Affine Radial Basis Function Neural Networks for the Robust Control of Hyperbolic Distributed Parameter Systems
In this work, a radial basis function (RBF) neural network is developed for the identification of hyperbolic distributed parameter systems (DPSs). This empirical model is based only on process input-output data and used for the estimation of the controlled variables at specific locations, without the need of online solution of partial differential equations (PDEs). The nonlinear model that is obtained is suitably transformed to a nonlinear state space formulation that also takes into account the model mismatch. A stable robust control law is implemented for the attenuation of external disturbances. The proposed identification and control methodology is applied on a long duct, a common component of thermal systems, for a flow based control of temperature distribution. The closed loop performance is significantly improved in comparison to existing control methodologies.
[1] E.M. Hanczyc and A. Palazoglu, "Nonlinear Control of a Distributed
Parameter Process: The Case of Multiple Characteristics," Ind. Eng.
Chem. Res., vol. 34, pp. 4406-4412, 1995.
[2] E.M. Hanczyc and A. Palazoglu, "Sliding Mode Control of Nonlinear
Distributed Parameter Chemical Processes," Ind. Eng. Chem. Res., vol.
34, pp. 557-566, 1995.
[3] P. Christofides and P. Daoutides, "Feedback control of hyperbolic PDE
systems," AIChe J., vol. 42, no.11, pp. 3063-3086, 1996.
[4] P. Christofides and P. Daoutides, "Robust control of hyperbolic PDE
systems," Chemical Engineering Science, vol. 53, no. 1, pp. 3063-3086,
1998.
[5] P. Christofides, Nonlinear and Robust Control of PDE Systems:
Methods and Applications to transport reaction processes. Boston:
Birkhäuser, 2001.
[6] S. Alotaibi, M. Sen, B. Goodwine and K.T. Yang, "Flow based control
of temperature in long ducts," International Journal of Heat and Mass
Transfer, vol. 47, pp. 4995-5009, 2004.
[7] H. Shang, J.F. Forbes and M. Guay, "Feedback control of hyperbolic
distributed parameter systems," Chemical Engineering Science, vol. 60,
pp. 969 - 980, 2005.
[8] I. Karafyllis and P. Daoutidis, "Control of hot spots in plug flow
reactors," Computers & Chemical Engineering, vol. 26, no. 7-8, pp.
1087-1094, 2002.
[9] A.A. Patwardhan, G.T. Wright and T.F. Edgar, "Nonlinear model
predictive control of distributed parameter systems," Chemical
Engineering Science, vol. 47, no. 4, pp. 721-735, 1992.
[10] S. Dubljevic, P. Mhaskar, N.H. El-Farra and P. Christofides, "Predictive
control of transport-reaction processes," Computers and Chemical
Engineering, vol. 29, pp. 2335-2345, 2005.
[11] H. Shang, J.F. Forbes and M. Guay, "Model predictive control of Quasilinear
Hyperbolic Distributed Parameter Systems," Ind. Eng. Chem. Res.,
vol. 43, pp. 2140-2149, 2004.
[12] R. Gonzáles-García, R. Rico-Martínez, I. Kevrekidis, "Identification of
distributed parameter systems: A neural net based approach," Comp.
Chem. Eng., vol. 22, pp. 965-968, 1998.
[13] R. Padh, S. Balakrishnan and T. Randolph, "Adaptive-critic based
optimal neuro control synthesis for distributed parameter systems,"
Automatica, vol. 37, pp. 1223-1234, 2001.
[14] E. Aggelogiannaki, H. Sarimveis, "Model predictive control for
distributed parameter systems using RBF neural networks," in: Proc.
2nd International Conference on Informatics in Control, Automation
and Robotics, Barcelona, 2005.
[15] L. Magni, G. De Nicolao, R. Scattolini, F. Allgöwer, "Robust model
predictive control for nonlinear discrete-time systems," International
Journal of Robust and Nonlinear Control, vol. 13, pp. 229-246, 2003.
[16] W. Lin and C.I. Byrnes, "Discrete-time Nonlinear H∞ Control with
Measurement Feedback", Automatica, vol. 31, pp. 419-434, 1995.
[17] W. Lin and L. Xie, "A link between H∞ control of a dicrete time
nonlinear system and its linearization", International Journal of control,
vol. 69, no. 2, pp. 301-314, 1998.
[18] H. Sarimveis, A. Alexandridis, G. Tsekouras and G. Bafas, "A fast and
efficient algorithm for training radial basis function neural networks
based on a fuzzy partition of the input space," Industrial Engineering
Chemistry Research, vol. 41, pp. 751-759, 2002.
[1] E.M. Hanczyc and A. Palazoglu, "Nonlinear Control of a Distributed
Parameter Process: The Case of Multiple Characteristics," Ind. Eng.
Chem. Res., vol. 34, pp. 4406-4412, 1995.
[2] E.M. Hanczyc and A. Palazoglu, "Sliding Mode Control of Nonlinear
Distributed Parameter Chemical Processes," Ind. Eng. Chem. Res., vol.
34, pp. 557-566, 1995.
[3] P. Christofides and P. Daoutides, "Feedback control of hyperbolic PDE
systems," AIChe J., vol. 42, no.11, pp. 3063-3086, 1996.
[4] P. Christofides and P. Daoutides, "Robust control of hyperbolic PDE
systems," Chemical Engineering Science, vol. 53, no. 1, pp. 3063-3086,
1998.
[5] P. Christofides, Nonlinear and Robust Control of PDE Systems:
Methods and Applications to transport reaction processes. Boston:
Birkhäuser, 2001.
[6] S. Alotaibi, M. Sen, B. Goodwine and K.T. Yang, "Flow based control
of temperature in long ducts," International Journal of Heat and Mass
Transfer, vol. 47, pp. 4995-5009, 2004.
[7] H. Shang, J.F. Forbes and M. Guay, "Feedback control of hyperbolic
distributed parameter systems," Chemical Engineering Science, vol. 60,
pp. 969 - 980, 2005.
[8] I. Karafyllis and P. Daoutidis, "Control of hot spots in plug flow
reactors," Computers & Chemical Engineering, vol. 26, no. 7-8, pp.
1087-1094, 2002.
[9] A.A. Patwardhan, G.T. Wright and T.F. Edgar, "Nonlinear model
predictive control of distributed parameter systems," Chemical
Engineering Science, vol. 47, no. 4, pp. 721-735, 1992.
[10] S. Dubljevic, P. Mhaskar, N.H. El-Farra and P. Christofides, "Predictive
control of transport-reaction processes," Computers and Chemical
Engineering, vol. 29, pp. 2335-2345, 2005.
[11] H. Shang, J.F. Forbes and M. Guay, "Model predictive control of Quasilinear
Hyperbolic Distributed Parameter Systems," Ind. Eng. Chem. Res.,
vol. 43, pp. 2140-2149, 2004.
[12] R. Gonzáles-García, R. Rico-Martínez, I. Kevrekidis, "Identification of
distributed parameter systems: A neural net based approach," Comp.
Chem. Eng., vol. 22, pp. 965-968, 1998.
[13] R. Padh, S. Balakrishnan and T. Randolph, "Adaptive-critic based
optimal neuro control synthesis for distributed parameter systems,"
Automatica, vol. 37, pp. 1223-1234, 2001.
[14] E. Aggelogiannaki, H. Sarimveis, "Model predictive control for
distributed parameter systems using RBF neural networks," in: Proc.
2nd International Conference on Informatics in Control, Automation
and Robotics, Barcelona, 2005.
[15] L. Magni, G. De Nicolao, R. Scattolini, F. Allgöwer, "Robust model
predictive control for nonlinear discrete-time systems," International
Journal of Robust and Nonlinear Control, vol. 13, pp. 229-246, 2003.
[16] W. Lin and C.I. Byrnes, "Discrete-time Nonlinear H∞ Control with
Measurement Feedback", Automatica, vol. 31, pp. 419-434, 1995.
[17] W. Lin and L. Xie, "A link between H∞ control of a dicrete time
nonlinear system and its linearization", International Journal of control,
vol. 69, no. 2, pp. 301-314, 1998.
[18] H. Sarimveis, A. Alexandridis, G. Tsekouras and G. Bafas, "A fast and
efficient algorithm for training radial basis function neural networks
based on a fuzzy partition of the input space," Industrial Engineering
Chemistry Research, vol. 41, pp. 751-759, 2002.
@article{"International Journal of Chemical, Materials and Biomolecular Sciences:59567", author = "Eleni Aggelogiannaki and Haralambos Sarimveis", title = "Affine Radial Basis Function Neural Networks for the Robust Control of Hyperbolic Distributed Parameter Systems", abstract = "In this work, a radial basis function (RBF) neural network is developed for the identification of hyperbolic distributed parameter systems (DPSs). This empirical model is based only on process input-output data and used for the estimation of the controlled variables at specific locations, without the need of online solution of partial differential equations (PDEs). The nonlinear model that is obtained is suitably transformed to a nonlinear state space formulation that also takes into account the model mismatch. A stable robust control law is implemented for the attenuation of external disturbances. The proposed identification and control methodology is applied on a long duct, a common component of thermal systems, for a flow based control of temperature distribution. The closed loop performance is significantly improved in comparison to existing control methodologies.
", keywords = "Hyperbolic Distributed Parameter Systems, Radial Basis Function Neural Networks, H∞ control, Thermal systems.", volume = "2", number = "10", pages = "231-7", }
