**报告题目：**滑模控制中的抖振问题：频率域法

**报 告 人：**Leonid Fridman 教授，墨西哥国立自治大学控制工程和机器人学系

**报告时间：**2020年12月10日 上午9:00-11:00

**会议平台：**ZOOM ID: 959 8953 4758,密码: 796551

**报告摘要：**

Professor Utkin proposed an example showing that the amplitude of chattering caused by the presence of parasitic dynamics (stable actuators) in some systems governed by the First-Order Sliding-Mode Controller is lower than that produced by the Super-Twisting Algorithm. This example served to motivate this paper reconsidering the problem of comparison of chattering in systems with stable actuators, and driven by Discontinuous Sliding-Mode Controllers (DSMCs) and Continuous Sliding-Mode Controllers (CSMCs). Comparison of chattering parameters produced by DSMC and CSMC considering their amplitudes, frequencies, and average power (AP) needed to maintain the system into real-sliding modes, allowing to conclude the following that for the systems for sufficiently*fast*actuators the amplitude of oscillations and AP produced by CSMC be smaller than those caused by DSMC.

Proposed parametrization of the actuator dynamics by a critically damped second-order system or by a constant delay, sets of STA and PID like gains for continuous sliding mode controllers are provided to minimize the amplitude of oscillations or the average power.

Moreover, an analysis of chattering in systems driven by Lipschitz continuous sliding-mode controllers (LCSMC) is performed using the describing function approach. Two kinds of LCSMC are considered: the first one is based on a linear sliding variable (LSV) and the second one on a terminal sliding variable (TSV). Predictions of the amplitude, frequency, and average power of self-excited oscillations, are used to compare such LCSMC respect to the Super-Twisting controller (STC) in systems with fast-actuators. Theoretical predictions and simulations allow the following conclusions: (i) LCSMC still may induce fast-oscillations (chattering) of smaller amplitude and average power, than ones caused by the STC in the absence of the measurement noises. (ii) The level of chattering with LSV-LCSMC could be smaller than one produced by TSV-LCSMC. (iii) The zero (sliding) dynamics of the LSV-LCSMC cannot be arbitrarily fast or the closed-loop system may lose even practical stability, unlike the TSV-LCSMC whose trajectories are finally bounded.

Proposed results confirm a second hypothesis by Professor Utkin: if designing sliding surface is correctly chosen, than for the Lipschitz Continuous SMC a finite time convergence to the output of the system is not a key issue.

**References**

1. U. Perez Ventura, Fridman L. Design of Super-Twisting control gains: a Describing Function based methodology. Automatica, 99(2019) pp.175-180, doi: 10.1016/j.automatica.2018.10.023

2. U. Perez Ventura, Fridman L. When it is reasonable to implement the discontinuous sliding-mode controllers instead of the continuous ones: Frequency Domain Criteria. International Journal of Robust and Nonlinear Control,2019, v.29(3),pp. 810-828, DOI:10.1002/rnc.4347.

3. Martínez-Fuentes CA, Pérez-Ventura U, Fridman L. Chattering analysis for Lipschitz continuous sliding-mode controllers.Int J Robust Nonlinear Control. 2020;1–16. https://doi.org/10.1002/rnc.5239

**报告****人简介：**

Leonid M. Fridman received an M.S. degree in mathematics from Kuibyshev (Samara) State University, Samara, Russia, in 1976, a Ph.D. degree in applied mathematics from the Institute of Control Science, Moscow, Russia, in 1988, and a Dr. Sc. degree in control science from Moscow State University of Mathematics and Electronics, Moscow, Russia, in 1998. From 1976 to 1999, he was with the Department of Mathematics, Samara State Architecture and Civil Engineering University. From 2000 to 2002, he was with the Department of Postgraduate Study and Investigations at the Chihuahua Institute of Technology, Chihuahua, Mexico. In 2002, he joined the Department of Control Engineering and Robotics, Division of Electrical Engineering of Engineering Faculty at National Autonomous University of Mexico (UNAM), Mexico. His research interests are Variable Structure Systems. In 2014-18 Professor Fridman served as a Chair of TC on Variable Structure and Sliding Mode Control. He is a winner of Scopus prize for the best cited Mexican Scientists in Mathematics and Engineering 2010 and 2019 UNAM Prize for research in exact sciences. Actually, he is International Chair of INRIA and High Level Research Expert in Secretary of Education of China. He was working as an invited professor in 20 universities and research laboratories of Argentina, Australia, Austria, China, France, Germany, Italy, Israel, and Spain.

个人主页：http://verona.fi-p.unam.mx/~lfridman/