Robust Control of Nonlinear System with Input and Output Nonlinear Constraints
Shuhui Bi*, Lei Wang**, and Chunyan Han*
*School of Electrical Engineering, University of Jinan
No.336, West Road of NanXinzhuang, Jinan, Shandong 250022, China
**Shandong Provincial Key Laboratory of Automotive Electronics Technology, Institute of Automation Shandong Academy of Sciences,
Qilu University of Technology (Shandong Academy of Sciences)
No.19, Keyuan Road, Jinan, Shandong 250014, China
With the development of modern technology, actuators and sensors composed of smart materials, such as piezoceramic and magnetostrictive materials, have been widely used in practice owing to their various advantages. However, in the working process of a smart material based actuator and sensor, non-smooth nonlinear constraints in their output responses may induce inaccuracies and oscillations, which severely degrade system performance. Therefore, input and output nonlinear constraints brought about by actuators and sensors should be considered. Generally, the output nonlinear constraint, namely, non-smooth effects from sensors, has been ignored. Therefore, in this paper, a robust control for a system with an output constraint as well as with both input and output constraints will be considered. Firstly, the generalized Prandtl-Ishlinskii (PI) hysteresis model is used for describing the input and output nonlinearities owing to its excellent characteristics, the model has proved suitable in theoretical operator based settings. Further, a robust control for a nonlinear system with an output nonlinear constraint is considered by using operator based robust right coprime factorization approach. Here, operator based robust stability is considered, and the control system structure including feedforward and feedback controllers is presented with a derivation of sufficient conditions for stable controller operation. Based on the proposed conditions, the influence from an output nonlinear constraint is rejected, the systems are robustly stable, and output tracking performance can be realized. Moreover, robust stability and output tracking performance for a nonlinear system with both input and output nonlinear constraints are also analyzed.
-  Y. Arkun and J. P. Calvet, “Robust stabilization of input/output linearizable systems under uncertainty and disturbances,” AIChE J., Vol.38, pp. 1145-1154, 1992.
-  P. D. Christofides, “Robust output feedback control of nonlinear singularly perturbed systems,” Automatica, Vol.36, No.1, pp. 45-52, 2000.
-  A. Nokbahti and H. Wang, “On design of simply structured robust controllers,” IET Control Theory and Applications, Vol.153, pp. 493-501, 2006.
-  R. Rebarber and G. Weiss, “Internal model based tracking and disturbance rejection for stable well-posed systems,” Automatica, Vol.39, No.9, pp. 1555-1569, 2003.
-  M. Brokate and J. Sprekels, “Hysteresis and Phase Transitions,” New York: Springer-Verlag, 1996.
-  J. W. Macki, P. Nistri, and P. Zecca, “Mathematical Models for Hysteresis,” Soc. Indust. Appl. Math., Vol.35, pp. 94-123, 1993.
-  M. Rakotondrabe, “Bouc-Wen modeling and inverse multiplicative structure to compensate hysteresis nonlinearity in piezoelectric actuators,” IEEE Trans. Automat. Sci. Eng., Vol.8, No.2, pp. 428-431, 2011.
-  G. Tao and F. L. Lewis, “Adaptive Control of Nonsmooth Dynamic Systems,” New York: Springer-Verlag, 2001.
-  C. Y. Su, Y. Stepanenko, J. Svoboda, and T. P. Leung, “Robust adaptive control of a class of nonlinear systems with unknown backlash-Like hysteresis,” IEEE Trans. on Automatic Control, Vol.45, No.12, pp. 2427-2432, 2000.
-  R. V. Iyer, X. Tan, and P. S. Krishnaprasad, “Approximate inversion of the Preisach hysteresis operator with application to control of smart actuators,” IEEE Trans. on Automatic Control, Vol.50, pp. 798-810, 2005.
-  M. A. Janaideh, S. Rakheja, and C. Y. Su, “An Analytical Generalized Prandtl-Ishlinskii Model Inversion for Hysteresis Compensation in Micropositioning Control,” IEEE Trans. on Mechatronics, Vol.16, No.4, pp. 734-744, 2011.
-  D. Wang, F. Li, S. Wen, X. Qi, P. Liu, and M. Deng, “Operator-Based Sliding-Mode Nonlinear Control Design for a Process with Input Constraint,” J. of Robotics and Mechatronics, Vol.27, No.1, pp. 83-90, 2015.
-  G. Chen and Z. Han, “Robust right coprime factorization and robust stabilization of nonlinear feedback control systems,” IEEE Trans. on Automatic Control, Vol.43, No.10, pp. 1505-1510, 1998.
-  M. Deng, A. Inoue, and K. Ishikawa, “Operator-based nonlinear feedback control design using robust right coprime factorization,” IEEE Trans. on Automatic Control, Vol.51, No.4, pp. 645-648, 2006.
-  S. Bi, M. Deng, and S. Wen, “Operator-based output tracking control for nonlinear uncertain systems with unknown time-varying delays,” IET Control Theory and Applications, Vol.5, No.5, pp. 693-699, 2011.
-  M. Deng, A. Inoue, and Y. Baba, “Operator-based nonlinear vibration control system design of a flexible arm with Piezoelectric actuator,” Int. J. of Advanced Mechatronic Systems, Vol.1, No.1, pp. 71-76, 2008.
-  S. Bi, X. Wang, J. Zheng, and L. Wang, “Operator based robust nonlinear control for system with generalized PI hysteresis,” Proc. of 2014 Int. Conf. on Advanced Mechatronic Systems, Kumamoto, Japan, Aug. 10-12, pp. 37-42, 2014
-  S. Bi, L. Wang, Y. Zhao, and M. Deng, “Operator-based Robust Control for Nonlinear Uncertain Systems with Unknown Backlash-Like Hysteresis,” Int. J. of Control, Automation and Systems, Vol.14, No.2, pp. 469-477, 2016.
-  S. Bi, L. Wang, S. Wen, and M. Deng, “Operator-based Robust Nonlinear Control for SISO and MIMO Nonlinear Systems with PI Hysteresis,” IEEE/CAA J. of Automatica Sinica, DOI: 10.1109/JAS.2016.7510175, 2017.
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