PID Control of Planar Nonlinear Uncertain Systems in the Presence of Actuator Saturation

Xujun Lyu; Zongli Lin

doi:10.1109/JAS.2021.1004281

Volume 9 Issue 1

Jan. 2022

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2022 > 9(1): 90-98

X. Lyu and Z. Lin, “PID control of planar nonlinear uncertain systems in the presence of actuator saturation,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 1, pp. 90–98, Jan. 2022. doi: 10.1109/JAS.2021.1004281

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X. Lyu and Z. Lin, “PID control of planar nonlinear uncertain systems in the presence of actuator saturation,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 1, pp. 90–98, Jan. 2022. doi: 10.1109/JAS.2021.1004281

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PID Control of Planar Nonlinear Uncertain Systems in the Presence of Actuator Saturation

doi: 10.1109/JAS.2021.1004281

Xujun Lyu^{1
,
,},
Zongli Lin^{2
,
,}

1.
College of Engineering, Huazhong Agricultural University, Wuhan 430070, China
2.
Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, P.O. Box 400743, Charlottesville, VA 22904-4743 USA

Funds: This work was supported in part by the Fundamental Research Funds for the Central Universities, China (2662018QD031) and the National Natural Science Foundation of China (51905205)

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Author Bio:
Xujun Lyu is a Lecturer in the College of Engineering at the Huazhong Agricultural University. She received the B.E. degree in electrical engineering and automation, the M.E. degree in mechanical engineering, and the Ph.D. degree in mechanical manufacturing and automation, all from Wuhan University of Technology in 2009, 2013 and 2018, respectively. She was a visiting Ph.D. student with the Charles L. Brown Department of Electrical and Computer Engineering at University of Virginia, USA, in 2013–2014. Her main research interests include magnetic suspension technology and control systems

Zongli Lin (Fellow, IEEE) is the Ferman W. Perry Professor in the School of Engineering and Applied Science and a Professor of electrical and computer engineering at University of Virginia. He received the B.S. degree in mathematics and computer science from Xiamen University in 1983, the master of engineering degree in automatic control from Chinese Academy of Space Technology in 1989, and the Ph.D. degree in electrical and computer engineering from Washington State University, USA, in 1994. His current research interests include nonlinear control, robust control, and control applications. He was an Associate Editor of IEEE Transactions on Automatic Control (2001–2003), IEEE/ASME Transactions on Mechatronics (2006–2009), and IEEE Control Systems Magazine (2005–2012). He was elected a Member of the Board of Governors of the IEEE Control Systems Society (2008–2010, 2019–2021) and chaired the IEEE Control Systems Society Technical Committee on Nonlinear Systems and Control (2013–2015). He has served on the operating committees of several conferences. He was the Program Chair of the 2018 American Control Conference and a General Chair of the 13th and 16th International Symposium on Magnetic Bearings, held in 2012 and 2018, respectively. He currently serves on the editorial boards of several journals and book series, including Automatica, Systems & Control Letters, and Springer/Birkhauser book series Control Engineering. He is a Fellow of IEEE, CAA, IFAC, and AAAS (American Association for the Advancement of Science)
Corresponding author: Xujun Lyu, e-mail: lyuxujun@mail.hzau.edu.cn; Zongli Lin, e-mail: zl5y@virginia.edu
Received Date: 2021-02-25
Revised Date: 2021-04-20
Accepted Date: 2021-05-21

Available Online: 2021-06-10

Abstract

Abstract

This paper investigates PID control design for a class of planar nonlinear uncertain systems in the presence of actuator saturation. Based on the bounds on the growth rates of the nonlinear uncertain function in the system model, the system is placed in a linear differential inclusion. Each vertex system of the linear differential inclusion is a linear system subject to actuator saturation. By placing the saturated PID control into a convex hull formed by the PID controller and an auxiliary linear feedback law, we establish conditions under which an ellipsoid is contractively invariant and hence is an estimate of the domain of attraction of the equilibrium point of the closed-loop system. The equilibrium point corresponds to the desired set point for the system output. Thus, the location of the equilibrium point and the size of the domain of attraction determine, respectively, the set point that the output can achieve and the range of initial conditions from which this set point can be reached. Based on these conditions, the feasible set points can be determined and the design of the PID control law that stabilizes the nonlinear uncertain system at a feasible set point with a large domain of attraction can then be formulated and solved as a constrained optimization problem with constraints in the form of linear matrix inequalities (LMIs). Application of the proposed design to a magnetic suspension system illustrates the design process and the performance of the resulting PID control law.
- Actuator saturation,
- domain of attraction,
- nonlinear systems,
- PID control,
- uncertainties

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References

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PID control design for planar nonlinear uncertain systems with input saturation
Robustness with respect to uncertain nonlinearities
Maximization of the domain of attraction and output tracking capacity
LMI based design algorithm
Application to a test rig for magnetic suspension systems

PID Control of Planar Nonlinear Uncertain Systems in the Presence of Actuator Saturation

doi: 10.1109/JAS.2021.1004281

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