Global robust output regulation of a class of MIMO nonlinear systems by nonlinear internal model control

Significance 

Output regulation theory has continued to attract significant attention of the control community due to its capability to solve trajectory tracking and disturbance rejection problem of practical systems in engineering application, for example, piezoelectric actuators with hysteresis, flexible/rigid spacecraft, and permanent magnet synchronous motor servo system. In particular, the key for solving the output regulation problem is to design an appropriate internal model, which can reproduce the necessary steady-state signals of the plant and guarantee that the stabilization problem of the augmented system is solvable. So far, output regulation problems have been extensively investigated in the literature for both linear and nonlinear uncertain systems.

Recently, the global robust output regulation problem for a class of uncertain multi-input multi-output (MIMO) nonlinear systems which may not have well defined relative degree and are subject to a nonlinear exosystem has been studied based on a constructive nonlinear internal model. However, the proposed nonlinear internal model-based control law is applicable to the case where the exogenous signals are reference input and/or measurable disturbance rather than unmeasurable disturbance. When unmeasurable disturbance is taken into account and is assumed to be generated by a nonlinear exosystem, the nonlinear internal model design remains a big challenge. Thus, the development of effective nonlinear internal model is highly desirable and has formed the basis of subsequent research.

To overcome this inherent challenge, Professor Zhaowu Ping, master student Yaoyi Li and Professor Yunzhi Huang from Hefei University of Technology, in collaboration with Professor Jun-Guo Lu from Shanghai Jiao Tong University and Dr. Hai Wang from Murdoch University, utilized a nonlinear internal control model that is not affected by exogenous signal to further study the global robust output regulation problem of MIMO nonlinear systems. Specifically, the MIMO system has two inputs and two outputs. The stabilization problem of the augmented system was decomposed into stabilization problem of two single-input systems. Finally, the effectiveness of the proposed nonlinear internal model-based control law was verified via computer simulations. Their research work is currently published in the International Journal of Robust Nonlinear Control.

The research team demonstrated the ability of the proposed nonlinear internal model in rejecting the unmeasurable disturbance produced by a nonlinear exosystem. Most importantly, it was possible to convert the control problem into a global robust stabilization problem for more complex MIMO nonlinear systems with various uncertainties. Furthermore, a global state feedback control law can be constructed recursively by combining various stabilization techniques including input-to-state stability theory and backstepping design.

In a nutshell, the authors studied the global robust output regulation problem for a class of uncertain MIMO nonlinear systems which may not have well defined relative degree and are subject to a nonlinear exosystem. From the results, the effectiveness of the proposed approach was successfully validated through numerical simulations. The proposed approach is versatile and could be extended to different MIMO nonlinear systems. In a statement to Advances in Engineering, Professor Zhaowu Ping said the study will expand the engineering application of MIMO nonlinear systems.

Global robust output regulation of a class of MIMO nonlinear systems by nonlinear internal model control - Advances in Engineering
Fig. 1. The block diagram of the proposed method
Global robust output regulation of a class of MIMO nonlinear systems by nonlinear internal model control - Advances in Engineering
Fig. 2. Profile on the phase portraits of the nonlinear internal model and nonlinear exosystem

About the author

Zhaowu Ping received the B.E. degree in electrical engineering and automation from Shanghai Maritime University, Shanghai, China, in 2005, the M.E. degree in control theory and control engineering from Shanghai Jiao Tong University, Shanghai, in 2008, and the Ph.D. degree in mechanical and automation engineering from The Chinese University of Hong Kong, Hong Kong, in 2011.

He was a Distributed Control System (DCS) Engineer with Bayer Technology and Engineering (Shanghai) Company, Ltd., Shanghai, for three months. From 2012 to 2013, he was a Postdoctoral Researcher with Seoul National University, Seoul, South Korea. He is currently a Professor with the School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, China. His current research interests include nonlinear output regulation theory and applications, electromechanical system control, neural network control, and control and estimation of switched systems.

About the author

Yaoyi Li received the B.E. degree in electrical engineering and automation from the Hefei University of Technology, Xuancheng, China, in 2018, and the M.E. degree in control engineering from the Hefei University of Technology, Hefei, China, in 2021.

He is currently an Electrical Designer with Expace Technology Co., Ltd., Fourth Academy of China Aerospace Science and Industry Corp, China Aerospace Science and Industry Corp, Wuhan, China. His current research interests include nonlinear output regulation theory and applications and electromechanical system control.

About the author

Yunzhi Huang received the Ph.D. degree in precision instruments and machinery from the Hefei University of Technology, Hefei, China, in 2005.

She is currently a Professor with the School of Electrical Engineering and Automation, Hefei University of Technology. Her current research interests include signal processing and electromagnetic nondestructive evaluation and intelligent instruments.

About the author

Jun-Guo Lu received the B.E. and Ph.D. degrees in control theory and control engineering from the Nanjing University of Science and Technology, Nanjing, China, in 1997 and 2002, respectively.

From 2001 to 2003, he was a Postdoctoral Fellow with the Department of Automation, Shanghai Jiao Tong University, Shanghai, China. In 2003, he joined Shanghai Jiao Tong University, where he is currently a Professor with the Department of Automation. His current research interests include nonlinear output regulation theory and applications, fractional-order control system, robot control and multirobot coordination, complex networks, big data, and three-dimensional (3-D) digitalization.

About the author

Hai Wang (M’13-SM’19) received the B.E. degree from Hebei Polytechnic University, Tangshan, China, in 2007, the M.E. degree from Guizhou University, Guiyang, China, in 2010, and the Ph.D. degree from the Swinburne University of Technology, Melbourne, VIC, Australia, in 2013, respectively, all in electrical and electronic engineering.

From 2014 to 2015, he was a Postdoctoral Research Fellow with the Faculty of Science, Engineering, and Technology, Swinburne University of Technology, Melbourne, VIC, Australia. From 2015 to 2019, he was a Professor with the School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, China. Since early 2019, he has been with the College of Science, Health, Engineering and Education, Murdoch University, Perth, WA, Australia, where he is currently a Senior Lecturer of Electrical Engineering and Academic Chair of Instrumentation and Control Engineering and Industrial Computer Systems Engineering. He is also the Director of Advanced Mechatronics, Robotics and Control Laboratory at Murdoch University. His current research interests include sliding mode control and observer, adaptive control, robotics and mechatronics, neural networks, nonlinear systems, and vehicle dynamics and control.

Dr. Wang is the Chair of IEEE IES Western Australia Chapter. He serves as an Associate Editor for the IEEE Access and the Leading Guest Editor for Computers and Electrical Engineering.

Reference

Ping, Z., Li, Y., Huang, Y., Lu, J., & Wang, H. (2021). Global robust output regulation of a class of MIMO nonlinear systems by nonlinear internal model controlInternational Journal of Robust and Nonlinear Control, 31(9), 4037-4051.

Go To International Journal of Robust and Nonlinear Control

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