Fuzzy Modelling of S-Type Microbial Growth Model for Ethanol Fermentation Process and the Optimal Control Using Simulink

In this work, the fuzzy modelling of S(ubstrate)-type microbial growth model for ethanol fermentation process is built using the sector nonlinearity of Takagi-Sugeno (T-S) fuzzy system. The optimal control for the T-S fuzzy system is obtained using simulink. The motivation is to provide the optimal control by the solutions of the matrix Riccati differential equation (MRDE) obtained from an alternative approach. Accuracy of the solution of the simulink approach to the problem is qualitatively better. An illustrative numerical example is presented for the proposed method.

[1]  M. Dohnal,et al.  Fuzzy bioengineering models , 1985, Biotechnology and bioengineering.

[2]  Malur K. Sundareshan,et al.  Identification and decentralized adaptive control using dynamical neural networks with application to robotic manipulators , 1993, IEEE Trans. Neural Networks.

[3]  John B. Moore,et al.  Indefinite Stochastic Linear Quadratic Control and Generalized Differential Riccati Equation , 2002, SIAM J. Control. Optim..

[4]  M. Razzaghi.  A computational solution for a Matrix Riccati differential equation , 1979 .

[5]  Bart Nicolai,et al.  S & P-Type Models: a Novel Class of Predictive Microbial Growth Models , 2006 .

[6]  P. Balasubramaniam J. Abdul Samath and N. Kumaresan.  Neuro approach for solving matrix Riccati differential equations , 2007 .

[7]  T Yoshida,et al.  Knowledge-based control of fermentation processes. , 1992, Biotechnology and bioengineering.

[8]  Akira Ichikawa,et al.  Quadratic control for linear periodic systems , 1988 .

[9]  Robert S. Germain,et al.  Large Scale Systems , 1996 .

[10]  B. P. Verma.  A FUZZY PHOTOSYNTHESIS MODEL FOR TOMATO , 1997 .

[11]  S. Kawamoto,et al.  An approach to stability analysis of second order fuzzy systems , 1992, [1992 Proceedings] IEEE International Conference on Fuzzy Systems.

[12]  Tsu-Tian Lee,et al.  Neural-network-based optimal fuzzy controller design for nonlinear systems , 2005, Fuzzy Sets Syst..

[13]  Jinghao Zhu,et al.  An iterative method for solving stochastic Riccati differential equations for the stochastic LQR problem , 2003, Optim. Methods Softw..

[14]  Milos Tomic,et al.  Analytic solution of the Riccati equation for the homing missile linear-quadratic control problem , 1994 .

[15]  J Baranyi,et al.  A dynamic approach to predicting bacterial growth in food. , 1994, International journal of food microbiology.