Improved EID approach to suppressing disturbances and nonlinearities in repetitive control systems


In most mechanical devices, e.g., manipulators, servo motors, and offshore steel jacket platforms, nonlinear dynamics is prevalent and has been identified as the epicenter of the difficulties experienced in control design of such systems. In order to track and/or reject a periodic reference/disturbance with high accuracy, repetitive control (RC) has been proven as an effective alternative. Unfortunately, there may still exist some disturbances in other forms. These disturbances have the potential to corrupt control performance of nonlinear systems.

To avert this, some strategies have been developed to enhance the disturbance-rejection performance for nonlinear systems. One popular approach is the equivalent-input-disturbance (EID) approach which is based on stable inversion. This method has been reported to being effective for both matched and mismatched disturbances. Better still, this method has been shown not to require an inverse model of the plant and is robust to model uncertainties. However, the conventional EID estimator brings many constraint conditions for system analysis and design.

In a recent publication, Chiba University scientists: Pan Yu (PhD candidate) and Professor Kang-Zhi Liu together with Professors Jinhua She and Min Wu at China University of Geosciences (Wuhan) and also Professor Yosuke Nakanishi at Waseda University  developed an improved EID (IEID) approach to deal with a larger class of nonlinearities in a modified RC system (MRCS) perturbed by an exogenous disturbance. They focused on developing a simple structure of IEID estimator that can eliminate requirements on the existence of the generalized inverses of the input and the observer gain matrices. Their work is currently published in International Journal of Robust and Nonlinear Control.

In brief, they started by providing an overview of the configuration of the IEID estimator. Next, they analyzed the IEID-based nonlinear MRCS and established a continuous-discrete two-dimensional hybrid system model and presented a design algorithm for the closed-loop control system. Then, they conducted comparisons of the developed method with the GESO and conventional EID methods in structural analysis. Finally, numerical methods to validate the developed method and compare it with the GESO and conventional EID methods were undertaken.

The authors avoided the restrictive commutative condition so as to reduce the conservativeness of system design. As such, they adopted a general form of Lyapunov functions for the system design. This way, a design algorithm based on two LMIs, which considered the relation of all the control gains, was devised.

In summary, an IEID-based disturbance-rejection method was developed for a nonlinear MRCS. Specifically, the researchers took advantage of stable inversion, to develop an improved equivalent-input-disturbance (EID) estimator, which was more relaxed than the conventional EID estimator for system design, for the purposes of estimating and canceling out the influence of the disturbance and nonlinearity in the low-frequency domain. Altogether, simulations demonstrated and proved the validity and the advantages of the developed approach.

Improved EID approach to suppressing disturbances and nonlinearities in repetitive control systems - Advances in Engineering

About the author

Pan Yu received her B.S. degree in engineering in 2014 from Central South University, Changsha, China, where she is currently studying for her Ph.D. degree in engineering. Her research interests include repetitive control, disturbance estimation and rejection, time-delay system, and robust control. She is also a research student with the Department of Electrical and Electronic Engineering, Chiba University, Chiba 263-8522, Japan, from Oct. 2017.


About the author

Kang-Zhi Liu received the B.E. degree from Northwestern Polytechnical University, Xi’an, China, in 1984, and the M.E. and Ph.D. degrees from Chiba University, Chiba, Japan, in 1991 and 1998, respectively.

Since then, he has been with Chiba University, where he is currently a Professor. His research interests include control theory, power systems, smart grids, and electrical drives. He has authored and coauthored six books.

Dr. Liu was the recipient of the Young Author Award and three Best Paper Awards from SICE, Japan. He is also the Director of SICE.

About the author

Jinhua She received his B.S. degree in engineering from Central South University, Changsha, China in 1983, and his M.S. and Ph.D. degrees in engineering from the Tokyo Institute of Technology, Tokyo, Japan in 1990 and 1993, respectively.

In 1993, he joined the School of Engineering, Tokyo University of Technology, Tokyo, where he is currently a professor. His research interests include the application of control theory, repetitive control, process control, Internet-based engineering education, and robotics.

Dr. She is a member of the Society of Instrument and Control Engineers, the Institute of Electrical Engineers of Japan, the Japan Society of Mechanical Engineers, and the Asian Control Association. He was the recipient of the International Federation of Automatic Control (IFAC) Control Engineering Practice Paper Prize in 1999 (jointly with M. Wu and M. Nakano).

About the author

Min Wu received his B.S. and M.S. degrees in engineering from Central South University, Changsha, China, in 1983 and 1986, respectively, and his Ph.D. degree in engineering from the Tokyo Institute of Technology, Tokyo, Japan, in 1999.

He was a faculty member of the School of Information Science and Engineering at Central South University from 1986 to 2014, and was promoted to Professor in 1994. In 2014, he moved to China University of Geosciences, Wuhan, China, where he is a professor in the School of Automation. He was a visiting scholar with the Department of Electrical Engineering, Tohoku University, Sendai, Japan, from 1989 to 1990, and a visiting research scholar with the Department of Control and Systems Engineering, Tokyo Institute of Technology, from 1996 to 1999.

He was a visiting professor at the School of Mechanical, Materials, Manufacturing Engineering and Management, University of Nottingham, Nottingham, UK, from 2001 to 2002. His current research interests include robust control and its applications, process control, and intelligent control.

Dr. Wu is a Fellow of the IEEE and a senior member of the Chinese Association of Automation. He received the IFAC Control Engineering Practice Prize Paper Award in 1999 (together with M. Nakano and J. She).

About the author

Yosuke Nakanishi received the B.S. and M.S. degrees in electrical engineering from Waseda University, Shinjuku, Japan, and the Ph.D. degree from Tokyo Metropolitan University, Tokyo, Japan, in 1978, 1980, and 1996, respectively.

In 1980, he joined the Fuji Electric Co. After starting his career in R&D section, he has mainly dedicated himself to power system analysis work as well as development of power system simulators and engineering programs for monitoring control systems. He is currently a Professor with the Graduate School of Environment and Energy Engineering, Waseda University. His research interests include simulation and analysis of power systems and distribution power systems.

Dr. Nakanishi was the recipient of the Prize Paper Award from the IEEE Power Engineering Education Committee, 1991. He is a senior member of the IEE of Japan, and a member of CIGRE. He is also a convenor of the Investigation Committee on Grid Technologies for large amount of wind power, IEEJ, and a member of the Investigation Committee on history of power system analysis, IEEJ.


Pan Yu, Kang-Zhi Liu, Jinhua She, Min Wu, Yosuke Nakanishi. Robust disturbance rejection for repetitive control systems with time-varying nonlinearities. International Journal of Robust and Nonlinear Control. 25 March, 2019; Volume29, Issue5, Pages 1597-1612.

Go To International Journal of Robust and Nonlinear Control

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