线性系统传感器故障的区间估计
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摘要
本文研究了离散时间线性系统传感器故障的区间估计问题.通过将传感器故障视为增广状态,原始系统转化为一个等效的广义系统.基于所得到的广义系统,利用H∞技术设计鲁棒增广状态观测器,从而得到系统传感器故障的估计.然后通过中心对称多胞体分析以实现对故障的区间估计.与已有的方法相比,本文所提出的方法具有更宽松的设计条件,并且可以得到更加准确的故障区间估计.最后,通过一个四容水箱系统的数值仿真验证了所提方法的有效性和优越性.
This paper studies the problem of sensor fault interval estimation for discrete-time linear systems. First, the original system is transformed into an equivalent descriptor system by considering the sensor fault as augmented state.Second, the robust augmented state observer is designed by using the H∞ technique to estimate the sensor fault. The proposed method uses the zonotpoes to realize the interval estimation of the fault. Compared with the existing methods,the proposed method has more relaxed design conditions and can obtain more accurate fault interval estimation. Finally,numerical simulations of a quadruple-tanks system are given to illustrate the effectiveness and superiority of the proposed approach.
This paper studies the problem of sensor fault interval estimation for discrete-time linear systems. First, the original system is transformed into an equivalent descriptor system by considering the sensor fault as augmented state.Second, the robust augmented state observer is designed by using the H∞ technique to estimate the sensor fault. The proposed method uses the zonotpoes to realize the interval estimation of the fault. Compared with the existing methods,the proposed method has more relaxed design conditions and can obtain more accurate fault interval estimation. Finally,numerical simulations of a quadruple-tanks system are given to illustrate the effectiveness and superiority of the proposed approach.
引文
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[10] COMBASTEL C. A state bounding observer for uncertain non-linear continuous-time systems based on zonotopes. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference. Seville:IEEE, 2005:7228–7234.
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[14] PUIG V, CUGUERO P, QUEVEDO J. Worst-case state estimation and simulation of uncertain discrete-time systems using zonotopes.Proceedings of the European Control Conference 2001. Porto:IEEE,2001:1691–1697.
[15] LE V T H, STOICA C, ALAMO T, et al. Zonotopic guaranteed state estimation for uncertain systems. Automatica, 2013, 49(11):3418–3424.
[16] Xu F, PUIG V, OCAMPO–MARTINEZ C, et al. Actuator-fault detection and isolation based on settheoretic approaches. Journal of Process Control, 2014, 24(6):947–956.
[17] TANG Wentao, WANG Zhenhua, WANG Ye, et al. Fault diagnosis for uncertain systems based on unknown input set-membership filters. Acta Automatica Sinica, DOI:10.26383/j.aas.2018.c170123.(汤文涛,王振华,王烨,等.基于未知输入集员滤波器的不确定系统故障诊断.自动化学报, DOI:10.26383/j.aas.2018.c170123.)
[18] WANG Z, RODRIGUES M, THEILLIOL D, et al. Actuator fault estimation observer design for discrete-time linear parameter-varying descriptor systems. International Journal of Adaptive Control and Signal Processing, 2015, 29(2):242–258.
[19] Xu S, LAM J. Robust Control and Filtering of Singular Systems.Berlin:Springer, 2006.
[20] BOYD S, EL GHAOUI L, FERON E, et al. Linear Matrix Inequalities in System and Control Theory. New York:SIAM, 1994.
[21] COMBASTEL C. Zonotopes and Kalman observers:gain optimality under distinct uncertainty paradigms and robust convergence. Automatica, 2015, 55:265–273.
[22] ALAMO T, BRAVO J M, CAMACHO E F. Guaranteed state estimation by zonotopes. Automatica, 2005, 41(6):1035–1043.
[23] JOHANSSON K H. The quadruple-tank process:a multivariable laboratory process with an adjustable zero. IEEE Transactions on Control Systems Technology, 2000, 8(3):456–465.
[24] GUO S, ZHU F, ZHU S, et al. State and sensor fault interval estimations for discrete-time systems. Proceedings of the 36th Chinese Control Conference. Dalian:IEEE, 2017:7280–7284.
[25] GUO Shenghui, ZHU Fanglai. Actuator fault detection based on interval observers. Control and Decision. 2016, 31(6):1118–1122.(郭胜辉,朱芳来.基于区间观测器的执行器故障检测.控制与决策,2016, 31(6):1118–1122.)
[2] GAO Z, CECATI C, DING S X. A survey of fault diagnosis and fault-tolerant techniques–part I:fault diagnosis with model-based and signal-based approaches. IEEE Transactions of Industrial Electronics, 2015, 62(6):3757–3767.
[3] HWANG I, KIM S, KIM Y, et al. A survey of fault detection, isolation and reconfiguration methods. IEEE Transactions of Control Systems Technology, 2010, 18(3):636–653.
[4] CARULLI A, VICINO A. Set membership localization of mobile robots via angle measurements. IEEE Transactions on Robotics and Automation, 2001, 17(4):450–463.
[5] ZHOU Bo, HAN Jianda. A UD factorization-based adaptive extended set-membership filter. Acta Automatica Sinica, 2008, 34(2):150–158.(周波,韩建达.基于UD分解的自适应扩展集员估计方法.自动化学报, 2008, 34(2):150–158.)
[6] SONG Dalei, WU Chong, QI Juntong, et al. A MIT-based nonlinear adaptive set-membership filter for ellipsoidal estimation. Acta Automatica Sinica, 2012, 38(11):1847–1860.(宋大雷,吴冲,齐俊桐,等.基于MIT规则的自适应扩展集员估计方法.自动化学报, 2012, 38(11):1847–1860.)
[7] ZHOU Bo, QIAN Kun, MA Xudong, et al. A new nonlinear set membership filter based on guaranteed bounding ellipsoid algorithm. Acta Automatica Sinica, 2013, 39(2):150–158.(周波,钱堃,马旭东,等.一种新的基于保证定界椭球算法的非线性集员滤波器.自动化学报, 2013, 39(2):150–158.
[8] SCOTT J K, RAIMONDO D M, MARSEGLIA G R, et al. Constrained zonotopes:a new tool for set-based estimation and fault detection. Automatica, 2016, 69:126–136.
[9] ALAMO T, BRAVO J M, CAMACHO E F. Guaranteed state estimation by zonotopes. Automatica, 2005, 41(6):1035–1043.
[10] COMBASTEL C. A state bounding observer for uncertain non-linear continuous-time systems based on zonotopes. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference. Seville:IEEE, 2005:7228–7234.
[11] LE V T H, STOICA C, ALAMO T, et al. Zonotope-based setmembership estimation for multi-output uncertain systems. Proceedings of the 2013 IEEE International Symposium on Intelligent Control. Hyderabad:IEEE, 2013:212–217.
[12] COMBASTEL C. Merging Kalman filtering and zonotopic state bounding for robust fault detection under noisy environment. International Federation of Automatic Control, 2015, 48(21):289–295.
[13] COMBASTEL C. An extended zonotopic and Gaussian Kalman filter(EZGKF)merging set-membership and stochastic paradigms:toward non-linear filtering and fault detection. Annual Reviews in Control,2016, 42:232–243.
[14] PUIG V, CUGUERO P, QUEVEDO J. Worst-case state estimation and simulation of uncertain discrete-time systems using zonotopes.Proceedings of the European Control Conference 2001. Porto:IEEE,2001:1691–1697.
[15] LE V T H, STOICA C, ALAMO T, et al. Zonotopic guaranteed state estimation for uncertain systems. Automatica, 2013, 49(11):3418–3424.
[16] Xu F, PUIG V, OCAMPO–MARTINEZ C, et al. Actuator-fault detection and isolation based on settheoretic approaches. Journal of Process Control, 2014, 24(6):947–956.
[17] TANG Wentao, WANG Zhenhua, WANG Ye, et al. Fault diagnosis for uncertain systems based on unknown input set-membership filters. Acta Automatica Sinica, DOI:10.26383/j.aas.2018.c170123.(汤文涛,王振华,王烨,等.基于未知输入集员滤波器的不确定系统故障诊断.自动化学报, DOI:10.26383/j.aas.2018.c170123.)
[18] WANG Z, RODRIGUES M, THEILLIOL D, et al. Actuator fault estimation observer design for discrete-time linear parameter-varying descriptor systems. International Journal of Adaptive Control and Signal Processing, 2015, 29(2):242–258.
[19] Xu S, LAM J. Robust Control and Filtering of Singular Systems.Berlin:Springer, 2006.
[20] BOYD S, EL GHAOUI L, FERON E, et al. Linear Matrix Inequalities in System and Control Theory. New York:SIAM, 1994.
[21] COMBASTEL C. Zonotopes and Kalman observers:gain optimality under distinct uncertainty paradigms and robust convergence. Automatica, 2015, 55:265–273.
[22] ALAMO T, BRAVO J M, CAMACHO E F. Guaranteed state estimation by zonotopes. Automatica, 2005, 41(6):1035–1043.
[23] JOHANSSON K H. The quadruple-tank process:a multivariable laboratory process with an adjustable zero. IEEE Transactions on Control Systems Technology, 2000, 8(3):456–465.
[24] GUO S, ZHU F, ZHU S, et al. State and sensor fault interval estimations for discrete-time systems. Proceedings of the 36th Chinese Control Conference. Dalian:IEEE, 2017:7280–7284.
[25] GUO Shenghui, ZHU Fanglai. Actuator fault detection based on interval observers. Control and Decision. 2016, 31(6):1118–1122.(郭胜辉,朱芳来.基于区间观测器的执行器故障检测.控制与决策,2016, 31(6):1118–1122.)