Feedback Linearization Optimal Control Approach for Bilinear Systems in CSTR Chemical Reactor

Affiliation(s)

College of Automation and Electronic Engineer, Qingdao University of Science & Technology, Qingdao, China.

Department of Computer Engineering, Qingdao Technological University Qingdao College, Qingdao, China.

College of Automation and Electronic Engineer, Qingdao University of Science & Technology, Qingdao, China.

Department of Computer Engineering, Qingdao Technological University Qingdao College, Qingdao, China.

ABSTRACT

This paper considers the optimal control problem for the bilinear system based on state feedback. Based on the concept of relative order of the output with respect to the input, first we change a bilinear system to a pseudo linear system model through the coordinate transformation. Then based on the theory of linear quadratic optimal control, the optimal controller is designed by solving the Riccati equation and introducing state feedback with state prediction. At last, the simulation results in CSTR Chemical reactor show the effectiveness of the method.

This paper considers the optimal control problem for the bilinear system based on state feedback. Based on the concept of relative order of the output with respect to the input, first we change a bilinear system to a pseudo linear system model through the coordinate transformation. Then based on the theory of linear quadratic optimal control, the optimal controller is designed by solving the Riccati equation and introducing state feedback with state prediction. At last, the simulation results in CSTR Chemical reactor show the effectiveness of the method.

Cite this paper

nullD. Gao, Q. Yang, M. Wang and Y. Yu, "Feedback Linearization Optimal Control Approach for Bilinear Systems in CSTR Chemical Reactor,"*Intelligent Control and Automation*, Vol. 3 No. 3, 2012, pp. 274-277. doi: 10.4236/ica.2012.33031.

nullD. Gao, Q. Yang, M. Wang and Y. Yu, "Feedback Linearization Optimal Control Approach for Bilinear Systems in CSTR Chemical Reactor,"

References

[1] Z. Aganovic and Z. Gajic, “The Successive Approximation Procedure for Finite-Time Optimal Control of Bilinear Systems,” IEEE Transactions Automatic Control, Vol. 39, No. 9, 1994, pp. 1932-1935. doi:10.1109/9.317128

[2] Z. Aganovic and Z. Gajic, “The Successive Approximation Procedure for Stead State Optimal Control of Bilinear Systems,” Journal of Optimization Theory and Application, Vol. 84, No. 2, 1995, pp. 273-291.

[3] J.-M. Li, K.-Y. Xing and B.-W. Wang, “DISOPE Algorithm of Optimal Control Based on Bilinear Model for Nonlinear Continuous time Systems,” Control and Decision, Vol. 15, No. 4, 2000, pp. 461-464.

[4] G.-Y. Tang, H. Ma and B.-L. Zhang, “Successive Approximation Approach of Optimal Control for Bilinear Discrete-Time Systems,” IEEE Proceedings of Control Theory & Applications, Vol. 152, No. 6, 2005, pp. 639-644.

[5] G.-Y. Tang, Y.-D. Zhao and H. Ma, “Optimal Output Tracking Control for Bilinear Systems,” Transactions of the Institute of Measurement and Control, Vol. 28, No. 4, 2006, pp. 387-397. doi:10.1177/0142331206073065

[6] G.-Y. Tang, “Feedforward and Feedback Optimal Control for Linear Systems with Sinusoidal Disturbances,” High Technology Letters, Vol. 7, No. 4, 2001, pp. 16-19. doi:10.1109/68.903206

[7] E. Hofer and B. Tibken, “An Iterative Method for the Finite-Time Bilinear Quadratic Control Problem,” Journal of Optimization Theory and Applications, Vol. 57, No. 3, 1988, pp. 411-427. doi:10.1007/BF02346161

[8] D.-X. Gao, G.-Y. Tang and Q. Yang, “Feedback Linearization Optimal Control of Nonlinear Systems with External Disturbance,” Control and Instruments in Chemical Industry, Vol. 34, No. 2, 2007, pp. 20-24.

[9] S.-H. Lee and K. Lee, “Bilinear Systems Controller Design with Approximation Techniques,” Journal of the Chungcheong Mathematical Society, Vol. 8, No. 1, 2005, pp. 101-116.

[1] Z. Aganovic and Z. Gajic, “The Successive Approximation Procedure for Finite-Time Optimal Control of Bilinear Systems,” IEEE Transactions Automatic Control, Vol. 39, No. 9, 1994, pp. 1932-1935. doi:10.1109/9.317128

[2] Z. Aganovic and Z. Gajic, “The Successive Approximation Procedure for Stead State Optimal Control of Bilinear Systems,” Journal of Optimization Theory and Application, Vol. 84, No. 2, 1995, pp. 273-291.

[3] J.-M. Li, K.-Y. Xing and B.-W. Wang, “DISOPE Algorithm of Optimal Control Based on Bilinear Model for Nonlinear Continuous time Systems,” Control and Decision, Vol. 15, No. 4, 2000, pp. 461-464.

[4] G.-Y. Tang, H. Ma and B.-L. Zhang, “Successive Approximation Approach of Optimal Control for Bilinear Discrete-Time Systems,” IEEE Proceedings of Control Theory & Applications, Vol. 152, No. 6, 2005, pp. 639-644.

[5] G.-Y. Tang, Y.-D. Zhao and H. Ma, “Optimal Output Tracking Control for Bilinear Systems,” Transactions of the Institute of Measurement and Control, Vol. 28, No. 4, 2006, pp. 387-397. doi:10.1177/0142331206073065

[6] G.-Y. Tang, “Feedforward and Feedback Optimal Control for Linear Systems with Sinusoidal Disturbances,” High Technology Letters, Vol. 7, No. 4, 2001, pp. 16-19. doi:10.1109/68.903206

[7] E. Hofer and B. Tibken, “An Iterative Method for the Finite-Time Bilinear Quadratic Control Problem,” Journal of Optimization Theory and Applications, Vol. 57, No. 3, 1988, pp. 411-427. doi:10.1007/BF02346161

[8] D.-X. Gao, G.-Y. Tang and Q. Yang, “Feedback Linearization Optimal Control of Nonlinear Systems with External Disturbance,” Control and Instruments in Chemical Industry, Vol. 34, No. 2, 2007, pp. 20-24.

[9] S.-H. Lee and K. Lee, “Bilinear Systems Controller Design with Approximation Techniques,” Journal of the Chungcheong Mathematical Society, Vol. 8, No. 1, 2005, pp. 101-116.