An ADRC-based PID tuning rule
Sheng Zhong
Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People's Republic of China
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, People's Republic of China
Beijing Aerospace Automatic Control Institute, Beijing, People's Republic of China
Search for more papers by this authorCorresponding Author
Yi Huang
Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People's Republic of China
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, People's Republic of China
Correspondence Yi Huang, Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People's Republic of China.
Email: [email protected]
Search for more papers by this authorLei Guo
Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People's Republic of China
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, People's Republic of China
Search for more papers by this authorSheng Zhong
Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People's Republic of China
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, People's Republic of China
Beijing Aerospace Automatic Control Institute, Beijing, People's Republic of China
Search for more papers by this authorCorresponding Author
Yi Huang
Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People's Republic of China
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, People's Republic of China
Correspondence Yi Huang, Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People's Republic of China.
Email: [email protected]
Search for more papers by this authorLei Guo
Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People's Republic of China
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, People's Republic of China
Search for more papers by this authorFunding information: National Key R & D Program of China, 2018YFA0703800; National Natural Science Foundation of China, U20B2054
Abstract
This article puts forward an active disturbance rejection control (ADRC) based tuning rule to the well-known proportional-integral-derivative (PID) control for a class of multi-input multi-output non-affine uncertain systems. It is proved that the PID control with the ADRC-based tuning rule can guarantee satisfied tracking performance, both for the transient phase and the steady state. Furthermore, it is illustrated that, with the new tuning rule, the PID control is able to timely estimate and compensate for the nonlinear and coupled uncertainties, which explains the reason why PID control does have large-scale robustness with respect to the uncertainties and can achieve decoupling control with a simple structure. The theoretical results are verified by simulations.
CONFLICT OF INTEREST
The authors declare no potential conflict of interests.
Open Research
DATA AVAILABILITY STATEMENT
All data generated or analyzed during this study are included in this article.
REFERENCES
- 1Samad T. A survey on industry impact and challenges thereof [technical activities]. IEEE Control Syst Mag. 2017; 37(1): 17-18.
- 2Åström KJ, Hägglund T. PID Controllers: Theory, Design, and Tuning. Vol 2. ISA Research; 1995.
- 3O'Dwyer A. PI and PID controller tuning rules: an overview and personal perspective. Proceedings of the IET, Irish Signals and Systems Conference; 2006:161-166.
- 4Guo L. Estimation, control, and games of dynamical systems with uncertainty (in Chinese). Sci China (Inf Sci). 2020; 60(9): 1327-1344.
- 5Zhang JK, Guo L. Theory and design of PID controller for nonlinear uncertain systems. IEEE Control Syst Lett. 2019; 3(3): 643-648.
10.1109/LCSYS.2019.2915306 Google Scholar
- 6Zhao C, Guo L. PID controller design for second order nonlinear uncertain systems. Sci China (Inf Sci). 2017; 60(2):022201.
- 7Zhao C, Guo L. PID control for a class of non-affine uncertain systems. Proceedings of the 37th Chinese Control Conference; 2018; Wuhan, China.
- 8Keel LH, Bhattacharyya SP. Controller synthesis free of analytical models: three term controllers. IEEE Trans Automat Contr. 2008; 53(6): 1353-1369.
- 9Ho M, Lin C. PID controller design for robust performance. IEEE Trans Automat Contr. 2003; 48(8): 1404-1409.
- 10Zhao C, Guo L. Towards a theoretical foundation of PID control for uncertain nonlinear systems; 2010. arXiv:2010.06864.
- 11Han J. From PID to active disturbance rejection control. IEEE Trans Ind Electron. 2009; 56(3): 900-906.
- 12 Texas Instruments. Technical Reference Manual, TMS320F28069M, TMS320F28068M InstaSPINTM-MOTION Software, Literature Number: SPRUHJ0A; 2013.
- 13Sira-Ramirez H, Linares-Flores J, Garcia-Rodriguez C, Contreras-Ordaz M. On the control of the permanent magnet synchronous motor: an active disturbance rejection control approach. IEEE Trans Control Syst Technol. 2014; 22(5): 2056-2063.
- 14Sun L, Shen J, Hua Q, Lee KY. Data-driven oxygen excess ratio control for proton exchange membrane fuel cell. Appl Energy. 2018; 231: 866-875.
- 15Xiang GF, Huang Y, Yu JR, Zhu MD, Su JB. Intelligence evolution for service robot: an ADRC perspective. Control Theory Technol. 2018; 16(4): 324-335.
10.1007/s11768-018-8073-6 Google Scholar
- 16Zheng Q, Gao ZQ. Active disturbance rejection control: some recent experimental and industrial case studies. Control Theory Technol. 2018; 16(4): 301-313.
10.1007/s11768-018-8142-x Google Scholar
- 17Li SH, Tang J, Chen WH, Chen XS. Generalized extended state observer based control for systems with mismatched uncertainties. IEEE Trans Ind Electron. 2012; 59(12): 4792-4802.
- 18Guo BZ, Wu ZH. Output tracking for a class of nonlinear systems with mismatched uncertainties by active disturbance rejection control. Syst Control Lett. 2017; 100: 21-31.
- 19Zhao ZL, Guo BZ. A novel extended state observer for output tracking of MIMO systems with mismatched uncertainty. IEEE Trans Automat Contr. 2017; 63(1): 211-218.
- 20Xue W, Huang Y. Performance analysis of 2-DOF tracking control for a class of nonlinear uncertain systems with discontinuous disturbances. Int J Robust Nonlinear Control. 2018; 28(4): 1456-1473.
- 21Chen S, Xue W, Zhong S, Huang Y. On comparison of modified ADRCs for nonlinear uncertain systems with time delay. Sci China Inf Sci. 2018; 61(7):70223.
- 22Chen S, Huang Y. The selection criterion of nominal model in active disturbance rejection control for non-affine uncertain systems. J Franklin Inst. 2020; 357: 3365-3386.
- 23Zhong S, Huang Y, Guo L. A parameter formula connecting PID and ADRC. Sci China (Inf Sci). 2020; 63(9):192203.
- 24Zhong S, Huang Y, Guo L. New tuning methods of both PID and ADRC for MIMO coupled nonlinear uncertain systems. Proceedings of the
IFAC; 2020; Berlin, Germany.
- 25Boulkroune A, M'Saad M, Farza M. Fuzzy approximation-based indirect adaptive controller for multi-input multi-output non-affine systems with unknown control direction. IET Control Theory Appl. 2012; 6(17): 2619-2629.
- 26Ren B, Zhong QC, Chen J. Robust control for a class of non-affine nonlinear systems based on the uncertainty and disturbance estimator. IEEE Trans Ind Electron. 2015; 62(9): 5881-5888.
- 27Boskovic JD, Chen L, Mehra RK. Adaptive control design for nonaffine models arising in flight control. J Guid Control Dyn. 2004; 27(2): 209-209.
- 28Bian T, Jiang Y, Jiang ZP. Adaptive dynamic programming and optimal control of nonlinear non-affine systems. Automatica. 2014; 50(10): 2624-2632.
- 29Young A, Cao C, Hovakimyan N, Lavretsky E. Control of a nonaffine double-pendulum system via dynamic inversion and time-scale separation. Proceedings of the 2006 American Control Conference; 2006.
- 30Meng W, Yang Q, Si J, Sun Y. Adaptive neural control of a class of output-constrained nonaffine systems. IEEE Trans Cybern. 2016; 46(1): 85-95.
- 31Li IH, Lee LW. A hierarchical structure of observer-based adaptive fuzzy-neural controller for MIMO systems. Fuzzy Sets Syst. 2011; 185(1): 52-82.
- 32Chen G, Zhao Y. Distributed adaptive output-feedback tracking control of non-affine multi-agent systems with prescribed performance. J Franklin Inst. 2018; 355(13): 6087-6110.
- 33Huang Y, Xue W. Active disturbance rejection control: methodology and theoretical analysis. ISA Trans. 2014; 53: 963-976.
- 34Zhao Y, Huang Y. Frequency properties of ADRC. Proceedings of the 40th Chinese Control Conference; 2021; Shanghai, China.
- 35Zhao Y, Huang Y. On the bandwidth of the extended state observer. Proceedings of the 40th Chinese Control Conference; 2021; Shanghai, China.
