium Mall Drive, West Lafayette, IN, 47907, USA

    Gintaras V. Reklaitis & Venkat Venkatasubramania

Authors
  1. Shuo-Huan Hsu
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  2. Gintaras V. Reklaitis
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  3. Venkat Venkatasubramania
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Correspondence to Venkat Venkatasubramania.

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Hsu, SH., Reklaitis, G.V. & Venkatasubramania, V. Modeling and Control of Roller Compaction for Pharmaceutical Manufacturing. J Pharm Innov 5, 24–36 (2010). https://doi.org/10.1007/s12247-010-9077-z

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