Underactuated System Control Based on Improved Active Disturbance Rejection Control

doi:10.1007/s12204-024-2703-6

Abstract

Abstract: To achieve the control effect of high precision, fast response speed, and good stability for a class of underactuated systems, a control strategy based on the improved active disturbance rejection controller is designed. First, a new sliding mode tracking differentiator is designed on the basis of a new sliding mode reaching rate. Given that traditional active disturbance rejection control is only suitable for single-input and single-output systems, two sliding mode tracking differentiators are used in the proposed model to obtain the given displacement and velocity as well as the actual displacement and velocity, respectively. Then, a new nonlinear function with enhanced smoothness and convergence is designed. Using the nonlinear function, an improved extended state observer for the underactuated system is designed to optimize its following error ability. Given that the parameter values of the control rate part are difficult to adjust, the particle swarm optimization algorithm is used to optimize the four parameter values of the control rate part. Finally, the simulation results show that the proposed control strategy can realize a fast and stable control of such underactuated systems.

Key words: active disturbance rejection control, nonlinear function, improved extended state observer

摘要： 为了实现对一类欠驱动系统高精度、响应速度快、稳定性好的控制效果，设计了一种基于改进型自抗扰控制器的控制策略。首先，根据新的滑模趋近率设计了新的滑模跟踪微分器。考虑到传统的自抗扰控制只适用于单输入单输出系统，在该模型中使用两个滑模跟踪微分器分别获得给定位移和速度以及实际位移和速度。然后，设计了一种新的非线性函数，增强了平滑性和收敛性。利用非线性函数，设计了改进的欠驱动系统扩张状态观测器，优化了欠驱动系统的跟随误差能力。考虑到控制率部分参数值难以调节，采用粒子群优化算法对控制率部分的4个参数值进行优化。最后，仿真结果表明，所提出的控制策略能够实现对此类欠驱动系统的快速稳定控制。

关键词: 自抗扰控制，非线性函数，改进型扩张状态观测器

CLC Number:

TP273

Chen Qiuzhuo, Zhu Biao, Ma Lixiang, Liu Bingyou, Wan Luanfei. Underactuated System Control Based on Improved Active Disturbance Rejection Control[J]. J Shanghai Jiaotong Univ Sci, 2026, 31(2): 428-439.

References

[1] JIANG J J, ASTOLFI A. Stabilization of a class of underactuated nonlinear systems via underactuated back-stepping [J]. IEEE Transactions on Automatic Control, 2021, 66(11): 5429-5435.

[2] NIE Z Y, LIU R J. Inverted pendulum angle control design and experimental studies under complex conditions [J]. Information and Control, 2016, 45(4): 506-512 (in Chinese).

[3] WANG J J, KUMBASAR T. Optimal PID control of spatial inverted pendulum with big Bang-big crunch optimization [J]. IEEE/CAA Journal of Automatica Sinica, 2018, 7(3): 822-832.

[4] EL-SOUSY F F M, ALATTAS K A, MOFID O, et al. Robust adaptive super-twisting sliding mode stability control of underactuated rotational inverted pendulum with experimental validation [J]. IEEE Access, 2022, 10: 100857-100866.

[5] KUMAR V, AGARWAL R. Modeling and Control of Inverted Pendulum cart system using PID-LQR based Modern Controller [C]//2022 IEEE Students Conference on Engineering and Systems. Prayagraj: IEEE, 2022: 1-5.

[6] CHEN Z Q, CHENG Y, SUN M W, et al. Surveys on theory and engineering applications for linear active disturbance rejection control [J]. Information and Control, 2017, 46(3): 257-266 (in Chinese).

[7] XIAO Y G, ZHU C Z, LU H, et al. CADRC for a class of underactuated MIMO systems [J]. Applied Mathematics and Mechanics, 2020, 41(11): 1197-1209 (in Chinese).

[8] MA Y. Rotating Inverted Pendulum Control Based on ADRC Method[J]. Automation Application, 2020(4): 161-164 (in Chinese).

[9] CHEN Z G, RUAN X G, LI Y. Dynamic modeling of a cubical robot balancing on its corner [J]. Control and Decision, 2019, 34(6): 1203-1210 (in Chinese).

[10] ZHANG Q, WEI Y X, LI X A. Quadrotor attitude control by fractional-order fuzzy particle swarm optimization-based active disturbance rejection control [J]. Applied Sciences, 2021, 11(24): 11583.

[11] WU M, XIAO Z J, SHANG M. Research on ADRC of inverted pendulum based on improved shark smell optimization algorithm [J]. Micromotors, 2019, 52(9): 92-97 (in Chinese).

[12] HONG J W, LIU B Y, WANG L C. High precision control of one-stage linear inverted pendulum based on improved ADRC [J]. Journal of Heilongjiang University of Technology (Comprehensive Edition), 2018, 18(12): 69-75 (in Chinese).

[13] GAO Q, CHEN S S, LI Y. Realization of linear active disturbance rejection control in inverted pendulum system [J]. Electric Drive, 2014, 44(10): 49-53 (in Chinese).

[14] CHEN Q, ZHUANG J, LIU B, et al. Inverted pendulum balance control based on improved active disturbance rejection control[C]//2022 China Automation Congress. Xiamen: IEEE, 2022: 1526-1531.

[15] ZHENG T H, FENG Z P, ZHAO S, et al. Active disturbance rejection controller based heading control of underwater flight vehicles [J]. Journal of Shanghai Jiao Tong University (Science), 2020, 25(4): 441-446.

[16] TIAN M H, WANG B, YU Y, et al. Discrete-time repetitive control-based ADRC for current loop disturbances suppression of PMSM drives [J]. IEEE Transactions on Industrial Informatics, 2022, 18(5): 3138-3149.

[17] WAN H, QI X, LI J. Linear matrix inequality based stability analysis of linear/nonlinear switching active disturbance rejection control system[J]. Journal of Shanghai Jiao Tong University, 2022, 56(11): 1491-1501 (in Chinese).

[18] GAO Z Q. Scaling and bandwidth-parameterization based controller tuning [C]// 2003 American Control Conference. Denver: IEEE, 2003: 4989-4996.

[19] WANG Y W, XING K X, MA J, et al. Implementation and design of active disturbance rejection control for the linear inverted pendulum[J]. Control Engineering of China, 2017, 24(4): 711-715 (in Chinese).

[20] CHEN Z L, LI Y F, ZHANG Y L. Optimization of ADRC parameters based on particle swarm optimization algorithm [C]//2021 IEEE 4th Advanced Information Management, Communicates, Electronic and Automation Control Conference. Chongqing: IEEE, 2021: 1956-1959.

[21] FENG J, WANG Y, WANG Q, et al. Fast steering mirror ADRC based on improved particle swarm optimizer[J]. Systems Engineering and Electronics, 2021, 43(12): 3675-3682 (in Chinese).