Rock shed is an effective protection measure against rockfall.To investigate the influences of falling rock’s shape and impact angle on the impact effect of the cushioned rock shed,a modeling approach for a rock shed...Rock shed is an effective protection measure against rockfall.To investigate the influences of falling rock’s shape and impact angle on the impact effect of the cushioned rock shed,a modeling approach for a rock shed with a cushion layer using PFC-FLAC.The granular cushion is modeled as an aggregate of discrete non-cohesion particles,while the concrete plate and the beam are modeled as zones.The falling rock with different sphericities and impact angles is modeled as a rigid assembly.The numerical model is validated by comparing the simulation results with experimental and numerical results from previous literature.This model is applied to analyze the effects of rock shape and impact angle on the dynamic interaction effects between falling rock and cushioned rock shed,including the impact force,transmitted bottom force,penetration depth,and plate deflection.The numerical results show that the variation in the falling rock’s shape has different effects on the falling rock with different impact angles.These findings could support rock shed design by revealing the limitations of the assumptions in the past research,which may result in unsafe rock sheds for some rockfall cases.展开更多
Final velocity and impact angle are critical to missile guidance.Computationally efficient guidance law with compre-hensive consideration of the two performance merits is challeng-ing yet remains less addressed.Theref...Final velocity and impact angle are critical to missile guidance.Computationally efficient guidance law with compre-hensive consideration of the two performance merits is challeng-ing yet remains less addressed.Therefore,this paper seeks to solve a type of optimal control problem that maximizes final velocity subject to equality point constraint of impact angle con-straint.It is proved that the crude problem of maximizing final velocity is equivalent to minimizing a quadratic-form cost of cur-vature.The closed-form guidance law is henceforth derived using optimal control theory.The derived analytical guidance law coincides with the widely-used optimal guidance law with impact angle constraint(OGL-IAC)with a set of navigation parameters of two and six.On this basis,the optimal emission angle is determined to further increase the final velocity.The derived optimal value depends solely on the initial line-of-sight angle and impact angle constraint,and thus practical for real-world appli-cations.The proposed guidance law is validated by numerical simulation.The results show that the OGL-IAC is superior to the benchmark guidance laws both in terms of final velocity and missing distance.展开更多
The terminal guidance problem for an unpowered lifting reentry vehicle against a sta- tionary target is considered. In addition to attacking the target with high accuracy, the vehicle is also expected to achieve a des...The terminal guidance problem for an unpowered lifting reentry vehicle against a sta- tionary target is considered. In addition to attacking the target with high accuracy, the vehicle is also expected to achieve a desired impact angle. In this paper, a sliding mode control （SMC）-based guidance law is developed to satisfy the terminal angle constraint. Firstly, a specific sliding mode function is designed, and the terminal requirements can be achieved by enforcing both the sliding mode function and its derivative to zero at the end of the flight. Then, a backstepping approach is used to ensure the finite-time reaching phase of the sliding mode and the analytic expression of the control effort can be obtained. The trajectories generated by this method only depend on the initial and terminal conditions of the terminal phase and the instantaneous states of the vehicle. In order to test the performance of the proposed guidance law in practical application, numerical simulations are carried out by taking all the aerodynamic parameters into consideration. The effec- tiveness of the proposed guidance law is verified by the simulation results in various scenarios.展开更多
Aimed at the guidance requirements of some missiles which attack targets with terminal impact angle at the terminal point,a new integrated guidance and control design scheme based on variable structure control approac...Aimed at the guidance requirements of some missiles which attack targets with terminal impact angle at the terminal point,a new integrated guidance and control design scheme based on variable structure control approach for missile with terminal impact angle constraint is proposed.First,a mathematical model of an integrated guidance and control model in pitch plane is established,and then nonlinear transformation is employed to transform the mathematical model into a standard form suitable for sliding mode control method design.A sufficient condition for the existence of linear sliding surface is given in terms of linear matrix inequalities（LMIs）,based on which the corresponding reaching motion controller is also developed.To verify the effectiveness of the proposed integrated design scheme,the numerical simulation of missile is made.The simulation results demonstrate that the proposed guidance and control law can guide missile to hit the target with desired impact angle and desired flight attitude angle simultaneously.展开更多
Sliding mode guidance laws based on a conventional terminal sliding mode guarantees only finite-time convergence, which verifies that the settling time is required to be estimated by selecting appropriate initial laun...Sliding mode guidance laws based on a conventional terminal sliding mode guarantees only finite-time convergence, which verifies that the settling time is required to be estimated by selecting appropriate initial launched conditions. However, rapid convergence to a desired impact angle within a uniform bounded finite time is important in most practical guidance applications. A uniformly finite-time/fixed-time convergent guidance law means that the convergence（settling） time is predefined independently on initial conditions, that is, a closed-loop convergence time can be estimated a priori by guidance parameters. In this paper, a novel adaptive fast fixed-time sliding mode guidance law to intercept maneuver targets at a desired impact angle from any initial heading angle,with no problems of singularity and chattering, is designed. The proposed guidance law achieves system stabilization within bounded settling time independent on initial conditions and achieves more rapid convergence than those of fixed-time stable control methods by accelerating the convergence rate when the system is close to the origin. The achieved acceleration-magnitude constraints are rigorously enforced, and the chattering-free property is guaranteed by adaptive switching gains.Extensive numerical simulations are presented to validate the efficiency and superiority of the proposed guidance law for different initial engagement geometries and impact angles.展开更多
An integral sliding mode guidance law(ISMGL)combined with the advantages of the integral sliding mode control(SMC)method is designed to address maneuvering target interception problems with impact angle constraints.Th...An integral sliding mode guidance law(ISMGL)combined with the advantages of the integral sliding mode control(SMC)method is designed to address maneuvering target interception problems with impact angle constraints.The relative motion equation of the missile and the target considering the impact angle constraint is established in the longitudinal plane,and an integral sliding mode surface is constructed.The proposed guidance law resolves the existence of a steady-state error problem in the traditional SMC.Such a guidance law ensures that the missile hits the target with an ideal impact angle in finite time and the missile is kept highly robust throughout the interception process.By adopting the dynamic surface control method,the ISMGL is designed considering the impact angle constraints and the autopilot dynamic characteristics.According to the Lyapunov stability theorem,all states of the closed-loop system are finally proven to be uniformly bounded.Simulation results are compared with the general sliding mode guidance law and the trajectory shaping guidance law,and the findings verify the effectiveness and superiority of the ISMGL.展开更多
The impact angle control over guidance(IACG) law against stationary targets is proposed by using feedback linearization control(FLC) and finite time control(FTC). First, this paper transforms the kinematics equation o...The impact angle control over guidance(IACG) law against stationary targets is proposed by using feedback linearization control(FLC) and finite time control(FTC). First, this paper transforms the kinematics equation of guidance systems into the feedbackable linearization model, in which the guidance law is obtained without considering the impact angle via FLC. For the purpose of the line of sight(LOS) angle and its rate converging to the desired values, the second-order LOS angle is considered as a double-integral system. Then, this paper utilizes FTC to design a controller which can guarantee the states of the double-integral system converging to the desired values. Numerical simulation illustrates the performance of the IACG, in contrast to the existing guidance law.展开更多
The extended optima straints of miss distance and Schwartz inequality. To reduce guidance law with terminal conmpact angle is derived by the terminal acceleration and eliminate gravity disturbance absolutely, the obje...The extended optima straints of miss distance and Schwartz inequality. To reduce guidance law with terminal conmpact angle is derived by the terminal acceleration and eliminate gravity disturbance absolutely, the object function, which designs the weight of control command to be the power function of time-to-go＇s reciprocal, is given. And the gravity is considered when building the state equation. Based on the parsing express of the guidance command change with varying time and adjoint system analysis method, the command characteristics and the non-dimensional miss distance of the guidance law are analyzed, a design principle of guidance order coefficients is discussed. Finally, based on the requirement of engineering, the method to calculate the guidance condition and maximal required acceleration of the guidance law is given. The simulation demonstrates that not only the guidance law can satisfy the terminal position and impact angle constraints, but also the terminal acceleration can be converged toward zero, which will support a good situation for the terminal angle of attacking control.展开更多
This paper investigates the problem of distributed cooperative guidance law design for multiple anti-ship missiles in the three-dimensional(3-D)space hitting simultaneously the same target with considering the desired...This paper investigates the problem of distributed cooperative guidance law design for multiple anti-ship missiles in the three-dimensional(3-D)space hitting simultaneously the same target with considering the desired terminal impact angle constraint.To address this issue,the problem formulation including 3-D nonlinear mathematical model description,and communication topology are built firstly.Then the consensus variable is constructed using the available information and can reach consensus under the proposed acceleration command along the line-of-sight(LOS)which satisfies the impact time constraint.However,the normal accelerations are designed to guarantee the convergence of the LOS angular rate.Furthermore,consider the terminal impact angle constraints,a nonsingular terminal sliding mode(NTSM)control is introduced,and a finite time convergent control law of normal acceleration is proposed.The convergence of the proposed guidance law is proved by using the second Lyapunov stability method,and numerical simulations are also conducted to verify its effectiveness.The results indicate that the proposed cooperative guidance law can regulate the impact time error and impact angle error in finite time if the connecting time of the communication topology is longer than the required convergent time.展开更多
In this paper, a new adaptive optimal guidance law with impact angle and seeker’s field-of-view(FOV) angle constraints is proposed. To this end, the generalized optimal guidance law is derived first. A changeable imp...In this paper, a new adaptive optimal guidance law with impact angle and seeker’s field-of-view(FOV) angle constraints is proposed. To this end, the generalized optimal guidance law is derived first. A changeable impact angle weighting(IAW) coefficient is introduced and used to modify the guidance law to make it adaptive for all guidance constraints. After integrating the closed-form solution of the guidance command with linearized engagement kinematics, the analytic predictive models of impact angle and FOV angle are built, and the available range of IAW corresponding to constraints is certain. Next, a calculation scheme is presented to acquire the real-time value of IAW during the entire guidance process. When applying the proposed guidance law, the IAW will keep small to avoid a trajectory climbing up to limit FOV angle at an initial time but will increase with the closing target to improve impact position and angle accuracy, thereby ensuring that the guidance law can juggle orders of guidance accuracy and constraints control.展开更多
To hit stationary ground targets in specified direction, a nonlinear impact angle control guidance law based on Lyapunov stability theory is proposed. The proposed law ensures the convergence of the heading angle and ...To hit stationary ground targets in specified direction, a nonlinear impact angle control guidance law based on Lyapunov stability theory is proposed. The proposed law ensures the convergence of the heading angle and the miss distance to guarantee a successful engagement. The impact angle can be adjusted by varying a single parameter. And the maximum value of acceleration has been analyzed to get the proper range for control parameter. Considering the achievable impact angle set is limited, an additional phase is added to form a two-phase control strategy.The first phase is to establish a proper initial condition for the second phase, and the second phase is to hit the target with a certain impact angle. An analysis of the proper selection of control parameters to expand the achievable impact angle set is presented. The performance of the proposed guidance law is illustrated with simulations.展开更多
A novel closed-form guidance law with impact time and impact angle constraints is pro- posed for salvo attack of anti-ship missiles, which employs missile＇s normal acceleration （not jerk） as the control command dir...A novel closed-form guidance law with impact time and impact angle constraints is pro- posed for salvo attack of anti-ship missiles, which employs missile＇s normal acceleration （not jerk） as the control command directly. Firstly, the impact time control problem is formulated as tracking the designated time-to-go （the difference between the designated impact time and the current flight time） for the actual time-to-go of missile, and the impact angle control problem is formulated as tracking the designated heading angle for the actual heading angle of missile. Secondly, a biased proportional navigation guidance （BPNG） law with designated heading angle constraint is constructed, and the actual time-to-go estimation for this BPNG is derived analytically by solving the system differential equations. Thirdly, by adding a feedback control to this constructed BPNG to eliminate the time-to-go errorthe difference between the standard time-to-go and the actual time-to-go, a guidance law with adjustable coefficients to control the impact time and impact angle simultaneously is developed. Finally, simulation results demonstrate the performance and feasibility of the proposed approach.展开更多
This paper deals with the problem of guidance law design for the single moving mass controlled reentry vehicle when impact angle constraints and maneuvering target are taken into consideration.More specifically,a modi...This paper deals with the problem of guidance law design for the single moving mass controlled reentry vehicle when impact angle constraints and maneuvering target are taken into consideration.More specifically,a modified rolling guidance law is proposed with the interactive virtual target and the landing point prediction strategy.First,considering the fact that the roll channel can be controlled directly,the relative motion between the single moving mass controlled reentry vehicle and the target is described by the error angle between the relative velocity and the line-ofsight.Second,a nonlinear error angle command is given to reduce the rotation rate.To satisfy impact angle constraints,an interactive virtual target is presented and the‘‘S”formed velocity of the virtual target is given to abate the error angle tracking difficulty at the final stage of the reentry phase.Then,the landing point prediction strategy is employed and the motion variation trend is also taken into consideration.As the maneuvering target is replaced with the predicted landing point,the error angle tracking difficulty caused by the target velocity decreases,which is helpful to meet impact angle constraints and improve guidance accuracy at the same time.Finally,the finite-time rolling guidance law is proposed and proved via Lyapunov stability theorem.Compared with the existing method,lower-speed rotation,smaller missing distance and less impact angle errors are obtained,which can be demonstrated by numerical simulations.展开更多
This paper proposes a cooperative guidance law for attacking a ground target with the impact angle constraint based on the motion camouflage strategy in the line-of-sight(LOS)frame.A dynamic model with the impact angl...This paper proposes a cooperative guidance law for attacking a ground target with the impact angle constraint based on the motion camouflage strategy in the line-of-sight(LOS)frame.A dynamic model with the impact angle constraint is established according to the relative motion between multiple missiles and the target.The process of cooperative guidance law design is divided into two stages.Firstly,based on the undirected graph theory,a new finite-time consensus protocol on the LOS direction is derived to guarantee relative distances reach consensus.And the value of acceleration command is positive,which is beneficial for engineering realization.Secondly,the acceleration command on the normal direction of the LOS is designed based on motion camouflage and finite-time convergence,which can ensure the missiles reach the target with the desired angle and satisfy the motion camouflage state.The finitetime stability analysis is proved by the Lyapunov theory.Numerical simulations for stationary and maneuver targets have demonstrated the effectiveness of the cooperative guidance law proposed.展开更多
In this paper, a novel fuzzy sliding mode control（FSMC） guidance law with terminal constraints of miss distance, impact angle and acceleration is presented for a constant speed missile against the stationary or slow...In this paper, a novel fuzzy sliding mode control（FSMC） guidance law with terminal constraints of miss distance, impact angle and acceleration is presented for a constant speed missile against the stationary or slowly moving target. The proposed guidance law combines the sliding mode control algorithm with a fuzzy logic control scheme for the lag-free system and the first-order lag system. Through using Lyapunov stability theory, we prove the sliding surface converges to zero in finite time. Furthermore, considering the uncertain information and system disturbances, the guidance gains are on-line optimized by fuzzy logic technique. Numerical simulations are performed to demonstrate the performance of the FSMC guidance law and the results illustrate the validity and effectiveness of the proposed guidance law.展开更多
Aiming at the guidance problem under impact angle constraint for homing missile against ground targets,a new adaptive robust nonlinear terminal guidance law was proposed in this paper.According to nonlinear kinetic re...Aiming at the guidance problem under impact angle constraint for homing missile against ground targets,a new adaptive robust nonlinear terminal guidance law was proposed in this paper.According to nonlinear kinetic relationship between the missile and target in vertical plane,a mathematic model was formulated while the motion of target and the system structure perturbation were regarded as limited disturbances.Based on the ideas of zeroing the rate of line-of-sight(LOS)angle and the impact angular tracking error,a nonlinear control strategy was contrived to obtain adaptive robust guidance law by adopting Nussbaum-type gain technique under a desired impact angle.The stability of guidance system in finite time is strictly proven by using Lyapunov stability theory.Finally,the numerical simulation verifies the effectiveness of the proposed scheme.展开更多
In order to strike hard targets underground or warships and tanks with expected impact angle by missiles or guided bombs, trajectory shaping guidance law with terminal position and impact angle constraints is derived ...In order to strike hard targets underground or warships and tanks with expected impact angle by missiles or guided bombs, trajectory shaping guidance law with terminal position and impact angle constraints is derived based on linear quadratic optimal control theory. The required accelera- tion expressed by impact angle and heading error is obtained in lag-free guidance system in order to find the optimal relationship of those angles in terminal phase. The adjoint systems of miss distance and impact angle error of first-order guidance system are established based on statistical linearization adjoint method （SLAM） in order to study the impact performances of the guidance law. Simulation results show that the miss distance and impact angle error of trajectory shaping guidance law are both according with the impact position and angle constraint and the required acceleration at impact can be decreased by an optimal relationship of impact angle and heading error.展开更多
An impact angle constrained fuzzy adaptive fault tolerant integrated guidance and control method for Ski-to-Turn(STT)missiles subject to unsteady aerodynamics and multiple disturbances is proposed.Unsteady aerodynamic...An impact angle constrained fuzzy adaptive fault tolerant integrated guidance and control method for Ski-to-Turn(STT)missiles subject to unsteady aerodynamics and multiple disturbances is proposed.Unsteady aerodynamics appears when flight vehicles are in a transonic state or confronted with unstable airflow.Meanwhile,actuator failures and multisource model uncertainties are introduced.However,the boundaries of these multisource uncertainties are assumed unknown.The target is assumed to execute high maneuver movement which is unknown to the missile.Furthermore,impact angle constraint puts forward higher requirements for the interception accuracy of the integrated guidance and control(IGC)method.The impact angle constraint and the precise interception are established as the object of the IGC method.Then,the boundaries of the lumped disturbances are estimated,and several fuzzy logic systems are introduced to compensate the unknown nonlinearities and uncertainties.Next,a series of adaptive laws are developed so that the undesirable effects arising from unsteady aerodynamics,actuator failures and unknown uncertainties could be suppressed.Consequently,an impact angle constrained fuzzy adaptive fault tolerant IGC method with three loops is constructed and a perfect hit-to-kill interception with specified impact angle can be implemented.Eventually,the numerical simulations are conducted to verify the effectiveness and superiority of the proposed method.展开更多
In order to improve the precision of guidance for the missile intercepting maneuvering targets, this paper proposes a sliding mode guidance law with impact angle constraints based on the equation of the relative motio...In order to improve the precision of guidance for the missile intercepting maneuvering targets, this paper proposes a sliding mode guidance law with impact angle constraints based on the equation of the relative motion of the missile and the target in a 2D plane. Two finite-time convergent guidance laws are proposed based on the nonsingular terminal sliding mode, while, two exponential convergent guidance laws involving dynamic delay are developed through applying the higher-order nonsingular terminal sliding mode. The simulations denote that, in all the four scenarios of the target＇s maneuvering, the guidance laws are able to inhibit the chattering phenomenon of the sliding modes effectively; and from an expected aspect angle, the missiles could attack the targets with high precision and fast speed.展开更多
Considering the problem that the optimal error dynamics can only converge at the terminal time,an impact angle/time constraint missile guidance law with finite-time convergence is designed in this paper,which is based...Considering the problem that the optimal error dynamics can only converge at the terminal time,an impact angle/time constraint missile guidance law with finite-time convergence is designed in this paper,which is based on the pure proportional navigation(PPN)guidance law and the fast terminal error dynamics(FTED)approach.The missile guidance model and FTED equation are given first,and the dynamic equation of impact angle/time error based on PPN is also derived.Then,the guidance law is designed based on FTED,and the guidance error can converge to 0 in a finite time.Furthermore,considering the field of view constraint,the guidance law is improved by using the saturation function mapping method.Finally,a numerical simulation example is given to verify the effectiveness of the guidance law,which shows that the guidance law proposed in this paper can make the missile quickly adjust to the desired states in advance,and effectively relieve the overload saturation pressure of the actuator.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.41941017 and U1702241).
文摘Rock shed is an effective protection measure against rockfall.To investigate the influences of falling rock’s shape and impact angle on the impact effect of the cushioned rock shed,a modeling approach for a rock shed with a cushion layer using PFC-FLAC.The granular cushion is modeled as an aggregate of discrete non-cohesion particles,while the concrete plate and the beam are modeled as zones.The falling rock with different sphericities and impact angles is modeled as a rigid assembly.The numerical model is validated by comparing the simulation results with experimental and numerical results from previous literature.This model is applied to analyze the effects of rock shape and impact angle on the dynamic interaction effects between falling rock and cushioned rock shed,including the impact force,transmitted bottom force,penetration depth,and plate deflection.The numerical results show that the variation in the falling rock’s shape has different effects on the falling rock with different impact angles.These findings could support rock shed design by revealing the limitations of the assumptions in the past research,which may result in unsafe rock sheds for some rockfall cases.
文摘Final velocity and impact angle are critical to missile guidance.Computationally efficient guidance law with compre-hensive consideration of the two performance merits is challeng-ing yet remains less addressed.Therefore,this paper seeks to solve a type of optimal control problem that maximizes final velocity subject to equality point constraint of impact angle con-straint.It is proved that the crude problem of maximizing final velocity is equivalent to minimizing a quadratic-form cost of cur-vature.The closed-form guidance law is henceforth derived using optimal control theory.The derived analytical guidance law coincides with the widely-used optimal guidance law with impact angle constraint(OGL-IAC)with a set of navigation parameters of two and six.On this basis,the optimal emission angle is determined to further increase the final velocity.The derived optimal value depends solely on the initial line-of-sight angle and impact angle constraint,and thus practical for real-world appli-cations.The proposed guidance law is validated by numerical simulation.The results show that the OGL-IAC is superior to the benchmark guidance laws both in terms of final velocity and missing distance.
基金co-supported by National Natural Science Foundation of China (No. 61104153)National Basic Research Program of China (No. 2012CB720000)
文摘The terminal guidance problem for an unpowered lifting reentry vehicle against a sta- tionary target is considered. In addition to attacking the target with high accuracy, the vehicle is also expected to achieve a desired impact angle. In this paper, a sliding mode control （SMC）-based guidance law is developed to satisfy the terminal angle constraint. Firstly, a specific sliding mode function is designed, and the terminal requirements can be achieved by enforcing both the sliding mode function and its derivative to zero at the end of the flight. Then, a backstepping approach is used to ensure the finite-time reaching phase of the sliding mode and the analytic expression of the control effort can be obtained. The trajectories generated by this method only depend on the initial and terminal conditions of the terminal phase and the instantaneous states of the vehicle. In order to test the performance of the proposed guidance law in practical application, numerical simulations are carried out by taking all the aerodynamic parameters into consideration. The effec- tiveness of the proposed guidance law is verified by the simulation results in various scenarios.
基金supported by the Nationa Natural Science Foundation of China(60434010)Outstanding Youth Fund of Heilongjiang Province(JC200606)
文摘Aimed at the guidance requirements of some missiles which attack targets with terminal impact angle at the terminal point,a new integrated guidance and control design scheme based on variable structure control approach for missile with terminal impact angle constraint is proposed.First,a mathematical model of an integrated guidance and control model in pitch plane is established,and then nonlinear transformation is employed to transform the mathematical model into a standard form suitable for sliding mode control method design.A sufficient condition for the existence of linear sliding surface is given in terms of linear matrix inequalities（LMIs）,based on which the corresponding reaching motion controller is also developed.To verify the effectiveness of the proposed integrated design scheme,the numerical simulation of missile is made.The simulation results demonstrate that the proposed guidance and control law can guide missile to hit the target with desired impact angle and desired flight attitude angle simultaneously.
基金supported in part by the National Natural Science Foundation of China (Nos.11202024,11572036)
文摘Sliding mode guidance laws based on a conventional terminal sliding mode guarantees only finite-time convergence, which verifies that the settling time is required to be estimated by selecting appropriate initial launched conditions. However, rapid convergence to a desired impact angle within a uniform bounded finite time is important in most practical guidance applications. A uniformly finite-time/fixed-time convergent guidance law means that the convergence（settling） time is predefined independently on initial conditions, that is, a closed-loop convergence time can be estimated a priori by guidance parameters. In this paper, a novel adaptive fast fixed-time sliding mode guidance law to intercept maneuver targets at a desired impact angle from any initial heading angle,with no problems of singularity and chattering, is designed. The proposed guidance law achieves system stabilization within bounded settling time independent on initial conditions and achieves more rapid convergence than those of fixed-time stable control methods by accelerating the convergence rate when the system is close to the origin. The achieved acceleration-magnitude constraints are rigorously enforced, and the chattering-free property is guaranteed by adaptive switching gains.Extensive numerical simulations are presented to validate the efficiency and superiority of the proposed guidance law for different initial engagement geometries and impact angles.
基金supported by the Joint Equipment Fund of the Ministry of Education(6141A02022340)
文摘An integral sliding mode guidance law(ISMGL)combined with the advantages of the integral sliding mode control(SMC)method is designed to address maneuvering target interception problems with impact angle constraints.The relative motion equation of the missile and the target considering the impact angle constraint is established in the longitudinal plane,and an integral sliding mode surface is constructed.The proposed guidance law resolves the existence of a steady-state error problem in the traditional SMC.Such a guidance law ensures that the missile hits the target with an ideal impact angle in finite time and the missile is kept highly robust throughout the interception process.By adopting the dynamic surface control method,the ISMGL is designed considering the impact angle constraints and the autopilot dynamic characteristics.According to the Lyapunov stability theorem,all states of the closed-loop system are finally proven to be uniformly bounded.Simulation results are compared with the general sliding mode guidance law and the trajectory shaping guidance law,and the findings verify the effectiveness and superiority of the ISMGL.
基金supported by the National Natural Science Foundation of China(51679201)
文摘The impact angle control over guidance(IACG) law against stationary targets is proposed by using feedback linearization control(FLC) and finite time control(FTC). First, this paper transforms the kinematics equation of guidance systems into the feedbackable linearization model, in which the guidance law is obtained without considering the impact angle via FLC. For the purpose of the line of sight(LOS) angle and its rate converging to the desired values, the second-order LOS angle is considered as a double-integral system. Then, this paper utilizes FTC to design a controller which can guarantee the states of the double-integral system converging to the desired values. Numerical simulation illustrates the performance of the IACG, in contrast to the existing guidance law.
基金supported by the National Natural Science Foundation of China(50875024)
文摘The extended optima straints of miss distance and Schwartz inequality. To reduce guidance law with terminal conmpact angle is derived by the terminal acceleration and eliminate gravity disturbance absolutely, the object function, which designs the weight of control command to be the power function of time-to-go＇s reciprocal, is given. And the gravity is considered when building the state equation. Based on the parsing express of the guidance command change with varying time and adjoint system analysis method, the command characteristics and the non-dimensional miss distance of the guidance law are analyzed, a design principle of guidance order coefficients is discussed. Finally, based on the requirement of engineering, the method to calculate the guidance condition and maximal required acceleration of the guidance law is given. The simulation demonstrates that not only the guidance law can satisfy the terminal position and impact angle constraints, but also the terminal acceleration can be converged toward zero, which will support a good situation for the terminal angle of attacking control.
文摘This paper investigates the problem of distributed cooperative guidance law design for multiple anti-ship missiles in the three-dimensional(3-D)space hitting simultaneously the same target with considering the desired terminal impact angle constraint.To address this issue,the problem formulation including 3-D nonlinear mathematical model description,and communication topology are built firstly.Then the consensus variable is constructed using the available information and can reach consensus under the proposed acceleration command along the line-of-sight(LOS)which satisfies the impact time constraint.However,the normal accelerations are designed to guarantee the convergence of the LOS angular rate.Furthermore,consider the terminal impact angle constraints,a nonsingular terminal sliding mode(NTSM)control is introduced,and a finite time convergent control law of normal acceleration is proposed.The convergence of the proposed guidance law is proved by using the second Lyapunov stability method,and numerical simulations are also conducted to verify its effectiveness.The results indicate that the proposed cooperative guidance law can regulate the impact time error and impact angle error in finite time if the connecting time of the communication topology is longer than the required convergent time.
基金supported by the Aeronautical Science Foundation of China(20150172001)
文摘In this paper, a new adaptive optimal guidance law with impact angle and seeker’s field-of-view(FOV) angle constraints is proposed. To this end, the generalized optimal guidance law is derived first. A changeable impact angle weighting(IAW) coefficient is introduced and used to modify the guidance law to make it adaptive for all guidance constraints. After integrating the closed-form solution of the guidance command with linearized engagement kinematics, the analytic predictive models of impact angle and FOV angle are built, and the available range of IAW corresponding to constraints is certain. Next, a calculation scheme is presented to acquire the real-time value of IAW during the entire guidance process. When applying the proposed guidance law, the IAW will keep small to avoid a trajectory climbing up to limit FOV angle at an initial time but will increase with the closing target to improve impact position and angle accuracy, thereby ensuring that the guidance law can juggle orders of guidance accuracy and constraints control.
基金co-supported in part by the National Natural Science Foundation of China (Nos. 61473124, 61573161)
文摘To hit stationary ground targets in specified direction, a nonlinear impact angle control guidance law based on Lyapunov stability theory is proposed. The proposed law ensures the convergence of the heading angle and the miss distance to guarantee a successful engagement. The impact angle can be adjusted by varying a single parameter. And the maximum value of acceleration has been analyzed to get the proper range for control parameter. Considering the achievable impact angle set is limited, an additional phase is added to form a two-phase control strategy.The first phase is to establish a proper initial condition for the second phase, and the second phase is to hit the target with a certain impact angle. An analysis of the proper selection of control parameters to expand the achievable impact angle set is presented. The performance of the proposed guidance law is illustrated with simulations.
基金supported by National Natural Science Foundation of China(No.61273058)
文摘A novel closed-form guidance law with impact time and impact angle constraints is pro- posed for salvo attack of anti-ship missiles, which employs missile＇s normal acceleration （not jerk） as the control command directly. Firstly, the impact time control problem is formulated as tracking the designated time-to-go （the difference between the designated impact time and the current flight time） for the actual time-to-go of missile, and the impact angle control problem is formulated as tracking the designated heading angle for the actual heading angle of missile. Secondly, a biased proportional navigation guidance （BPNG） law with designated heading angle constraint is constructed, and the actual time-to-go estimation for this BPNG is derived analytically by solving the system differential equations. Thirdly, by adding a feedback control to this constructed BPNG to eliminate the time-to-go errorthe difference between the standard time-to-go and the actual time-to-go, a guidance law with adjustable coefficients to control the impact time and impact angle simultaneously is developed. Finally, simulation results demonstrate the performance and feasibility of the proposed approach.
基金supported by the National Natural Science Foundation of China (Nos. 61627810, 61790562, 61403096)
文摘This paper deals with the problem of guidance law design for the single moving mass controlled reentry vehicle when impact angle constraints and maneuvering target are taken into consideration.More specifically,a modified rolling guidance law is proposed with the interactive virtual target and the landing point prediction strategy.First,considering the fact that the roll channel can be controlled directly,the relative motion between the single moving mass controlled reentry vehicle and the target is described by the error angle between the relative velocity and the line-ofsight.Second,a nonlinear error angle command is given to reduce the rotation rate.To satisfy impact angle constraints,an interactive virtual target is presented and the‘‘S”formed velocity of the virtual target is given to abate the error angle tracking difficulty at the final stage of the reentry phase.Then,the landing point prediction strategy is employed and the motion variation trend is also taken into consideration.As the maneuvering target is replaced with the predicted landing point,the error angle tracking difficulty caused by the target velocity decreases,which is helpful to meet impact angle constraints and improve guidance accuracy at the same time.Finally,the finite-time rolling guidance law is proposed and proved via Lyapunov stability theorem.Compared with the existing method,lower-speed rotation,smaller missing distance and less impact angle errors are obtained,which can be demonstrated by numerical simulations.
基金This work was supported by the National Nature Science Foundation of China(11572097).
文摘This paper proposes a cooperative guidance law for attacking a ground target with the impact angle constraint based on the motion camouflage strategy in the line-of-sight(LOS)frame.A dynamic model with the impact angle constraint is established according to the relative motion between multiple missiles and the target.The process of cooperative guidance law design is divided into two stages.Firstly,based on the undirected graph theory,a new finite-time consensus protocol on the LOS direction is derived to guarantee relative distances reach consensus.And the value of acceleration command is positive,which is beneficial for engineering realization.Secondly,the acceleration command on the normal direction of the LOS is designed based on motion camouflage and finite-time convergence,which can ensure the missiles reach the target with the desired angle and satisfy the motion camouflage state.The finitetime stability analysis is proved by the Lyapunov theory.Numerical simulations for stationary and maneuver targets have demonstrated the effectiveness of the cooperative guidance law proposed.
基金supported by the National Natural Science Foundation of China(6130422461305018+1 种基金61472423)the National Advanced Research Project of China(51301010206)
文摘In this paper, a novel fuzzy sliding mode control（FSMC） guidance law with terminal constraints of miss distance, impact angle and acceleration is presented for a constant speed missile against the stationary or slowly moving target. The proposed guidance law combines the sliding mode control algorithm with a fuzzy logic control scheme for the lag-free system and the first-order lag system. Through using Lyapunov stability theory, we prove the sliding surface converges to zero in finite time. Furthermore, considering the uncertain information and system disturbances, the guidance gains are on-line optimized by fuzzy logic technique. Numerical simulations are performed to demonstrate the performance of the FSMC guidance law and the results illustrate the validity and effectiveness of the proposed guidance law.
基金Sponsored by Fundamental Science Foundation Grant of Northwestern Polytechnical University(JC201024)
文摘Aiming at the guidance problem under impact angle constraint for homing missile against ground targets,a new adaptive robust nonlinear terminal guidance law was proposed in this paper.According to nonlinear kinetic relationship between the missile and target in vertical plane,a mathematic model was formulated while the motion of target and the system structure perturbation were regarded as limited disturbances.Based on the ideas of zeroing the rate of line-of-sight(LOS)angle and the impact angular tracking error,a nonlinear control strategy was contrived to obtain adaptive robust guidance law by adopting Nussbaum-type gain technique under a desired impact angle.The stability of guidance system in finite time is strictly proven by using Lyapunov stability theory.Finally,the numerical simulation verifies the effectiveness of the proposed scheme.
基金Supported by the Aeronautical Science Foundation of China(20060112123)
文摘In order to strike hard targets underground or warships and tanks with expected impact angle by missiles or guided bombs, trajectory shaping guidance law with terminal position and impact angle constraints is derived based on linear quadratic optimal control theory. The required accelera- tion expressed by impact angle and heading error is obtained in lag-free guidance system in order to find the optimal relationship of those angles in terminal phase. The adjoint systems of miss distance and impact angle error of first-order guidance system are established based on statistical linearization adjoint method （SLAM） in order to study the impact performances of the guidance law. Simulation results show that the miss distance and impact angle error of trajectory shaping guidance law are both according with the impact position and angle constraint and the required acceleration at impact can be decreased by an optimal relationship of impact angle and heading error.
基金supported by the National Natural Science Foundation of China(62003264).
文摘An impact angle constrained fuzzy adaptive fault tolerant integrated guidance and control method for Ski-to-Turn(STT)missiles subject to unsteady aerodynamics and multiple disturbances is proposed.Unsteady aerodynamics appears when flight vehicles are in a transonic state or confronted with unstable airflow.Meanwhile,actuator failures and multisource model uncertainties are introduced.However,the boundaries of these multisource uncertainties are assumed unknown.The target is assumed to execute high maneuver movement which is unknown to the missile.Furthermore,impact angle constraint puts forward higher requirements for the interception accuracy of the integrated guidance and control(IGC)method.The impact angle constraint and the precise interception are established as the object of the IGC method.Then,the boundaries of the lumped disturbances are estimated,and several fuzzy logic systems are introduced to compensate the unknown nonlinearities and uncertainties.Next,a series of adaptive laws are developed so that the undesirable effects arising from unsteady aerodynamics,actuator failures and unknown uncertainties could be suppressed.Consequently,an impact angle constrained fuzzy adaptive fault tolerant IGC method with three loops is constructed and a perfect hit-to-kill interception with specified impact angle can be implemented.Eventually,the numerical simulations are conducted to verify the effectiveness and superiority of the proposed method.
基金supported by National Natural Science Foundation of China(No.61021002)
文摘In order to improve the precision of guidance for the missile intercepting maneuvering targets, this paper proposes a sliding mode guidance law with impact angle constraints based on the equation of the relative motion of the missile and the target in a 2D plane. Two finite-time convergent guidance laws are proposed based on the nonsingular terminal sliding mode, while, two exponential convergent guidance laws involving dynamic delay are developed through applying the higher-order nonsingular terminal sliding mode. The simulations denote that, in all the four scenarios of the target＇s maneuvering, the guidance laws are able to inhibit the chattering phenomenon of the sliding modes effectively; and from an expected aspect angle, the missiles could attack the targets with high precision and fast speed.
基金the National Natural Science Foundation of China(No.12002370)。
文摘Considering the problem that the optimal error dynamics can only converge at the terminal time,an impact angle/time constraint missile guidance law with finite-time convergence is designed in this paper,which is based on the pure proportional navigation(PPN)guidance law and the fast terminal error dynamics(FTED)approach.The missile guidance model and FTED equation are given first,and the dynamic equation of impact angle/time error based on PPN is also derived.Then,the guidance law is designed based on FTED,and the guidance error can converge to 0 in a finite time.Furthermore,considering the field of view constraint,the guidance law is improved by using the saturation function mapping method.Finally,a numerical simulation example is given to verify the effectiveness of the guidance law,which shows that the guidance law proposed in this paper can make the missile quickly adjust to the desired states in advance,and effectively relieve the overload saturation pressure of the actuator.
