Advances in Engineering Advances in Engineering features breaking research judged by Advances in Engineering advisory team to be of key importance in the Engineering field. Papers are selected from over 10,000 published each week from most peer reviewed journals.
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.
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 control. International Journal of Robust and Nonlinear Control, 31(9), 4037-4051.
