In this paper, a novel modeling technique has been attempted to develop the mathematical model for a bioreactor functioning at multiple operating regions. The first principle mathematical equations of the reactor are used with the POLYMATH software to generate essential data for the model development. A relative analysis is also carried out with the existing models in the literature. An optimal PID controller is then designed using a multiobjective particle swarm optimization algorithm. The controller tuning procedure is individually discussed for both the stable and unstable steady state regions. The controller tuned for each region is scheduled using a set-point scheduler to achieve a complete control over the bioreactor. The effectiveness of the proposed scheme has been confirmed through a comparative study with the controller tuning methods proposed in the literature. The results show that, the proposed method provides enhanced performance in effective reference tracking and load disturbance rejection with minimal ISE and IAE. Finally the proposed method is validated on the nonlinear bioreactor model in the presence of a measurement noise. The results testify that the PSO tuned PID performs well in tracking the change in biomass concentration at the entire operating region. 1. Introduction Bioreactor plays a vital role in chemical process industries to produce important chemical and biochemical compounds. In this system, living organisms also known as microbes are converted into marketable products such as beverages, antibiotics, vaccines, and industrial solvents [1–3]. The quality of the final product from a bioreactor depends mainly on the control loop employed to monitor and control the microbial growth based on the reference input. Apart from this, incidental external and internal disturbances in a reactor may result in reactor failure. Therefore, there is a strong financial inspiration to develop a finest control scheme that would facilitate rapid startup and stabilization of continuous bioreactors subject to redundant disturbances [4]. In the literature, a variety of methods have been discussed to implement a robust controller for the bioreactor operating at single or multiple steady-states. Kumar et al. have examined a bioreactor with input multiplicities. With an experimental study, the mathematical models for the different steady state operating regions are developed, and a nonlinear PI controller was implemented [5]. Sivakumaran et al. have discussed recurrent neural network (RNN) based modeling method for a nonlinear bioreactor operating
References
[1]
A. K. Jana, Chemical Process Modeling and Computer Simulation, Prentice-Hall, New Delhi, India, 2008.
[2]
E. M. T. El-Mansi and C. F. A. Bryce, Fermentation Microbiology and Biotechnology, Taylor and Francis, 2003.
[3]
H. Scott Fogler, Elements of Chemical Reaction Engineering, Prentice Hall, New Delhi, India, 2006.
[4]
Y. Zhao and S. Skogestad, “Comparison of various control configurations for continuous bioreactors,” Industrial and Engineering Chemistry Research, vol. 36, no. 3, pp. 697–705, 1997.
[5]
S. V. S. Kumar, V. R. Kumar, and G. P. Reddy, “Nonlinear control of bioreactors with input multiplicities—an experimental work,” Bioprocess and Biosystems Engineering, vol. 28, no. 1, pp. 45–53, 2005.
[6]
N. Sivakumaran, T. K. Radhakrishnan, and J. S. C. Babu, “Identification and control of bioreactor using recurrent networks,” Instrumentation Science and Technology, vol. 34, no. 6, pp. 635–651, 2006.
[7]
Z. K. Nagy, “Model based control of a yeast fermentation bioreactor using optimally designed artificial neural networks,” Chemical Engineering Journal, vol. 127, no. 1–3, pp. 95–109, 2007.
[8]
S. M. Giriraj Kumar, R. Jain, N. Anantharaman, V. Dharmalingam, and K. M. M. Sheriffa Begam, “Genetic algorithm based PID controller tuning for a model bioreactor,” Indian Institute of Chemical Engineers, vol. 50, no. 3, pp. 214–226, 2008.
[9]
I. Ananth and M. Chidambaram, “Closed-loop identification of transfer function model for unstable systems,” Journal of the Franklin Institute, vol. 336, no. 7, pp. 1055–1061, 1999.
[10]
S. Pramod and M. Chidambaram, “Closed loop identification of transfer function model for unstable bioreactors for tuning PID controllers,” Bioprocess Engineering, vol. 22, no. 2, pp. 185–188, 2000.
[11]
B. Wayne Bequette, Process Control: Modeling, Design and Simulation, Prentice Hall, 2003.
[12]
A. O'Dwyer, Handbook of PI and PID Controller Tuning Rules, Imperial College Press, London, UK, 3rd edition, 2009.
[13]
R. Padma Sree and M. Chidambaram, Control of Unstable Systems, Narosa Publishing House, New Delhi, India, 2006.
[14]
J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks, pp. 1942–1948, December 1995.
[15]
W. D. Chang and S. P. Shih, “PID controller design of nonlinear systems using an improved particle swarm optimization approach,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 11, pp. 3632–3639, 2010.
[16]
M. Khalilzadeh, F. Kianfar, A. S. Chaleshtari, S. Shadrokh, and M. Ranjbar, “A modified PSO algorithm for minimizing the total costs of resources in MRCPSP,” Mathematical Problems in Engineering, vol. 2012, Article ID 365697, 18 pages, 2012.
[17]
P. Umapathy, C. Venkataseshaiah, and M. S. Arumugam, “Particle Swarm Optimization with various inertia weight variants for optimal power flow solution,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 462145, 15 pages, 2010.
[18]
R. F. Abdel-Kader, “Particle swarm optimization for constrained instruction scheduling,” VLSI Design, vol. 2008, Article ID 930610, 7 pages, 2008.
[19]
R. M. Chen and C. M. Wang, “Project scheduling heuristics-based standard PSO for task-resource assignment in heterogeneous grid,” Abstract and Applied Analysis, vol. 2011, Article ID 589862, 20 pages, 2011.
[20]
M. S. Arumugam and M. V. C. Rao, “On the optimal control of single-stage hybrid manufacturing systems via novel and different variants of particle swarm optimization algorithm,” Discrete Dynamics in Nature and Society, vol. 2005, no. 3, pp. 257–279, 2005.
[21]
M. S. Arumugam and M. V. C. Rao, “On the performance of the particle swarm optimization algorithm with various inertia weight variants for computing optimal control of a class of hybrid systems,” Discrete Dynamics in Nature and Society, vol. 2006, Article ID 79295, 17 pages, 2006.
[22]
T. S. Zhan and C. C. Kao, “Modified PSO method for robust control of 3RPS parallel manipulators,” Mathematical Problems in Engineering, vol. 2010, Article ID 302430, 25 pages, 2010.
[23]
V. Rajinikanth and K. Latha, “Bacterial foraging optimization algorithm based pid controller tuning for time delayedunstable systems,” Mediterranean Journal of Measurement and Control, vol. 7, no. 1, pp. 197–203, 2011.
[24]
W. M. Korani, H. T. Dorrah, and H. M. Emara, “Bacterial foraging oriented by particle swarm optimization strategy for PID tuning,” in Proceedings of the IEEE International Symposium on Computational Intelligence in Robotics and Automation (CIRA '09), pp. 445–450, December 2009.
[25]
M. Zamani, M. Karimi-Ghartemani, N. Sadati, and M. Parniani, “Design of a fractional order PID controller for an AVR using particle swarm optimization,” Control Engineering Practice, vol. 17, no. 12, pp. 1380–1387, 2009.
[26]
M. Zamani, N. Sadati, and M. K. Ghartemani, “Design of an H∞, PID controller using particle swarm optimization,” International Journal of Control, Automation and Systems, vol. 7, no. 2, pp. 273–280, 2009.
[27]
U. S. Banu and G. Uma, “Fuzzy gain scheduled continuous stirred tank reactor with particle swarm optimization based PID control minimizing integral square error,” Instrumentation Science and Technology, vol. 36, no. 4, pp. 394–409, 2008.
[28]
V. Rajinikanth and K. Latha, “Identification and control of unstable biochemical reactor,” International Journal of Chemical Engineering and Applications, vol. 1, no. 1, pp. 106–111, 2010.
[29]
V. Rajinikanth and K. Latha, “Optimization of PID controller parameters for unstable chemical systems using soft computing technique,” International Review of Chemical Engineering, vol. 3, no. 3, pp. 350–358, 2011.
[30]
R. Garduno-Ramirez and K. Y. Lee, “Multiobjective optimal power plant operation through coordinate control with pressure set point scheduling,” IEEE Transactions on Energy Conversion, vol. 16, no. 2, pp. 115–122, 2001.
