Multi-variable Linear Extended State Observer for a Class of Nonlinear Systems and Its Convergence Analysis
-
摘要: 针对一类非线性不确定系统，构造了一种多变量线性扩张状态观测器（Multi-variable linear extended state observer，MVLESO），用于实时估计非线性系统的不确定动态.采用频域分析方法，剖析了所构造的MVLESO在非线性系统不确定动态估计方面的收敛性，并推导出不确定动态的频域估计误差模型.仿真结果表明，所设计的MVLESO可以较为精准地估计出非线性系统当前的不确定动态，该特性为基于MVLESO鲁棒控制方案的有效实施奠定了基础.Abstract: For a class of nonlinear uncertain systems, a multi-variable extended state observer (MVLESO) is constructed, and it is employed to estimate the uncertain dynamics of nonlinear system in real time. By means of the analysis method in frequency domain, the convergence property with respect to the estimation on uncertain dynamics of nonlinear system is analyzed. Furthermore, the estimation error model of uncertain dynamics is deduced in the form of frequency domain. Simulation results show that the as-built MVLESO can accurately estimate the current uncertain dynamics in nonlinear systems. This feature lays a foundation for the effective implementation of MVLESO-based robust control scheme.
-
图 2 不同 $\beta _{si}$ 取值时估计误差模型传递函数的幅频特性曲线
Fig. 2 Magnitude-frequency curves of transfer functions in estimation error models with different $\beta _{si
图 3 SMDO对各干扰量的估计曲线
Fig. 3 Estimation curves of different disturbance variables by using SMDO
图 4 ISMDO和MVLESO对各干扰量的估计曲线
Fig. 4 Estimation curves of different disturbance variables by using ISMDO and MVLESO
-
[1] 武雷, 保宏, 杜敬利, 王从思. 一种自抗扰控制器参数的学习算法. 自动化学报, 2014, 40(3): 556-560 http://www.aas.net.cn/CN/abstract/abstract18321.shtmlWu Lei, Bao Hong, Du Jing-Li, Wang Cong-Si. A learning algorithm for parameters of automatic disturbances rejection controller. Acta Automatica Sinica, 2014, 40(3): 556-560 http://www.aas.net.cn/CN/abstract/abstract18321.shtml [2] 韩京清. 自抗扰控制技术—估计补偿不确定因素的控制技术. 北京: 国防工业出版社, 2008.Han Jing-Qing. Active Disturbance Rejection Control Technique—The Technique for Estimating and Compensating the Uncertainties. Beijing: National Defense Industry Press, 2008. [3] Han J Q. From PID to active disturbance rejection control. IEEE Transactions on Industrial Electronics, 2009, 56(3): 900-906 doi: 10.1109/TIE.2008.2011621 [4] Sira-Ramírez H, Linares-Flores J, García-Rodríguez C, Contreras-Ordaz M A. On the control of the permanent magnet synchronous motor: an active disturbance rejection control approach. IEEE Transactions on Control Systems Technology, 2014, 22(5): 2056-2063 doi: 10.1109/TCST.2014.2298238 [5] Yao J Y, Jiao Z X, Ma D M. Extended-state-observer-based output feedback nonlinear robust control of hydraulic systems with backstepping. IEEE Transactions on Industrial Electronics, 2014, 61(11): 6285-6293 doi: 10.1109/TIE.2014.2304912 [6] 马红雨, 苏剑波. 基于自抗扰控制器的机器人无标定三维手眼协调. 自动化学报, 2004, 30(3): 400-406 http://www.aas.net.cn/CN/abstract/abstract16332.shtmlMa Hong-Yu, Su Jian-Bo. Uncalibrated robotic 3D hand-eye coordination based on auto disturbance rejection controller. Acta Automatica Sinica, 2004, 30(3): 400-406 http://www.aas.net.cn/CN/abstract/abstract16332.shtml [7] Castañeda L A, Luviano-Juárez A, Chairez I. Robust trajectory tracking of a Delta robot through adaptive active disturbance rejection control. IEEE Transactions on Control Systems Technology, 2015, 23(4): 1387-1398 doi: 10.1109/TCST.2014.2367313 [8] Zhu Z, Xu D, Liu J M, Xia Y Q. Missile guidance law based on extended state observer. IEEE Transactions on Industrial Electronics, 2013, 60(12): 5882-5891 doi: 10.1109/TIE.2012.2232254 [9] 薛文超, 黄朝东, 黄一. 飞行制导控制一体化设计方法综述. 控制理论与应用, 2013, 30(12): 1511-1520 http://www.cnki.com.cn/Article/CJFDTOTAL-KZLY201312007.htmXue Wen-Chao, Huang Chao-Dong, Huang Yi. Design methods for the integrated guidance and control system. Control Theory and Applications, 2013, 30(12): 1511-1520 http://www.cnki.com.cn/Article/CJFDTOTAL-KZLY201312007.htm [10] 熊少锋, 王卫红, 刘晓东, 王森, 武亮. 考虑导弹自动驾驶仪动态特性的带攻击角度约束制导律. 控制与决策, 2015, 30(4): 585-592 http://youxian.cnki.com.cn/yxdetail.aspx?filename=KZYC20141205002&dbname=CAPJ2015Xiong Shao-Feng, Wang Wei-Hong, Liu Xiao-Dong, Wang Sen, Wu Liang. Impact angle guidance law considering missile's dynamics of autopilot. Control and Decision, 2015, 30(4): 585-592 http://youxian.cnki.com.cn/yxdetail.aspx?filename=KZYC20141205002&dbname=CAPJ2015 [11] 刘晓东, 黄万伟, 禹春梅. 含扩张状态观测器的高超声速飞行器动态面姿态控制. 宇航学报, 2015, 36(8): 916-922 http://www.cnki.com.cn/Article/CJFDTOTAL-YHXB201508008.htmLiu Xiao-Dong, Huang Wan-Wei, Yu Chun-Mei. Dynamic surface attitude control for hypersonic vehicle containing extended state observer. Journal of Astronautics, 2015, 36(8): 916-922 http://www.cnki.com.cn/Article/CJFDTOTAL-YHXB201508008.htm [12] 黄一, 张文革. 自抗扰控制器的发展. 控制理论与应用, 2002, 19(4): 485-492 http://www.cnki.com.cn/Article/CJFDTOTAL-KZLY200204000.htmHuang Yi, Zhang Wen-Ge. Development of active disturbance rejection controller. Control Theory and Applications, 2002, 19(4): 485-492 http://www.cnki.com.cn/Article/CJFDTOTAL-KZLY200204000.htm [13] 夏元清, 付梦印, 邓志红, 任雪梅. 滑模控制和自抗扰控制的研究进展. 控制理论与应用, 2013, 30(2): 137-147 http://www.cnki.com.cn/Article/CJFDTOTAL-KZLY201302000.htmXia Yuan-Qing, Fu Meng-Yin, Deng Zhi-Hong, Ren Xue-Mei. Recent developments in sliding mode control and active disturbance rejection control. Control Theory and Applications, 2013, 30(2): 137-147 http://www.cnki.com.cn/Article/CJFDTOTAL-KZLY201302000.htm [14] 高志强. 自抗扰控制思想探究. 控制理论与应用, 2013, 30(12): 1497-1509 http://www.cnki.com.cn/Article/CJFDTOTAL-KZLY201312006.htmGao Zhi-Qiang. On the foundation of active disturbance rejection control. Control Theory and Applications, 2013, 30(12): 1497-1509 http://www.cnki.com.cn/Article/CJFDTOTAL-KZLY201312006.htm [15] Zheng Q, Gao L Q, Gao Z Q. On stability analysis of active disturbance rejection control for nonlinear time-varying plants with unknown dynamics. In: Proceedings of the 46th IEEE Conference on Decision and Control. New Orleans, USA: IEEE, 2007. 3501-3506 [16] Guo B Z, Zhao Z L. On the convergence of an extended state observer for nonlinear systems with uncertainty. Systems and Control Letters, 2011, 60(6): 420-430 doi: 10.1016/j.sysconle.2011.03.008 [17] Zheng Q, Gao L Q, Gao Z Q. On validation of extended state observer through analysis and experimentation. Journal of Dynamic Systems, Measurement, and Control, 2012, 134(2): 024505, DOI: 10.1115/1.4005364 [18] 陈增强, 孙明玮, 杨瑞光. 线性自抗扰控制器的稳定性研究. 自动化学报, 2013, 39(5): 574-580 http://www.aas.net.cn/CN/abstract/abstract17868.shtmlChen Zeng-Qiang, Sun Ming-Wei, Yang Rui-Guang. On the stability of linear active disturbance rejection control. Acta Automatica Sinica, 2013, 39(5): 574-580 http://www.aas.net.cn/CN/abstract/abstract17868.shtml [19] 张洪华, 关轶峰, 胡锦昌, 王泽国. 分区四元数姿态控制. 自动化学报, 2015, 41(7): 1341-1349 http://www.aas.net.cn/CN/abstract/abstract18707.shtmlZhang Hong-Hua, Guan Yi-Feng, Hu Jin-Chang, Wang Ze-Guo. A novel attitude control strategy based on quaternion partition. Acta Automatica Sinica, 2015, 41(7): 1341-1349 http://www.aas.net.cn/CN/abstract/abstract18707.shtml [20] 杨明, 董晨, 王松艳, 晁涛. 基于有限时间输出反馈的线性扩张状态观测器. 自动化学报, 2015, 41(1): 59-66 http://www.aas.net.cn/CN/abstract/abstract18583.shtmlYang Ming, Dong Chen, Wang Song-Yan, Chao Tao. Linear extended state observer based on finite-time output feedback. Acta Automatica Sinica, 2015, 41(1): 59-66 http://www.aas.net.cn/CN/abstract/abstract18583.shtml -
下载:
图(5)
计量
- 文章访问数: 2004
- HTML全文浏览量: 263
- PDF下载量: 988
- 被引次数: 0
