To better understand dragonflies’remarkable flapping wing aerodynamic performance,we measured the kinematic parameters of the wings in two different flight modes(Normal Flight Mode(NFM)and Escape Flight Mode(EFM)).Wh...To better understand dragonflies’remarkable flapping wing aerodynamic performance,we measured the kinematic parameters of the wings in two different flight modes(Normal Flight Mode(NFM)and Escape Flight Mode(EFM)).When the specimens switched from normal to escape mode the flapping frequency was invariant,but the stroke plane of the wings was more horizontally inclined.The flapping of both wings was adjusted to be more ventral with a change of the pitching angle that resulted in a larger angle of attack during downstroke and smaller during upstroke to affect the flow directions and the added mass effect.Noticeably,the phasing between the fore and hind pair of wings varies between two flight modes,which affects the wing-wing interaction as well as body oscillations.It is found that the momentum stream in the wake of EFM is qualitatively different from that in NFM.The change of the stroke plane angle and the varied pitching angle of the wings diverts the momentum downwards,while the smaller flapping amplitude and less phase difference between the wings compresses the momentum stream.It seems that in order to achieve greater flight maneuverability a flight vehicle needs to actively control positional angle as well as the pitching angle of the flapping wings.展开更多
As an attractive transition approach,the altitude-hold transition is a special type of super-maneuvering and the vertical/horizontal flight mode transition that an agile aircraft conducts at fixed altitude.However,it ...As an attractive transition approach,the altitude-hold transition is a special type of super-maneuvering and the vertical/horizontal flight mode transition that an agile aircraft conducts at fixed altitude.However,it is still challenging to implement an autonomous control of the altitude-hold transition while the existing optimal transition planning methods cannot avoid an evident altitude change during the transition process.This paper proposes a corridor-based flight mode transition strategy and presents a successful flight demonstration of the altitude-hold transition on a small ducted-fan tail-sitter unmanned aerial vehicle.In the proposed corridor-based methodology,we model and analyze the transition corridor,concentrate on the dynamic characteristics of the altitude-hold transition,and emphasize that a valid transition trajectory should be governed by its transition corridor.The identified transition corridor reveals that for a given velocity trajectory,the solution for the corresponding trajectories of pitch angle and thrust is unique.Based on this,the transition trajectory generation problem is addressed simply on the velocity-acceleration plane.Furthermore,a proper flight control scheme is devised to track the generated transition trajectories.Finally,the effectiveness of the proposed method is verified through practical flight tests,in which the altitude change is less than 1.1 m during the entire transition course.展开更多
Flight simulator is an important device and a typical high-performance position and speed servo system used in the hardware-in-the-loop simulation of flight control system. Friction is the main nonlinear resistance in...Flight simulator is an important device and a typical high-performance position and speed servo system used in the hardware-in-the-loop simulation of flight control system. Friction is the main nonlinear resistance in the flight simulator servo system, especially in a low-speed state. Based on the description of dynamic and static models of a nonlinear Stribeck friction model, this paper puts forward sliding mode controller to overcome the friction, whose stability is展开更多
The dynamic flight stability of a model dronefly in hovering and upward flight is studied.The method of computational fluid dynamics is used to compute the stability derivatives and the techniques of eigenvalue and ei...The dynamic flight stability of a model dronefly in hovering and upward flight is studied.The method of computational fluid dynamics is used to compute the stability derivatives and the techniques of eigenvalue and eigenvector used to solve the equations of motion.The major finding is as following.Hovering flight of the model dronefly is unstable because of the existence of an unstable longitudinal and an unstable lateral natural mode of motion.Upward flight of the insect is also unstable,and the instability increases as the upward flight speed increases.Inertial force generated by the upward flight velocity coupled with the disturbance in pitching angular velocity is responsible for the enhancement of the instability.展开更多
The lateral dynamic flight stability of a hovering model insect （dronefly） was studied using the method of computational fluid dynamics to compute the stability derivatives and the techniques of eigenvalue and eigen...The lateral dynamic flight stability of a hovering model insect （dronefly） was studied using the method of computational fluid dynamics to compute the stability derivatives and the techniques of eigenvalue and eigenvector analysis for solving the equations of motion. The main results are as following. （i） Three natural modes of motion were identified： one unstable slow divergence mode （mode 1）, one stable slow oscillatory mode （mode 2）, and one stable fast subsidence mode （mode 3）. Modes 1 and 2 mainly consist of a rotation about the horizontal longitudinal axis （x-axis） and a side translation; mode 3 mainly consists of a rotation about the x-axis and a rotation about the vertical axis. （ii） Approximate analytical expressions of the eigenvalues are derived, which give physical insight into the genesis of the natural modes of motion. （iii） For the unstable divergence mode, td, the time for initial disturbances to double, is about 9 times the wingbeat period （the longitudinal motion of the model insect was shown to be also unstable and td of the longitudinal unstable mode is about 14 times the wingbeat period）. Thus, although the flight is not dynamically stable, the instability does not grow very fast and the insect has enough time to control its wing motion to suppress the disturbances.展开更多
To alleviate the chattering problem, a new type of fuzzy global sliding mode controller （FGSMC） is presented. In this controller, the switching gain is estimated by fuzzy logic system based on the reachable conditio...To alleviate the chattering problem, a new type of fuzzy global sliding mode controller （FGSMC） is presented. In this controller, the switching gain is estimated by fuzzy logic system based on the reachable conditions of sliding mode controller（SMC）, and genetic algorithm （GA） is used to optimize scaling factor of the switching gain, thus the switch chattering of SMC can be alleviated. Moreover, global sliding mode is realized by designing an exponential dynamic sliding surface. Simulation and real-time application for flight simulator servo system with Lugre friction are given to indicate that the proposed controller can guarantee high robust performance all the time and can alleviate chattering phenomenon effectively.展开更多
Based on nominal model, a novel global sliding mode controller （GSMC） with a new control scheme is proposed for a practical uncertain servo system. This control scheme consists of two combined controllers, One is th...Based on nominal model, a novel global sliding mode controller （GSMC） with a new control scheme is proposed for a practical uncertain servo system. This control scheme consists of two combined controllers, One is the global sliding mode controller for practical plant, the other is the integral backstepping controller for nominal model. Modeling error between practical plant and nominal model is used to design GSMC. The steady-state control accuracy can be guaranteed by the integral backstepping control law, and the global robustness can be obtained by GSMC. The stability of the proposed controller is proved according to the Lyapunov approach. The simulation results both of sine signal and step signal tracking for 3-axis flight table are investigated to show good position tracking performance and high robustness with respect to large and parameter changes over all the response time.展开更多
在民机自动飞行过程中,飞行导引系统的模式转换是影响安全的重要因素,应对其进行充分的安全性分析。传统安全分析方法主要关注各个组件的失效因素,忽略了由组件间非线性交互产生的安全问题。为此,采用系统理论过程分析(System Theory Pr...在民机自动飞行过程中,飞行导引系统的模式转换是影响安全的重要因素,应对其进行充分的安全性分析。传统安全分析方法主要关注各个组件的失效因素,忽略了由组件间非线性交互产生的安全问题。为此,采用系统理论过程分析(System Theory Process Analysis,STPA)方法,对飞行导引系统模式转换进行系统且完整的分析。同时,鉴于STPA方法中存在需人工分析的部分,引入了基于时间自动机理论的形式化模型检查工具UPPAAL对系统进行建模与验证,以确保控制结构图的正确性,并识别真正不安全控制行为(Unsafe Control Action,UCA),从而避免资源的浪费。最后,提出规范化的致因因素分析框架对通过验证的UCA进行逐一分析。实例证明,所提方法对航空类复杂系统安全性分析具有较好的效果。展开更多
This article proposes a novel approach combining exponential-reaching-law-based equivalent control law with radial basis function (RBF) network-based switching law to strengthen the sliding mode control (SMC) tracking...This article proposes a novel approach combining exponential-reaching-law-based equivalent control law with radial basis function (RBF) network-based switching law to strengthen the sliding mode control (SMC) tracking capacity for systems with uncertainties and disturbances. First, SMC discrete equivalent control law is designed on the basis of the nominal model of the system and the adaptive exponential reaching law, and subsequently, stability of the algorithm is analyzed. Second, RBF network is used to f...展开更多
The longitudinal dynamic flight stability of a bumblebee in forward flight is studied. The method of computational fluid dynamics is used to compute the aerodynamic derivatives and the techniques of eigenvalue and eig...The longitudinal dynamic flight stability of a bumblebee in forward flight is studied. The method of computational fluid dynamics is used to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are employed for solving the equations of motion. The primary findings are as the following. The forward flight of the bumblebee is not dynamically stable due to the existence of one （or two） unstable or approximately neutrally stable natural modes of motion. At hovering to medium flight speed [flight speed Ue = （0-3.5）m s^-1; advance ratio J = 0-0.44], the flight is weakly unstable or approximately neutrally stable; at high speed （Ue = 4.5 m s^-1; J = 0.57）, the flight becomes strongly unstable （initial disturbance double its value in only 3.5 wingbeats）.展开更多
An adaptive fuzzy sliding mode control （AFSMC） ap- proach is proposed for a robotic airship. First, the mathematical model of an airship is derived in the form of a nonlinear control system. Second, an AFSMC approac...An adaptive fuzzy sliding mode control （AFSMC） ap- proach is proposed for a robotic airship. First, the mathematical model of an airship is derived in the form of a nonlinear control system. Second, an AFSMC approach is proposed to design the attitude control system of airship, and the global stability of the closed-loop system is proved by using the Lyapunov stability theorem. Finally, simulation results verify the effectiveness and robustness of the proposed control approach in the presence of model uncertainties and external disturbances.展开更多
The nonlinear aircraft model with heavy cargo moving inside is derived by using the sep- aration body method, which can describe the influence of the moving cargo on the aircraft attitude and altitude accurately. Furt...The nonlinear aircraft model with heavy cargo moving inside is derived by using the sep- aration body method, which can describe the influence of the moving cargo on the aircraft attitude and altitude accurately. Furthermore, the nonlinear system is decoupled and linearized through the input^utput feedback linearization method. On this basis, an iterative quasi-sliding mode （SM） flight controller for speed and pitch angle control is proposed. At the first-level SM, a global dynamic switching function is introduced thus eliminating the reaching phase of the sliding motion. At the second-level SM, a nonlinear function with the property of ＂smaUer errors correspond to bigger gains and bigger errors correspond to saturated gains＂ is designed to form an integral sliding manifold, and the overcompensation of the integral term to big errors is weakened. Lyapunov- based analysis shows that the controller with strong robustness can reject both constant and time-varying model uncertainties. The performance of the proposed control strategy is verified in a maximum load airdrop mission.展开更多
This paper investigates the problem of designing a fast convergent sliding mode flight controller of a transport aircraft for heavyweight airdrop operations in the presence of bounded uncertainties without the prior k...This paper investigates the problem of designing a fast convergent sliding mode flight controller of a transport aircraft for heavyweight airdrop operations in the presence of bounded uncertainties without the prior knowledge of the bounds. On the basis of feedback linearization of the aircraft-cargo motion system, a novel integral sliding mode flight control law with gains adaptation is proposed. It contains a nominal control law used to achieve finite-time stabilization performance and a compensated control law used to reject the uncertainties. The switching gains of the compensated control law are tuned using adaptation algorithms, and the knowledge of the bounds of the uncertainties is not required to be known in advance. Meanwhile, the severe chattering of the sliding mode control that caused by high switching gains is effectively reduced. The controller and its performance are evaluated on a transport aircraft performing a maximum load airdrop task in a number of simulation scenarios.展开更多
This paper proposes a finite-time robust flight controller, targeting for a reentry vehicle with blended aerodynamic surfaces and a reaction control system（RCS）. Firstly, a novel finite-time attitude controller is p...This paper proposes a finite-time robust flight controller, targeting for a reentry vehicle with blended aerodynamic surfaces and a reaction control system（RCS）. Firstly, a novel finite-time attitude controller is pointed out with the introduction of a nonsingular finite-time sliding mode manifold. The attitude tracking errors are mathematically proved to converge to zero within finite time which can be estimated. In order to improve the performance, a second-order finite-time sliding mode controller is further developed to effectively alleviate chattering without any deterioration of robustness and accuracy. Moreover, an optimization control allocation algorithm, using linear programming and a pulse-width pulse-frequency（PWPF） modulator, is designed to allocate torque commands for all the aerodynamic surface deflections and on–off switching-states of RCS thrusters.Simulations are provided for the reentry vehicle considering uncertain parameters and external disturbances for practical purposes, and the results demonstrate the effectiveness and robustness of the attitude control system.展开更多
The nonlinear dynamic model of spinning ballistic missiles is established during the first boosting phase of the missile. Based on the conventional backstepping sliding mode control and the assumption of a two time-sc...The nonlinear dynamic model of spinning ballistic missiles is established during the first boosting phase of the missile. Based on the conventional backstepping sliding mode control and the assumption of a two time-scale separation of missile dynamics, a graded sliding mode controller is designed with two sub-sliding surfaces which have invariability to external disturbances and parameter perturbations, and a matrix which comprises three first order low pass filters is introduced to prevent “explosion of terms”. Owing to the upper bounds of the uncertainties are difficult to obtain in advance, adaptive laws are introduced to estimate the values of the uncertainties in real-time. Eventually, the numerical simulation results given to show the proposed controller can ensure the steady flight of missiles.展开更多
基金This work was supported by the Research Grants Council(RGC)of the Government of the Hong Kong Special Administrative Region(HKSAR)with Project No.16205018.
文摘To better understand dragonflies’remarkable flapping wing aerodynamic performance,we measured the kinematic parameters of the wings in two different flight modes(Normal Flight Mode(NFM)and Escape Flight Mode(EFM)).When the specimens switched from normal to escape mode the flapping frequency was invariant,but the stroke plane of the wings was more horizontally inclined.The flapping of both wings was adjusted to be more ventral with a change of the pitching angle that resulted in a larger angle of attack during downstroke and smaller during upstroke to affect the flow directions and the added mass effect.Noticeably,the phasing between the fore and hind pair of wings varies between two flight modes,which affects the wing-wing interaction as well as body oscillations.It is found that the momentum stream in the wake of EFM is qualitatively different from that in NFM.The change of the stroke plane angle and the varied pitching angle of the wings diverts the momentum downwards,while the smaller flapping amplitude and less phase difference between the wings compresses the momentum stream.It seems that in order to achieve greater flight maneuverability a flight vehicle needs to actively control positional angle as well as the pitching angle of the flapping wings.
基金supported by Scientific Instruments Development Program of National Natural Science Foundation of China(No.61527810)the Fundamental Research Funds for the Central Universities,Chinathe Key Laboratory of Autonomous Systems and Networked Control,Ministry of Education and the Unmanned Aerial Vehicle Systems Engineering Technology Research Center of Guangdong(China)for supporting this research.
文摘As an attractive transition approach,the altitude-hold transition is a special type of super-maneuvering and the vertical/horizontal flight mode transition that an agile aircraft conducts at fixed altitude.However,it is still challenging to implement an autonomous control of the altitude-hold transition while the existing optimal transition planning methods cannot avoid an evident altitude change during the transition process.This paper proposes a corridor-based flight mode transition strategy and presents a successful flight demonstration of the altitude-hold transition on a small ducted-fan tail-sitter unmanned aerial vehicle.In the proposed corridor-based methodology,we model and analyze the transition corridor,concentrate on the dynamic characteristics of the altitude-hold transition,and emphasize that a valid transition trajectory should be governed by its transition corridor.The identified transition corridor reveals that for a given velocity trajectory,the solution for the corresponding trajectories of pitch angle and thrust is unique.Based on this,the transition trajectory generation problem is addressed simply on the velocity-acceleration plane.Furthermore,a proper flight control scheme is devised to track the generated transition trajectories.Finally,the effectiveness of the proposed method is verified through practical flight tests,in which the altitude change is less than 1.1 m during the entire transition course.
基金This project was supported by the Aeronautics Foundation of China (00E21022).
文摘Flight simulator is an important device and a typical high-performance position and speed servo system used in the hardware-in-the-loop simulation of flight control system. Friction is the main nonlinear resistance in the flight simulator servo system, especially in a low-speed state. Based on the description of dynamic and static models of a nonlinear Stribeck friction model, this paper puts forward sliding mode controller to overcome the friction, whose stability is
基金supported by the National Natural Science Foundation of China(11232002)
文摘The dynamic flight stability of a model dronefly in hovering and upward flight is studied.The method of computational fluid dynamics is used to compute the stability derivatives and the techniques of eigenvalue and eigenvector used to solve the equations of motion.The major finding is as following.Hovering flight of the model dronefly is unstable because of the existence of an unstable longitudinal and an unstable lateral natural mode of motion.Upward flight of the insect is also unstable,and the instability increases as the upward flight speed increases.Inertial force generated by the upward flight velocity coupled with the disturbance in pitching angular velocity is responsible for the enhancement of the instability.
基金supported by the National Natural Science Foundation of China(10732030)the 111 Project(B07009)
文摘The lateral dynamic flight stability of a hovering model insect （dronefly） was studied using the method of computational fluid dynamics to compute the stability derivatives and the techniques of eigenvalue and eigenvector analysis for solving the equations of motion. The main results are as following. （i） Three natural modes of motion were identified： one unstable slow divergence mode （mode 1）, one stable slow oscillatory mode （mode 2）, and one stable fast subsidence mode （mode 3）. Modes 1 and 2 mainly consist of a rotation about the horizontal longitudinal axis （x-axis） and a side translation; mode 3 mainly consists of a rotation about the x-axis and a rotation about the vertical axis. （ii） Approximate analytical expressions of the eigenvalues are derived, which give physical insight into the genesis of the natural modes of motion. （iii） For the unstable divergence mode, td, the time for initial disturbances to double, is about 9 times the wingbeat period （the longitudinal motion of the model insect was shown to be also unstable and td of the longitudinal unstable mode is about 14 times the wingbeat period）. Thus, although the flight is not dynamically stable, the instability does not grow very fast and the insect has enough time to control its wing motion to suppress the disturbances.
基金This project is supported by Aeronautics Foundation of China (No. 00E51022)
文摘To alleviate the chattering problem, a new type of fuzzy global sliding mode controller （FGSMC） is presented. In this controller, the switching gain is estimated by fuzzy logic system based on the reachable conditions of sliding mode controller（SMC）, and genetic algorithm （GA） is used to optimize scaling factor of the switching gain, thus the switch chattering of SMC can be alleviated. Moreover, global sliding mode is realized by designing an exponential dynamic sliding surface. Simulation and real-time application for flight simulator servo system with Lugre friction are given to indicate that the proposed controller can guarantee high robust performance all the time and can alleviate chattering phenomenon effectively.
文摘Based on nominal model, a novel global sliding mode controller （GSMC） with a new control scheme is proposed for a practical uncertain servo system. This control scheme consists of two combined controllers, One is the global sliding mode controller for practical plant, the other is the integral backstepping controller for nominal model. Modeling error between practical plant and nominal model is used to design GSMC. The steady-state control accuracy can be guaranteed by the integral backstepping control law, and the global robustness can be obtained by GSMC. The stability of the proposed controller is proved according to the Lyapunov approach. The simulation results both of sine signal and step signal tracking for 3-axis flight table are investigated to show good position tracking performance and high robustness with respect to large and parameter changes over all the response time.
文摘在民机自动飞行过程中,飞行导引系统的模式转换是影响安全的重要因素,应对其进行充分的安全性分析。传统安全分析方法主要关注各个组件的失效因素,忽略了由组件间非线性交互产生的安全问题。为此,采用系统理论过程分析(System Theory Process Analysis,STPA)方法,对飞行导引系统模式转换进行系统且完整的分析。同时,鉴于STPA方法中存在需人工分析的部分,引入了基于时间自动机理论的形式化模型检查工具UPPAAL对系统进行建模与验证,以确保控制结构图的正确性,并识别真正不安全控制行为(Unsafe Control Action,UCA),从而避免资源的浪费。最后,提出规范化的致因因素分析框架对通过验证的UCA进行逐一分析。实例证明,所提方法对航空类复杂系统安全性分析具有较好的效果。
文摘This article proposes a novel approach combining exponential-reaching-law-based equivalent control law with radial basis function (RBF) network-based switching law to strengthen the sliding mode control (SMC) tracking capacity for systems with uncertainties and disturbances. First, SMC discrete equivalent control law is designed on the basis of the nominal model of the system and the adaptive exponential reaching law, and subsequently, stability of the algorithm is analyzed. Second, RBF network is used to f...
基金the National Natural Science Foundation of China (10732030)
文摘The longitudinal dynamic flight stability of a bumblebee in forward flight is studied. The method of computational fluid dynamics is used to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are employed for solving the equations of motion. The primary findings are as the following. The forward flight of the bumblebee is not dynamically stable due to the existence of one （or two） unstable or approximately neutrally stable natural modes of motion. At hovering to medium flight speed [flight speed Ue = （0-3.5）m s^-1; advance ratio J = 0-0.44], the flight is weakly unstable or approximately neutrally stable; at high speed （Ue = 4.5 m s^-1; J = 0.57）, the flight becomes strongly unstable （initial disturbance double its value in only 3.5 wingbeats）.
基金supported by the Hunan Provincial Innovation Foundation for Postgraduate (CX2011B005)the National University of Defense Technlolgy Innovation Foundation for Postgraduate (B110105)
文摘An adaptive fuzzy sliding mode control （AFSMC） ap- proach is proposed for a robotic airship. First, the mathematical model of an airship is derived in the form of a nonlinear control system. Second, an AFSMC approach is proposed to design the attitude control system of airship, and the global stability of the closed-loop system is proved by using the Lyapunov stability theorem. Finally, simulation results verify the effectiveness and robustness of the proposed control approach in the presence of model uncertainties and external disturbances.
基金co-supported by the National Natural Science Foundation of China (No. 60904038)the Aeronautical Science Foundation of China (Nos. 20141396012 and 20121396008)
文摘The nonlinear aircraft model with heavy cargo moving inside is derived by using the sep- aration body method, which can describe the influence of the moving cargo on the aircraft attitude and altitude accurately. Furthermore, the nonlinear system is decoupled and linearized through the input^utput feedback linearization method. On this basis, an iterative quasi-sliding mode （SM） flight controller for speed and pitch angle control is proposed. At the first-level SM, a global dynamic switching function is introduced thus eliminating the reaching phase of the sliding motion. At the second-level SM, a nonlinear function with the property of ＂smaUer errors correspond to bigger gains and bigger errors correspond to saturated gains＂ is designed to form an integral sliding manifold, and the overcompensation of the integral term to big errors is weakened. Lyapunov- based analysis shows that the controller with strong robustness can reject both constant and time-varying model uncertainties. The performance of the proposed control strategy is verified in a maximum load airdrop mission.
基金supported by the National Natural Science Foundation of China(61273141)Aviation Science Foundation of China(20141396012)
文摘This paper investigates the problem of designing a fast convergent sliding mode flight controller of a transport aircraft for heavyweight airdrop operations in the presence of bounded uncertainties without the prior knowledge of the bounds. On the basis of feedback linearization of the aircraft-cargo motion system, a novel integral sliding mode flight control law with gains adaptation is proposed. It contains a nominal control law used to achieve finite-time stabilization performance and a compensated control law used to reject the uncertainties. The switching gains of the compensated control law are tuned using adaptation algorithms, and the knowledge of the bounds of the uncertainties is not required to be known in advance. Meanwhile, the severe chattering of the sliding mode control that caused by high switching gains is effectively reduced. The controller and its performance are evaluated on a transport aircraft performing a maximum load airdrop task in a number of simulation scenarios.
基金co-supported by the National Basic Research Program of China(No.2012CB720000)the National Natural Science Foundation of China(No.61104153)the Research Fund for the Doctoral Program of Higher Education of China(No.20091101110025)
文摘This paper proposes a finite-time robust flight controller, targeting for a reentry vehicle with blended aerodynamic surfaces and a reaction control system（RCS）. Firstly, a novel finite-time attitude controller is pointed out with the introduction of a nonsingular finite-time sliding mode manifold. The attitude tracking errors are mathematically proved to converge to zero within finite time which can be estimated. In order to improve the performance, a second-order finite-time sliding mode controller is further developed to effectively alleviate chattering without any deterioration of robustness and accuracy. Moreover, an optimization control allocation algorithm, using linear programming and a pulse-width pulse-frequency（PWPF） modulator, is designed to allocate torque commands for all the aerodynamic surface deflections and on–off switching-states of RCS thrusters.Simulations are provided for the reentry vehicle considering uncertain parameters and external disturbances for practical purposes, and the results demonstrate the effectiveness and robustness of the attitude control system.
文摘The nonlinear dynamic model of spinning ballistic missiles is established during the first boosting phase of the missile. Based on the conventional backstepping sliding mode control and the assumption of a two time-scale separation of missile dynamics, a graded sliding mode controller is designed with two sub-sliding surfaces which have invariability to external disturbances and parameter perturbations, and a matrix which comprises three first order low pass filters is introduced to prevent “explosion of terms”. Owing to the upper bounds of the uncertainties are difficult to obtain in advance, adaptive laws are introduced to estimate the values of the uncertainties in real-time. Eventually, the numerical simulation results given to show the proposed controller can ensure the steady flight of missiles.
