A novel control scheme of active disturbance rejection internal model control(ADRIMC) is proposed to improve the anti-interference ability and robustness for the dead-time process. The active anti-interference concept...A novel control scheme of active disturbance rejection internal model control(ADRIMC) is proposed to improve the anti-interference ability and robustness for the dead-time process. The active anti-interference concept is introduced into the internal model control(IMC) by analyzing the relationship between IMC and disturbance observer control(DOB). Further, a design process of disturbance filter is presented to realize the active anti-interference ability for ADRIMC scheme. The disturbance filter is used to estimate an equivalent disturbance consisting of both external disturbances and internal disturbances caused by model mismatches.Simulation results demonstrate that the proposed method possesses a good disturbance rejection performance, though losing some partial dynamic performance. In other words, the proposed method shows a tradeoff between the dynamic performance and the system robust.展开更多
Objective To evaluate the efficacy and safety of Huanglian Wendan Decoction(黄连温胆汤,HLWDD)alone or combined with western medicine in treating insomnia caused by phlegm-heat internal disturbance in recent 10 years.M...Objective To evaluate the efficacy and safety of Huanglian Wendan Decoction(黄连温胆汤,HLWDD)alone or combined with western medicine in treating insomnia caused by phlegm-heat internal disturbance in recent 10 years.Methods The randomized controlled trials of HLWDD alone or combined with western medicine in treating insomnia caused by phlegm-heat internal disturbance from January 1,2012 to April 1,2022 were searched in China National Knowledge Infrastructure(CNKI),China Science and Technology Journal Database(VIP),Wanfang Database,China BioMedical Literature Database(CBM),PubMed,Web of Science,Embase,and Cochrane Library databases.After being screening,the included literature was analyzed to evaluate the effective rate,Pittsburgh Sleep Quality Index(PSQI)score,traditional Chinese medicine(TCM)syndrome score,and adverse reactions of HLWDD on insomnia caused by phlegm-heat internal disturbance.The subgroup analyzed the effect of HLWDD after different treatment courses,and compared the therapeutic effects of HLWDD alone and HLWDD combined with western medicine.Results Twenty-seven randomized controlled trials were finally included,with a total of 2395 patients.The results of the meta-analysis showed that the curative effect of HLWDD alone or combined with the western medicine group was better than that of the western medicine group[RR=1.14,95%CI(1.06,1.22),P=0.000].The PSQI score[SMD=-0.31,95%CI(-0.42,-0.20),P=0.000],TCM syndrome score[SMD=-0.40,95%CI(-0.67,-0.12),P=0.005],and adverse reaction rate[RR=0.21,95%CI(0.15,0.29),P=0.000]of HLWDD alone or combined with western medicine group were significantly reduced compared with the western medicine group.The subgroup’s analysis showed that the curative effect of HLWDD alone or combined with western medicine group of 4 weeks treatment course was better than that of the western medicine group[RR=1.14,95%CI(1.03,1.26),P<0.05].The TCM syndrome score of HLWDD alone or combined with the western medicine group of 4 weeks treatment course decreased more obviously than that of the western medicine group[SMD=-0.60,95%CI(-0.96,-0.25),P<0.05].There were no significant differences between HLWDD alone or combined with western medicine group and western medicine group with different treatment courses based on PSQI score and adverse reaction rate.Based on the effective rate,the comparison between the HLWDD alone group and the western medicine group[RR=1.09,95%CI(1.00,-1.20)P<0.05],and between the HLWDD combined with western medicine group and the western medicine group[RR=1.15,95%CI(1.03,1.29),P<0.05]was the same.PSQI score[SMD=-0.44,95%CI(-0.59,-0.30),P<0.05]and TCM syndrome score[SMD=-1.10,95%CI(-1.59,-0.61),P<0.05]of HLWDD combined with western medicine group were significantly lower than those of the western medicine group.There were no significant differences of adverse reaction rate between HLWDD alone group[RR=0.08,95%CI(0.04,0.17),P<0.05]and HLWDD combined with western medicine group[RR=0.36,95%CI(0.24,0.53),P<0.05].Conclusion HLWDD alone or combined with western medicine is an effective treatment for insomnia caused by phlegm-heat internal disturbance,which has a high effective rate,significantly reduced PSQI score and TCM syndrome score,and favorable safety.The best course of treatment is 4 weeks.展开更多
In this paper,a multi-loop internal model control(IMC) scheme in conjunction with feed-forward strategy based on the dynamic partial least squares(DyPLS) framework is proposed.Unlike the traditional methods to decoupl...In this paper,a multi-loop internal model control(IMC) scheme in conjunction with feed-forward strategy based on the dynamic partial least squares(DyPLS) framework is proposed.Unlike the traditional methods to decouple multi-input multi-output(MIMO) systems,the DyPLS framework automatically decomposes the MIMO process into a multi-loop system in the PLS subspace in the modeling stage.The dynamic filters with identical structure are used to build the dynamic PLS model,which retains the orthogonality among the latent variables.To address the model mismatch problem,an off-line least squares method is applied to obtain a set of optimal filter parameters in each latent space.Without losing the merits of model-based control,a simple and easy-tuned IMC structure is readily carried over to the dynamic PLS control framework.In addition,by projecting the measurable disturbance into the latent subspace,a multi-loop feed-forward control is yielded to achieve better performance for disturbance rejection.Simulation results of a distillation column are used to further demonstrate this new strategy outperforms conventional control schemes in servo behavior and disturbance rejection.展开更多
Because of vehicle's external disturbances and model uncertainties,robust control algorithms have obtained popularity in vehicle stability control.The robust control usually gives up performance in order to guarantee...Because of vehicle's external disturbances and model uncertainties,robust control algorithms have obtained popularity in vehicle stability control.The robust control usually gives up performance in order to guarantee the robustness of the control algorithm,therefore an improved robust internal model control(IMC) algorithm blending model tracking and internal model control is put forward for active steering system in order to reach high performance of yaw rate tracking with certain robustness.The proposed algorithm inherits the good model tracking ability of the IMC control and guarantees robustness to model uncertainties.In order to separate the design process of model tracking from the robustness design process,the improved 2 degree of freedom(DOF) robust internal model controller structure is given from the standard Youla parameterization.Simulations of double lane change maneuver and those of crosswind disturbances are conducted for evaluating the robust control algorithm,on the basis of a nonlinear vehicle simulation model with a magic tyre model.Results show that the established 2-DOF robust IMC method has better model tracking ability and a guaranteed level of robustness and robust performance,which can enhance the vehicle stability and handling,regardless of variations of the vehicle model parameters and the external crosswind interferences.Contradiction between performance and robustness of active steering control algorithm is solved and higher control performance with certain robustness to model uncertainties is obtained.展开更多
An adaptive internal mode control is proposed to eliminate effectively periodic disturbance with uncertain frequency caused by input error angle of PIGA (Pendulous Integrating Gyro Accelerometer). An adaptive algori...An adaptive internal mode control is proposed to eliminate effectively periodic disturbance with uncertain frequency caused by input error angle of PIGA (Pendulous Integrating Gyro Accelerometer). An adaptive algorithm with periodic disturbance frequency identification on line is applied and the internal model controller parameters are adjusted to eliminate disturbance. Then the convergence of this algorithm and the stability of the system are proved by the averaging method. Simulation results verify the proposed scheme can eliminate periodic disturbance and improve the test precision for PIGA effectively.展开更多
Currently most of control methods are of one degree of freedom(1-DOF) control structure for the robot systems which are affected by unmeasurable harmonic disturbances,at the same time in order to obtain perfect dist...Currently most of control methods are of one degree of freedom(1-DOF) control structure for the robot systems which are affected by unmeasurable harmonic disturbances,at the same time in order to obtain perfect disturbance attenuation level,the controller gain must be increased.In practice,however,for robotic actuators,there are physical constraints that limit the amplitude of the available torques.This paper considers the problem of tracking control under input constraints for robot manipulators which are affected by unmeasurable harmonic disturbances.A new control scheme is proposed for the problem,which is composed of a parameter-dependent nonlinear observer and a tracking controller.The parameter-dependent nonlinear observer,designed based on the internal model principle,can achieve an estimation and compensation of a class of harmonic disturbances with unknown frequencies.The tracking controller,designed via adaptive control techniques,can make the systems asymptotically track the desired trajectories.In the control design,the continuous piecewise differentiable increasing function is used to limit control input amplitude,such that the control input saturation is avoided.The Lyapunov stability of closed loop systems is analyzed.To validate proposed control scheme,simulation results are provided for a two link horizontal robot manipulator.The simulation results show that the proposed control scheme ensures asymptotic tracking in presence of an uncertain external disturbance acting on the system.An important feature of the methodology consists of the fact that the designed controller is of 2-DOF control structure,namely,it has the ability to overcome the conflict between controller gain and robustness against external disturbances in the traditional 1 -DOF control structure framework.展开更多
The problem of almost disturbance decoupling (ADD) with internal stability is discussed, for a class of high_order cascade nonlinear systems having zero dynamics. Using adding power integrator techniques, the ADD prob...The problem of almost disturbance decoupling (ADD) with internal stability is discussed, for a class of high_order cascade nonlinear systems having zero dynamics. Using adding power integrator techniques, the ADD problems via a smooth static state feedback is solved.展开更多
According to the Rodrigues parameter and the internal model principle,an adaptive state feedback control law is proposed for a rigid spacecraft with inertia uncertainty and exotic disturbances generated by an unknown ...According to the Rodrigues parameter and the internal model principle,an adaptive state feedback control law is proposed for a rigid spacecraft with inertia uncertainty and exotic disturbances generated by an unknown nonlinear exosystem.The uncertainty of parameters is treated by an adaptive control law.And a new internal model is proposed to estimate the exotic disturbances.By using the Lyapunov analysis method,the control law is designed to ensure that the system's state variables asymptotically converge to stable,and the disturbances can be completely rejected.Finally,numerical simulations are included to demonstrate the performance of the presented controller.展开更多
Resilient motion planning and control,without prior knowledge of disturbances,are crucial to ensure the safe and robust flight of quadrotors.The development of a motion planning and control architecture for quadrotors...Resilient motion planning and control,without prior knowledge of disturbances,are crucial to ensure the safe and robust flight of quadrotors.The development of a motion planning and control architecture for quadrotors,considering both internal and external disturbances(i.e.,motor damages and suspended payloads),is addressed.Firstly,the authors introduce the use of exponential functions to formulate trajectory planning.This choice is driven by its ability to predict thrust responses with minimal computational overhead.Additionally,a reachability analysis is incorporated for error dynamics resulting from multiple disturbances.This analysis sits at the interface between the planner and controller,contributing to the generation of more robust and safe spatial–temporal trajectories.Lastly,the authors employ a cascade controller,with the assistance of internal and external loop observers,to further enhance resilience and compensate the disturbances.The authors’benchmark experiments demonstrate the effectiveness of the proposed strategy in enhancing flight safety,particularly when confronted with motor damages and payload disturbances.展开更多
This paper investigates the problem of global disturbance rejection for a class of switched nonlinear systems where the solvability of the disturbance rejection problem for subsystems is not assumed. The disturbances ...This paper investigates the problem of global disturbance rejection for a class of switched nonlinear systems where the solvability of the disturbance rejection problem for subsystems is not assumed. The disturbances are assumed to be sinusoidal with completely unknown frequencies, phases and amplitudes. First, as an extension of the classic concept of internal model for non-switched systems, a switched internal model is proposed. Second, in order to solve the problem under study, an adaptive control method is established on the basis of the multiple Lyapunov functions method. Also,adaptive state-feedback controllers of subsystems are designed and incorporated with a switching law to asymptotically reject the unknown disturbances. Finally, an example is provided to demonstrate the effectiveness of the proposed design method.展开更多
In this paper,the authors address the attitude regulation problem of uncertain flexible spacecraft with unknown control directions and input disturbances.The major challenges of the problem include the concurrence of ...In this paper,the authors address the attitude regulation problem of uncertain flexible spacecraft with unknown control directions and input disturbances.The major challenges of the problem include the concurrence of the unknown actuation sign and the unknown parameters in both the plant and the external disturbances,along with the impact of vibrations from flexible appendages.To overcome these challenges,the authors transform the conventional mathematical model of a flexible spacecraft to a multivariable strict-feedback normal form and adopt a systematic approach within the framework of nonlinear output regulation.To solve the attitude regulation and disturbance rejection problem,the authors introduce a nonlinear internal model candidate to convert the problem into a stabilization problem for an augmented system.Then,a Nussbaum function-based stabilizer is designed to handle unknown control directions and complete the design.Simulation results are provided to show the effectiveness of the proposed controller.展开更多
基金Project(61273132)supported by the National Natural Foundation of ChinaProject(20110010010)supported by Higher School Specialized Research Fund for the Doctoral Program,China
文摘A novel control scheme of active disturbance rejection internal model control(ADRIMC) is proposed to improve the anti-interference ability and robustness for the dead-time process. The active anti-interference concept is introduced into the internal model control(IMC) by analyzing the relationship between IMC and disturbance observer control(DOB). Further, a design process of disturbance filter is presented to realize the active anti-interference ability for ADRIMC scheme. The disturbance filter is used to estimate an equivalent disturbance consisting of both external disturbances and internal disturbances caused by model mismatches.Simulation results demonstrate that the proposed method possesses a good disturbance rejection performance, though losing some partial dynamic performance. In other words, the proposed method shows a tradeoff between the dynamic performance and the system robust.
基金Basic Research Fund Project of the Central Public Welfare Research Institute of China Academy of Chinese Medical Sciences(Zz13-zd-09).
文摘Objective To evaluate the efficacy and safety of Huanglian Wendan Decoction(黄连温胆汤,HLWDD)alone or combined with western medicine in treating insomnia caused by phlegm-heat internal disturbance in recent 10 years.Methods The randomized controlled trials of HLWDD alone or combined with western medicine in treating insomnia caused by phlegm-heat internal disturbance from January 1,2012 to April 1,2022 were searched in China National Knowledge Infrastructure(CNKI),China Science and Technology Journal Database(VIP),Wanfang Database,China BioMedical Literature Database(CBM),PubMed,Web of Science,Embase,and Cochrane Library databases.After being screening,the included literature was analyzed to evaluate the effective rate,Pittsburgh Sleep Quality Index(PSQI)score,traditional Chinese medicine(TCM)syndrome score,and adverse reactions of HLWDD on insomnia caused by phlegm-heat internal disturbance.The subgroup analyzed the effect of HLWDD after different treatment courses,and compared the therapeutic effects of HLWDD alone and HLWDD combined with western medicine.Results Twenty-seven randomized controlled trials were finally included,with a total of 2395 patients.The results of the meta-analysis showed that the curative effect of HLWDD alone or combined with the western medicine group was better than that of the western medicine group[RR=1.14,95%CI(1.06,1.22),P=0.000].The PSQI score[SMD=-0.31,95%CI(-0.42,-0.20),P=0.000],TCM syndrome score[SMD=-0.40,95%CI(-0.67,-0.12),P=0.005],and adverse reaction rate[RR=0.21,95%CI(0.15,0.29),P=0.000]of HLWDD alone or combined with western medicine group were significantly reduced compared with the western medicine group.The subgroup’s analysis showed that the curative effect of HLWDD alone or combined with western medicine group of 4 weeks treatment course was better than that of the western medicine group[RR=1.14,95%CI(1.03,1.26),P<0.05].The TCM syndrome score of HLWDD alone or combined with the western medicine group of 4 weeks treatment course decreased more obviously than that of the western medicine group[SMD=-0.60,95%CI(-0.96,-0.25),P<0.05].There were no significant differences between HLWDD alone or combined with western medicine group and western medicine group with different treatment courses based on PSQI score and adverse reaction rate.Based on the effective rate,the comparison between the HLWDD alone group and the western medicine group[RR=1.09,95%CI(1.00,-1.20)P<0.05],and between the HLWDD combined with western medicine group and the western medicine group[RR=1.15,95%CI(1.03,1.29),P<0.05]was the same.PSQI score[SMD=-0.44,95%CI(-0.59,-0.30),P<0.05]and TCM syndrome score[SMD=-1.10,95%CI(-1.59,-0.61),P<0.05]of HLWDD combined with western medicine group were significantly lower than those of the western medicine group.There were no significant differences of adverse reaction rate between HLWDD alone group[RR=0.08,95%CI(0.04,0.17),P<0.05]and HLWDD combined with western medicine group[RR=0.36,95%CI(0.24,0.53),P<0.05].Conclusion HLWDD alone or combined with western medicine is an effective treatment for insomnia caused by phlegm-heat internal disturbance,which has a high effective rate,significantly reduced PSQI score and TCM syndrome score,and favorable safety.The best course of treatment is 4 weeks.
基金Supported by the National Natural Science Foundation of China(60574047) the National High Technology Research and Development Program of China(2007AA04Z168 2009AA04Z154) the Research Fund for the Doctoral Program of Higher Education in China(20050335018)
文摘In this paper,a multi-loop internal model control(IMC) scheme in conjunction with feed-forward strategy based on the dynamic partial least squares(DyPLS) framework is proposed.Unlike the traditional methods to decouple multi-input multi-output(MIMO) systems,the DyPLS framework automatically decomposes the MIMO process into a multi-loop system in the PLS subspace in the modeling stage.The dynamic filters with identical structure are used to build the dynamic PLS model,which retains the orthogonality among the latent variables.To address the model mismatch problem,an off-line least squares method is applied to obtain a set of optimal filter parameters in each latent space.Without losing the merits of model-based control,a simple and easy-tuned IMC structure is readily carried over to the dynamic PLS control framework.In addition,by projecting the measurable disturbance into the latent subspace,a multi-loop feed-forward control is yielded to achieve better performance for disturbance rejection.Simulation results of a distillation column are used to further demonstrate this new strategy outperforms conventional control schemes in servo behavior and disturbance rejection.
基金Supported by National Natural Science Foundation of China(Grant No.51375009)PhD Research Foundation of Liaocheng University,China(Grant No.318051523)Tsinghua University Initiative Scientific Research Program,China
文摘Because of vehicle's external disturbances and model uncertainties,robust control algorithms have obtained popularity in vehicle stability control.The robust control usually gives up performance in order to guarantee the robustness of the control algorithm,therefore an improved robust internal model control(IMC) algorithm blending model tracking and internal model control is put forward for active steering system in order to reach high performance of yaw rate tracking with certain robustness.The proposed algorithm inherits the good model tracking ability of the IMC control and guarantees robustness to model uncertainties.In order to separate the design process of model tracking from the robustness design process,the improved 2 degree of freedom(DOF) robust internal model controller structure is given from the standard Youla parameterization.Simulations of double lane change maneuver and those of crosswind disturbances are conducted for evaluating the robust control algorithm,on the basis of a nonlinear vehicle simulation model with a magic tyre model.Results show that the established 2-DOF robust IMC method has better model tracking ability and a guaranteed level of robustness and robust performance,which can enhance the vehicle stability and handling,regardless of variations of the vehicle model parameters and the external crosswind interferences.Contradiction between performance and robustness of active steering control algorithm is solved and higher control performance with certain robustness to model uncertainties is obtained.
文摘An adaptive internal mode control is proposed to eliminate effectively periodic disturbance with uncertain frequency caused by input error angle of PIGA (Pendulous Integrating Gyro Accelerometer). An adaptive algorithm with periodic disturbance frequency identification on line is applied and the internal model controller parameters are adjusted to eliminate disturbance. Then the convergence of this algorithm and the stability of the system are proved by the averaging method. Simulation results verify the proposed scheme can eliminate periodic disturbance and improve the test precision for PIGA effectively.
基金supported by National Natural Science Foundation of China(Grant No.60736022)
文摘Currently most of control methods are of one degree of freedom(1-DOF) control structure for the robot systems which are affected by unmeasurable harmonic disturbances,at the same time in order to obtain perfect disturbance attenuation level,the controller gain must be increased.In practice,however,for robotic actuators,there are physical constraints that limit the amplitude of the available torques.This paper considers the problem of tracking control under input constraints for robot manipulators which are affected by unmeasurable harmonic disturbances.A new control scheme is proposed for the problem,which is composed of a parameter-dependent nonlinear observer and a tracking controller.The parameter-dependent nonlinear observer,designed based on the internal model principle,can achieve an estimation and compensation of a class of harmonic disturbances with unknown frequencies.The tracking controller,designed via adaptive control techniques,can make the systems asymptotically track the desired trajectories.In the control design,the continuous piecewise differentiable increasing function is used to limit control input amplitude,such that the control input saturation is avoided.The Lyapunov stability of closed loop systems is analyzed.To validate proposed control scheme,simulation results are provided for a two link horizontal robot manipulator.The simulation results show that the proposed control scheme ensures asymptotic tracking in presence of an uncertain external disturbance acting on the system.An important feature of the methodology consists of the fact that the designed controller is of 2-DOF control structure,namely,it has the ability to overcome the conflict between controller gain and robustness against external disturbances in the traditional 1 -DOF control structure framework.
文摘The problem of almost disturbance decoupling (ADD) with internal stability is discussed, for a class of high_order cascade nonlinear systems having zero dynamics. Using adding power integrator techniques, the ADD problems via a smooth static state feedback is solved.
基金National Natural Science Foundation of China(No.61663030,No.61663032)Natural Science Foundation of Jiangxi Province,China(No.20142BAB207021)+4 种基金the Innovation Fund Designated for Graduate Students of Jiangxi Province(YC2016-S350)the Foundation of Jiangxi Educational Committee,China(No.GJJ150753)the Open Fund of Key Laboratory of Image Processing and Pattern Recognition of Jiangxi Province,China(Nanchang Hangkong University)(No.TX201404003)Key Laboratory of Nondestructive Testing(Nanchang Hangkong University),Ministry of Education,China(No.ZD29529005)The Twelfth "Sanxiao" College Students Extracurricular Innovation and Entrepreneurship Practice and Training Project of Nanchang Hangkong University,China(No.2017ZD021)
文摘According to the Rodrigues parameter and the internal model principle,an adaptive state feedback control law is proposed for a rigid spacecraft with inertia uncertainty and exotic disturbances generated by an unknown nonlinear exosystem.The uncertainty of parameters is treated by an adaptive control law.And a new internal model is proposed to estimate the exotic disturbances.By using the Lyapunov analysis method,the control law is designed to ensure that the system's state variables asymptotically converge to stable,and the disturbances can be completely rejected.Finally,numerical simulations are included to demonstrate the performance of the presented controller.
基金National Natural Science Foundation of China,Grant/Award Numbers:62303412,62322314China Postdoctoral Science Foundation,Grant/Award Number:2022M722739Natural Science Foundation of Zhejiang Province,Grant/Award Number:2023YZ01。
文摘Resilient motion planning and control,without prior knowledge of disturbances,are crucial to ensure the safe and robust flight of quadrotors.The development of a motion planning and control architecture for quadrotors,considering both internal and external disturbances(i.e.,motor damages and suspended payloads),is addressed.Firstly,the authors introduce the use of exponential functions to formulate trajectory planning.This choice is driven by its ability to predict thrust responses with minimal computational overhead.Additionally,a reachability analysis is incorporated for error dynamics resulting from multiple disturbances.This analysis sits at the interface between the planner and controller,contributing to the generation of more robust and safe spatial–temporal trajectories.Lastly,the authors employ a cascade controller,with the assistance of internal and external loop observers,to further enhance resilience and compensate the disturbances.The authors’benchmark experiments demonstrate the effectiveness of the proposed strategy in enhancing flight safety,particularly when confronted with motor damages and payload disturbances.
基金supported by the National Natural Science Foundation of China under Grant Nos.61773100 and 61773098IAPI Fundamental Research Funds under Grant No.2013ZCX03-02Fundamental Research Funds for the Central Universities under Grant No.N150404024
文摘This paper investigates the problem of global disturbance rejection for a class of switched nonlinear systems where the solvability of the disturbance rejection problem for subsystems is not assumed. The disturbances are assumed to be sinusoidal with completely unknown frequencies, phases and amplitudes. First, as an extension of the classic concept of internal model for non-switched systems, a switched internal model is proposed. Second, in order to solve the problem under study, an adaptive control method is established on the basis of the multiple Lyapunov functions method. Also,adaptive state-feedback controllers of subsystems are designed and incorporated with a switching law to asymptotically reject the unknown disturbances. Finally, an example is provided to demonstrate the effectiveness of the proposed design method.
基金supported by the National Natural Science Foundation of China under Grant No.62073168。
文摘In this paper,the authors address the attitude regulation problem of uncertain flexible spacecraft with unknown control directions and input disturbances.The major challenges of the problem include the concurrence of the unknown actuation sign and the unknown parameters in both the plant and the external disturbances,along with the impact of vibrations from flexible appendages.To overcome these challenges,the authors transform the conventional mathematical model of a flexible spacecraft to a multivariable strict-feedback normal form and adopt a systematic approach within the framework of nonlinear output regulation.To solve the attitude regulation and disturbance rejection problem,the authors introduce a nonlinear internal model candidate to convert the problem into a stabilization problem for an augmented system.Then,a Nussbaum function-based stabilizer is designed to handle unknown control directions and complete the design.Simulation results are provided to show the effectiveness of the proposed controller.