一体化执行器饱和线性矩阵不等式跟踪容错控制器设计
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摘要
针对一类执行器幅值饱和的不确定非线性系统,提出了基于线性矩阵不等式的一体化主动容错控制器设计方法.考虑执行器传感器同时故障情形,采用系统增维方法,将原系统等效转化为仅含执行器故障虚拟系统,简化了容错控制器设计.其次采用凸组合法对执行器饱和非线性进行描述,确保控制输入始终在幅值范围以内.在此基础上,设计了集自适应估计律与控制器于一体的主动容错控制器,并将控制器增益解算方法,转化线性矩阵不等式约束下的优化问题.最后通过飞机数值算例验证了设计方法的有效性.
The scheme of integrated active fault tolerant controller by linear matrix inequality(LMI) is proposed in this paper, which is used for the uncertain nonlinear system with actuator saturation. Firstly the case that both actuator and sensor faults exist simultaneously is considered, the expanding dimensions is introduced to the new system, and the original system is transformed to the virtual system which only contains the actuator faults, thus it will be more convenient for the controller design. Then the nonlinearity of actuator saturation is described by the convex composing method, and this will make the control input avoid the saturation. Meanwhile an active fault tolerant controller with adaptive estimated algorithm is designed, and the calculating algorithm is provided under LMI constraints. Finally an airplane example is given to demonstrate the effectiveness of the algorithm.
The scheme of integrated active fault tolerant controller by linear matrix inequality(LMI) is proposed in this paper, which is used for the uncertain nonlinear system with actuator saturation. Firstly the case that both actuator and sensor faults exist simultaneously is considered, the expanding dimensions is introduced to the new system, and the original system is transformed to the virtual system which only contains the actuator faults, thus it will be more convenient for the controller design. Then the nonlinearity of actuator saturation is described by the convex composing method, and this will make the control input avoid the saturation. Meanwhile an active fault tolerant controller with adaptive estimated algorithm is designed, and the calculating algorithm is provided under LMI constraints. Finally an airplane example is given to demonstrate the effectiveness of the algorithm.
引文
[1]FAN J H,ZHENG Z Q.Fault-tolerant control for output tracking systems subject to actuator saturation and constant disturbances:an L-MI approach.AIAA Guidance,Navigation,and Control Conference.Portland,Oregon:AIAA,2011:1-15.
[2]HU Qinglei,ZHANG Aihua,LI Bo.Adaptive variable structure fault tolerant control of rigid spacecraft under thruster faults.Acta Aeronautica ET Astronautica Sinica,2013,34(4):909-918.(胡庆雷,张爱华,李波.推力器故障的刚体航天器自适应变结构容错控制.航空学报,2013,34(4):909-918.)
[3]HUO Xing,HU Qinglei,XIAO Bing,et al.Variable structure fault tolerant attitude control for flexible satellite with input saturation.Control Theory&Applications,2011,28(9):1063-1068.(霍星,胡庆雷,肖冰,等.带有饱和受限的挠性卫星变结构姿态容错控制.控制理论与应用,2011,28(9):1063-1068.)
[4]XIAO B,HU Q L,ZHANG Y M.Adaptive sliding mode fault tolerant attitude tracking control for flexible spacecraft under actuator saturation.IEEE Transaction on Control Systems Technology,2012,20(6):1605-1612.
[5]ZUO Z Q,HO D W C,WANG Y J.Fault tolerant control for singular systems with actuator saturation and nonlinear perturbation.Automatica,2010,46(3):569-576.
[6]LIU Cong,LI Yinghui,ZHU Xihua,et al.The adaptive sliding mode observer for the actuator fault reconstruction of nonlinear system with mismatched uncertainties.Control Theory&Applications,2014,31(4):431-437.(刘聪,李颖晖,朱喜华,等.基于自适应滑模观测器的不匹配非线性系统执行器故障重构.控制理论与应用,2014,31(4):431-437.)
[7]LIU Cong,LI Yinghui,WU Chen,et al.Design of the robust adaptive sliding mode observer for multiple fault reconstruction.Control and Decision,2016,31(7):1219-1224.(刘聪,李颖晖,吴辰,等.基于鲁棒自适应滑模观测器的多故障重构.控制与决策,2016,31(7):1219-1224.)
[8]LIU Cong,LI Yinghui.Design of high gain observers with sliding m ode for the actuator robust fault detection of nonlinear system.Systems Engineering and Electronics,2014,36(8):1626-1631.(刘聪,李颖晖.基于高增益滑模观测器的非线性系统执行器鲁棒故障检测.系统工程与电子技术,2014,36(8):1626-1631.)
[9]LIU Cong,LI Yinghui,LIU Yongzhi,et al.Unknown actuator fault reconstruction based on the high order terminal sliding mode observer.Journal of Xi’an Jiaotong University,2015,49(9):126-133.(刘聪,李颖晖,刘勇智,等.采用高阶终端滑模观测器的执行器未知故障重构.西安交通大学学报,2015,49(9):126-133.)
[10]FAN Jinhua.Actuator fault-tolerant control against saturation.Changsha:National University of Defense Technology,2013.(范金华.针对执行器故障的抗饱和容错控制方法研究.长沙:国防科学技术大学,2013.)
[11]CAO Huichao,LI Wei.Non-fragile robust fault-tolerant control for uncertain NCS with actuator saturation.Control and Decision,2013,28(12):1874-1883.(曹慧超,李炜.执行器饱和不确定NCS非脆弱鲁棒容错控制.控制与决策,2013,28(12):1874-1883.)
[12]FORSSELL L,NILSSON U.ADMIRE the aero-data model in a research environment version 4.0,model description:FOI-R-1624-SE.Sweden:Swedish Defence Agency,2005:25-34.
[2]HU Qinglei,ZHANG Aihua,LI Bo.Adaptive variable structure fault tolerant control of rigid spacecraft under thruster faults.Acta Aeronautica ET Astronautica Sinica,2013,34(4):909-918.(胡庆雷,张爱华,李波.推力器故障的刚体航天器自适应变结构容错控制.航空学报,2013,34(4):909-918.)
[3]HUO Xing,HU Qinglei,XIAO Bing,et al.Variable structure fault tolerant attitude control for flexible satellite with input saturation.Control Theory&Applications,2011,28(9):1063-1068.(霍星,胡庆雷,肖冰,等.带有饱和受限的挠性卫星变结构姿态容错控制.控制理论与应用,2011,28(9):1063-1068.)
[4]XIAO B,HU Q L,ZHANG Y M.Adaptive sliding mode fault tolerant attitude tracking control for flexible spacecraft under actuator saturation.IEEE Transaction on Control Systems Technology,2012,20(6):1605-1612.
[5]ZUO Z Q,HO D W C,WANG Y J.Fault tolerant control for singular systems with actuator saturation and nonlinear perturbation.Automatica,2010,46(3):569-576.
[6]LIU Cong,LI Yinghui,ZHU Xihua,et al.The adaptive sliding mode observer for the actuator fault reconstruction of nonlinear system with mismatched uncertainties.Control Theory&Applications,2014,31(4):431-437.(刘聪,李颖晖,朱喜华,等.基于自适应滑模观测器的不匹配非线性系统执行器故障重构.控制理论与应用,2014,31(4):431-437.)
[7]LIU Cong,LI Yinghui,WU Chen,et al.Design of the robust adaptive sliding mode observer for multiple fault reconstruction.Control and Decision,2016,31(7):1219-1224.(刘聪,李颖晖,吴辰,等.基于鲁棒自适应滑模观测器的多故障重构.控制与决策,2016,31(7):1219-1224.)
[8]LIU Cong,LI Yinghui.Design of high gain observers with sliding m ode for the actuator robust fault detection of nonlinear system.Systems Engineering and Electronics,2014,36(8):1626-1631.(刘聪,李颖晖.基于高增益滑模观测器的非线性系统执行器鲁棒故障检测.系统工程与电子技术,2014,36(8):1626-1631.)
[9]LIU Cong,LI Yinghui,LIU Yongzhi,et al.Unknown actuator fault reconstruction based on the high order terminal sliding mode observer.Journal of Xi’an Jiaotong University,2015,49(9):126-133.(刘聪,李颖晖,刘勇智,等.采用高阶终端滑模观测器的执行器未知故障重构.西安交通大学学报,2015,49(9):126-133.)
[10]FAN Jinhua.Actuator fault-tolerant control against saturation.Changsha:National University of Defense Technology,2013.(范金华.针对执行器故障的抗饱和容错控制方法研究.长沙:国防科学技术大学,2013.)
[11]CAO Huichao,LI Wei.Non-fragile robust fault-tolerant control for uncertain NCS with actuator saturation.Control and Decision,2013,28(12):1874-1883.(曹慧超,李炜.执行器饱和不确定NCS非脆弱鲁棒容错控制.控制与决策,2013,28(12):1874-1883.)
[12]FORSSELL L,NILSSON U.ADMIRE the aero-data model in a research environment version 4.0,model description:FOI-R-1624-SE.Sweden:Swedish Defence Agency,2005:25-34.
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