Abstract
In this paper, we investigate the state estimation, unknown input and measurement noise reconstruction problems and the feedback controller design issues for a linear discrete-time system with both unknown inputs and measurement noises. First, an augmented system is constructed and the state vector of the augmented system consists of the original system state and the measurement noise, and the preconditions between the original system and the augmented system is discussed in detail. Second, for the augmented system, a reduced-order observer is designed so that the original system state estimates and the measurement noise reconstruction can be obtained. Third, in order to get the asymptotical unknown input reconstruction, an interval observer for part of the measurable output is proposed and an unknown input reconstruction method based on the interval observer is developed. Finally, an observer-based state feedback and unknown input controller is designed and the closed-loop system stability is analyzed. We point out that the closed-loop system satisfies the so-called separation property. At last, two simulation examples are given to verify the effectiveness of the proposed methods.
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Recommended by Associate Editor Xiangpeng Xie under the direction of Editor Hamid Reza Karimi. This work is supported by National Natural Science Foundation (NNSF) of China under Grants 61973236, 61573256, 61803181 and the Project of the New Mode of Intelligent Manufacturing.
Fanglai Zhu was born in Xing’an county, Guangxi province, China, on December 28, 1965. He received his Ph.D. degree in control theory and control engineering from Shanghai Jiao Tong University, Shanghai, China. He worked in Guilin University of Electronic Technology (GLIET), Guangxi province, China as an associated professor for 3 years and a professor for 2 years, respectively. Then joined Tongji University (TJU), Shanghai, China, in July, 2007 as a professor. His primary areas of research are nonlinear observer design, sliding model control, model-based fault diagnosis, fault-tolerate control, T-S fuzzy models.
Wei Zhang received his Ph.D. degree in control theory and control engineering from Shanghai Jiao Tong University, Shanghai, China, in 2010. He was a senior visiting scholar in electronics and computer engineering at Texas A & M University from 2015 to 2016. He is currently a professor with the Laboratory of Intelligent Control and Robotics, Shanghai University of Engineering Science. He is also a commentator for the U.S. “Math Review” and a member of the Shanghai Automation Institute. His primary areas of research are nonlinear control and observer design, robust control, UAV control and state estimation for vehicle.
Jiancheng Zhang received his Ph.D. degree in control theory and control engineering from Tongji University, Shanghai, China, in 2017. He is currently a lecturer in the Department of Information and Computational Science, College of Science, Jiangnan University. His primary areas of research are unknown input observer design, fault diagnosis, fault reconstruction and observer-based sliding mode control.
Shenghui Guo received his Ph.D. degree in control theory and control engineering from Tongji University, Shanghai, China, in 2016. He is currently an associate professor with the College of Electronics and Information Engineering, Suzhou University of Science and Technology, China, and also a post-doctor with the College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, China. His primary areas of research are observer design, model-based fault detection and fault tolerant control.
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Zhu, F., Zhang, W., Zhang, J. et al. Unknown Input Reconstruction via Interval Observer and State and Unknown Input Compensation Feedback Controller Designs. Int. J. Control Autom. Syst. 19, 145–157 (2021). https://doi.org/10.1007/s12555-019-1087-0
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DOI: https://doi.org/10.1007/s12555-019-1087-0