Abstract
A fuzzy-neural adaptive terminal iterative learning controller is proposed in this paper for uncertain fed-batch fermentation processes with iteration-varying initial states. In order to derive a terminal output tracking error model, a technique of sampled-data transformation for differentiation is firstly utilized to transform the fed-batch fermentation process into a sampled-data system. An input and output algebraic function is then derived based on the sampled-data formulation of fed-batch fermentation process as well as the differential mean value theorem. According to the derived terminal output tracking error model, a fuzzy neural network is applied to approximate the unknown terminal desired input. In order to overcome a lumped uncertainty from the error induced by fuzzy-neural function approximation and the unknown initial states, an iteration-varying boundary layer is developed to construct an auxiliary terminal output error. This auxiliary terminal output error is then used to derive suitable adaptive laws for the weights of fuzzy neural network and the width of boundary layer. Based on a Lyapunov-like analysis, we show that the boundedness of control parameters, control input, and process output are guaranteed for each iteration. Furthermore, the norm of terminal output error will asymptotically converge to a tunable residual set whose size depends on the width of boundary layer as iteration number goes to infinity.
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References
Lee, J.H., Lee, K.S.: Iterative learning control applied to batch processes: an overview. Control Eng. Pract. 15(10), 1306–1318 (2007)
Wang, Y.Q., Gao, F.R., Doyle, F.J.: Survey on iterative learning control, repetitive control, and run-to-run control. J. Process Control 19(10), 1589–1600 (2009)
Xiong, Z.H., Zhang, J., Wang, X., Xu, Y.M.: Integrated tracking control strategy for batch processes using a batch-wise linear time-varying perturbation model. Control Theory Appl. 1(1), 178–188 (2007)
Lu, N., Gao, F.: Stage-based process analysis and quality prediction for batch processes. Ind. Eng. Chem. Res. 44(10), 3547–3555 (2005)
Chen, C., Xiong, Z., Zhong, Y.: Design and analysis of integrated predictive iterative learning control for batch process based on two-dimensional system theory. Chin. J. Chem. Eng. 22(7), 762–768 (2014)
Wang, Y., Liu, T., Zhao, Z.: Advanced PI control with simple learning set-point design: application on batch processes and robust stability analysis. Chem. Eng. Sci. 71(26), 153–165 (2012)
Shi, J., Zhou, H., Cao, Z., Jiang, Q.: A design method for indirect iterative learning control based on two-dimensional generalized predictive control algorithm. J. Process Control 24(10), 1527–1537 (2014)
Wang, Y.Q., Zhou, D., Gao, F.: Iterative learning reliable control of batch processes with sensor faults. Chem. Eng. Sci. 63(4), 1039–1051 (2008)
Wang, L.M., Mo, S.Y., Zhou, D.H., Gao, F.R., Chen, X.: Robust delay dependent iterative learning fault-tolerant control for batch processes with state delay and actuator failures. J. Process Control 22(7), 1273–1286 (2012)
Liu, T., Gao, F., Wang, Y.: IMC-based iterative learning control for batch processes with uncertain time delay. J. Process Control 20(2), 173–180 (2010)
Wang, L.M., Mo, S.Y., Zhou, D.H., Gao, F.R.: Robust design of feedback integrated with iterative learning control for batch processes with uncertainties and interval time-varying delays. J. Process Control 21(7), 987–996 (2011)
Liu, T., Gao, F.: Robust two dimensional iterative learning control for batch processes with state delay and time-varying uncertainties. Chem. Eng. Sci. 65(23), 6134–6144 (2010)
Wang, L.M., Mo, S.Y., Zhou, D.H., Gao, F.R., Chen, X.: Delay-range-dependent robust 2D iterative learning control for batch processes with state delay and uncertainties. J. Process Control 23(5), 715–730 (2013)
Zhang, J., Feng, Y., Al-Mahrouqi, M.H.: Reliable optimal control of a fed-batch fermentation process using ant colony optimisation and bootstrap aggregated neural network models. Comput Aided Chem. Eng. 29, 663–667 (2012)
Hosena, M.A., Hussaina, M.A., Mjalli, F.S.: Control of polystyrene batch reactors using neural network based model predictive control (NNMPC): an experimental investigation. Control Eng. Pract. 19(5), 454–467 (2011)
Dovzan, D., Skrjanc, I.: Predictive functional control based on an adaptive fuzzy model of a hybrid semi-batch reactor. Control Eng. Pract. 18(8), 979–989 (2010)
Cosenza, B., Galluzzo, M.: Nonlinear fuzzy control of a fed-batch reactor for penicillin production. Comput. Chem. Eng. 36, 273–281 (2012)
Xiong, Z., Zhang, J.: A batch-to-batch iterative optimal control strategy based on recurrent neural network models. J. Process Control 15(1), 11–21 (2005)
Marquez-Vera, M.A., Ramos-Velasco, L.E., Suarez-Cansino, J., Marquez-Vera, C.A.: Fuzzy iterative learning control applied in a biological reactor using a reduced number of measures. Appl. Math. Comput. 246, 608–618 (2014)
Jia, L., Shi, J., Chiu, M.S.: Integrated neuro-fuzzy model and dynamic R-parameter based quadratic criterion-iterative learning control for batch process. Neurocomputing 98(3), 24–33 (2012)
Ban Impe, J.F., Bastin, G.: Optimal adaptive control of fed-batch fermentation processes. Control Eng. Pract. 3(7), 939–954 (1995)
Wang, J., Xue, Y., Yu, T., Zhao, L.: Run-to-run optimization for fed-batch fermentation process with swarm energy conservation particle swarm optimization algorithm. Chin. J. Chem. Eng. 18(5), 787–794 (2010)
Wang, J., Zhao, L., Yu, T.: On-line estimation in fed-batch fermentation process using state space model and unscented kalman filter. Chin. J. Chem. Eng. 18(2), 258–264 (2010)
Xiong, Z., Xu, Y., Zhang, J., Dong, J.: Batch-to-batch control of fed-batch processes using control-affine feedforward neural network. Neural Comput. Appl. 17(4), 425–432 (2008)
Zhang, J., Nguyan, J., Morris J., Xiong, Z. Batch to batch iterative learning control of a fed-batch fermentation process using linearised models. In: 10th International Conference on Control, Automation, Robotics and Vision, (2008)
Jewaratnam, J., Zhang, J., Hussain, A., Morris, J. Batch-to-batch iterative learning control of a fed-batch fermentation process using incrementally updated models. In: Proceedings of the 11th International Symposium on Computer Applications in Biotechnology, (2010)
Jewaratnam, J., Zhang, J., Morris, J., Hussain, A. Batch-to-batch iterative learning control using linearised models with adaptive model updating. In: 2012 UKACC International Conference on Control, (2012)
Zhang, J., Xiong, Z., Guillaume, D., Lamande, A.: Batch to batch iterative learning control of a fed-batch fermentation process. Mech. Eng. Technol. Adv. Intell. Soft Comput. 125, 253–260 (2012)
Xu, J.X., Chen, Y.Q., Heng, L.T., Yamamoto, S.: Terminal iterative learning control with an application to RTPCVD thickness control. Automatica 35(9), 1535–1542 (1999)
Gauthier, G., Boulet, B. Terminal iterative learning control design with singular value decomposition decoupling for thermoforming ovens. In: American Control Conference, pp. 1640–1645 (2009)
Xiong, Z., Zhang, J.: A batch-to-batch iterative optimal control strategy based on recurrent neural network models. J. Process Control 15, 11–21 (2005)
Arimoto, S., Sekimoto, M., Kawamura, S. Iterative learning of specified motions in task-space for redundant multi-joint hand-arm robots. In: IEEE International Conference on Robotics and Automation, pp. 2867–2873 (2007)
Modal, S., Yun, Y., Chung W. K. Terminal iterative learning control for calibrating systematic odometry errors in mobile robots. In: 2010 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pp. 311–316. Montreal (2010)
Hou, Z.S., Wang, Y., Yin, C., Tang, T.: Terminal iterative learning control based station stop control of a train. Int. J. Control 84(7), 1263–1274 (2011)
Freeman, C.T., Tan, Y.: Iterative learning control with mixed constraints for point-to-point tracking. IEEE Trans. Control Syst. Technol. 21(3), 604–616 (2013)
Son, T. D., Ahn, H. S. Terminal iterative learning control with multiple intermediate pass points. In: Proceedings on American Control Conference, pp. 3651–3656 (2011)
Chen, Y., Xu, J.X., Wen, C. A high-order terminal iterative learning control scheme. In: Proceedings of the 36th Conference on Decision and Control, pp. 3771–3772. San Diego (1997)
Chi, R.H., Wang, D.W., Hou, Z.S., Jin, S.T.: Data-driven optimal terminal iterative learning control. J. Process Control 22(10), 2026–2037 (2012)
Chi, R.H., Wang, D.W., Lewis, F.L., Hou, Z.S., Jin, S.T.: Adaptive terminal ILC for iteration-varying target points. Asian J. Control 17(3), 952–962 (2015)
Liu, T. Q., Wang, D.W., Chi, R.H. Neural network based terminal iterative learning control for tracking run-varying reference point with initial state variance. In: 13th International Conference on Control, Automation and Systems (2013)
Wang, Y.C., Chien, C.J.: Repetitive tracking control of nonlinear systems using reinforcement fuzzy-neural adaptive iterative learning controller. Appl. Math. Inf. Sci. 6(3), 473–481 (2012)
Xiong, Z., Zhang, J.: Modelling and optimal control of fed-batch processes using a novel control affine feedforward neural network. Neurocomputing 61, 317–337 (2004)
Acknowledgments
This work is supported by Ministry of Science and Technology, R.O.C., under Grants MOST103-2221-E-211-010, MOST103-2221-E-211-012 and by National Science Foundation of China, under Grant No. 61374102, 61120106009, 61433002.
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Wang, YC., Chien, CJ., Chi, R. et al. A Fuzzy-Neural Adaptive Terminal Iterative Learning Control for Fed-Batch Fermentation Processes. Int. J. Fuzzy Syst. 17, 423–433 (2015). https://doi.org/10.1007/s40815-015-0059-7
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DOI: https://doi.org/10.1007/s40815-015-0059-7