Sliding mode–based simultaneous control of impact angle and impact time

2021 ◽  
pp. 095441002110298
Author(s):  
Kakoli Majumder ◽  
Shashi Ranjan Kumar
Keyword(s):  
Sliding Mode ◽  
Impact Angle ◽  
Line Of Sight ◽  
Impact Time ◽  
Guidance Law ◽  
Simultaneous Control ◽  
Terminal Constraints ◽  
Time Requirements ◽  
Target Interception ◽  
The Impact

In this article, a sliding mode control–based nonlinear guidance scheme for controlling both impact angle and impact time simultaneously is proposed. The problem of impact angle control is first transformed to that of controlling line-of-sight angle and its rate, while the requirement of impact time is achieved by tracking the desired time-to-go. The chosen time-to-go estimate accounts for the curvature required to meet the impact angle requirements toward the target interception. In order to satisfy both of these terminal constraints, the sliding surface is defined as a combination of impact time error and the variable pertaining to the errors in line-of-sight angle and its rate, with appropriate gains assigned to them. The interceptor first performs necessary maneuvers to meet the impact time requirements and then steers its course to achieve the target interception at a desired impact angle. The guidance law is initially derived using nonlinear engagement kinematics against stationary targets and then extended to cater to constant velocity targets using the concept of predicted interception point. Numerical simulations are performed to validate the efficacy of the proposed guidance scheme for various initial engagement geometries. The performance of the proposed guidance scheme is also compared with those of the existing guidance laws and shown to be superior.

Sliding mode guidance for impact time and angle constraints

2017 ◽  
Vol 232 (16) ◽  
pp. 2961-2977 ◽  
Author(s):  
Shashi Ranjan Kumar ◽  
Debasish Ghose
Keyword(s):  
Constant Velocity ◽  
Sliding Mode ◽  
Impact Angle ◽  
Time Error ◽  
Impact Time ◽  
Guidance Law ◽  
Terminal Constraints ◽  
Noisy Measurements ◽  
The Impact ◽  
Guidance Laws

This paper proposes a guidance strategy, which caters to both impact angle and impact time terminal constraints. This guidance scheme is based on switching between impact time and impact angle guidance laws. Unlike the existing impact time guidance laws, the proposed guidance strategy takes into account the curvature of the trajectory due to requirement of impact angle. The guidance law is derived using sliding mode control theory with the switching surface based on impact time error. The interceptor first corrects its course to nullify the impact time error and then aims to achieve interception with desired impact angle. In order to reduce transitions between the two guidance laws, a novel hysteresis loop is introduced in the switching conditions. The guidance law is initially designed for stationary targets, and later it is extended to constant velocity targets using the notion of predicted interception point. In order to validate the efficacy of the proposed guidance strategy, simulation results are presented with constant as well as realistic time-varying speed interceptor models for different engagement scenarios against stationary and constant velocity targets. The performance of the guidance law is evaluated under noisy measurements and the presence of system lag and its performance is compared with other existing guidance laws.

scholarly journals A New Impact Time and Angle Control Guidance Law for Stationary and Nonmaneuvering Targets

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Zhe Yang ◽  
Hui Wang ◽  
Defu Lin ◽  
Luyao Zang
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Impact Angle ◽  
Accurate Solution ◽  
Control Surface ◽  
Impact Time ◽  
Tuning Parameters ◽  
Mode Control ◽  
Guidance Law ◽  
The Impact

A guidance problem for impact time and angle control applicable to cooperative attack is considered based on the sliding mode control. In order to satisfy the impact angle constraint, a line-of-sight rate polynomial function is introduced with four tuning parameters. And the time-to-go derivative with respect to a downrange orientation is derived to minimize the impact time error. Then the sliding mode control surface with impact time and angle constraints is constructed using nonlinear engagement dynamics to provide an accurate solution. The proposed guidance law is easily extended to a nonmaneuvering target using the predicted interception point. Numerical simulations are performed to verify the effectiveness of the proposed guidance law for different engagement scenarios.

Impact angle control based on integral sliding mode manifold and extended state observer

2018 ◽  
Vol 233 (6) ◽  
pp. 2131-2140
Author(s):  
Xiaojian Zhang ◽  
Mingyong Liu ◽  
Yang Li ◽  
Feihu Zhang
Keyword(s):  
Sliding Mode ◽  
Impact Angle ◽  
State Observer ◽  
Extended State Observer ◽  
Line Of Sight ◽  
Extended State ◽  
Integral Sliding Mode ◽  
Guidance Law ◽  
Switched Nonlinear System ◽  
The Impact

This paper discusses the issue of impact angle control over guidance in scenarios of an interceptor against the maneuvering targets. Inspired by switched nonlinear system, an integral sliding mode manifold is first developed. Then, the impact angle control over guidance is derived by using the integral sliding mode manifold with finite time control. To obtain precise guidance effect, the second-order of extended state observer is proposed in the case of unknown target acceleration. Finally, composited impact angle control over guidance based on extended state observer is developed. The stability analysis of the proposed guidance law is demonstrated by using Lyapunov function, and theoretical proof that the line-of-sight angle and line-of-sight angular rate can converge to the desired value in finite steps, respectively. Numerical simulation results are illustrated to validate the performance of the proposed guidance law.

Trajectory shaping guidance law design using constraint-combining multiplier

2021 ◽  
pp. 095441002098637
Author(s):  
Min-Guk Seo ◽  
Chang-Hun Lee ◽  
Tae-Hun Kim
Keyword(s):  
Design Method ◽  
Impact Angle ◽  
State Variables ◽  
Flight Trajectory ◽  
Potential Significance ◽  
Guidance Law ◽  
Terminal Constraints ◽  
The Impact ◽  
Guidance Laws ◽  
Impact Angle Constraint

A new design method for trajectory shaping guidance laws with the impact angle constraint is proposed in this study. The basic idea is that the multiplier introduced to combine the equations for the terminal constraints is used to shape a flight trajectory as desired. To this end, the general form of impact angle control guidance (IACG) is first derived as a function of an arbitrary constraint-combining multiplier using the optimal control. We reveal that the constraint-combining multiplier satisfying the kinematics can be expressed as a function of state variables. From this result, the constraint-combining multiplier to achieve a desired trajectory can be obtained. Accordingly, when the desired trajectory is designed to satisfy the terminal constraints, the proposed method directly can provide a closed form of IACG laws that can achieve the desired trajectory. The potential significance of the proposed result is that various trajectory shaping IACG laws that can cope with various guidance goals can be readily determined compared to existing approaches. In this study, several examples are shown to validate the proposed method. The results also indicate that previous IACG laws belong to the subset of the proposed result. Finally, the characteristics of the proposed guidance laws are analyzed through numerical simulations.

scholarly journals Two-Phase Optimal Guidance Law considering Impact Angle Constraint with Bearings-Only Measurements

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Tianning Wang ◽  
Shengjing Tang ◽  
Jie Guo ◽  
Haoqiang Zhang
Keyword(s):  
Sliding Mode ◽  
Information Matrix ◽  
Impact Angle ◽  
Estimation Accuracy ◽  
Two Phase ◽  
Terminal Sliding Mode ◽  
Guidance Law ◽  
Optimal Guidance ◽  
The Impact ◽  
Impact Angle Constraint

The implementation of advanced guidance laws with bearings-only measurements requires estimation of the range information. To improve estimation accuracy and satisfy the impact angle constraint, this paper proposes a two-phase optimal guidance law consisting of an observing phase and an attacking phase. In the observing phase, the determinant of Fisher information matrix is maximized to achieve the optimal observability and a suboptimal solution expressed by leading angle is derived analytically. Then, a terminal sliding-mode guidance law is designed to track the desired leading angle. In the followed attacking phase, an optimal guidance law is integrated with a switching term to satisfy both the impact angle constraint and the field-of-view constraint. Finally, comparison studies of the proposed guidance law and a traditional optimal guidance law are conducted on stationary targets and maneuvering targets cases. Simulation results demonstrate that the proposed guidance law is able to improve the range observability and achieve better terminal performances including impact angle accuracy and miss distance.

Fixed-time three-dimensional guidance law with input constraint and actuator faults

2020 ◽  
pp. 095441002097197
Author(s):  
Peng Li ◽  
Qi Liu ◽  
Chen-Yu He ◽  
Xiao-Qing Liu
Keyword(s):  
Fault Tolerant ◽  
Sliding Mode ◽  
Input Saturation ◽  
Three Dimensional ◽  
Impact Angle ◽  
Actuator Faults ◽  
Input Constraint ◽  
Guidance Law ◽  
The Impact ◽  
Impact Angle Constraint

This paper investigates the three-dimensional guidance with the impact angle constraint, actuator faults and input constraint. Firstly, an adaptive three-dimensional guidance law with impact angle constraint is designed by using the terminal sliding mode control and nonhomogeneous disturbance observer. Then, in order to solve the problem of the input saturation and actuator faults, an adaptive anti-saturation fault-tolerant three-dimensional law is proposed by using the hyperbolic tangent function based on the passive fault-tolerant control. Finally, the effectiveness of the designed guidance laws is verified by using the Lyapunov function and simulation.

Impact Time Control Guidance Law Considering Seeker's Field-of-View Constraint Without Time-to-Go Information

2016 ◽  
Vol 20 (3) ◽  
pp. 412-417
Author(s):  
Zhe Yang ◽  
◽  
Defu Lin ◽  
Luyao Zang
Keyword(s):  
Sliding Mode ◽  
Field Of View ◽  
Impact Time ◽  
Time Control ◽  
Guidance Law ◽  
Heading Angle ◽  
One And Many ◽  
The Look ◽  
The Impact ◽  
Guidance Laws

Accurate time-to-go estimation with large heading angle error is difficult for homing guidance laws, especially for the impact time control. Considering this, a new cooperative guidance law which requires no time-to-go estimation is investigated. First, the impact time control problem is transformed to the look angle command tracking problem. The look angle command guarantees that the range-to-go error converges to zero asymptotically. Then the proposed guidance law considering the seeker's field-of-view constraint is derived using sliding mode control to track the desired look angle signal. Numerical simulations are performed to verify the effectiveness of the proposed guidance law for one-to-one and many-to-one engagement scenarios.

scholarly journals Field-of-View Constrained Impact Time Control Guidance via Time-Varying Sliding Mode Control

Aerospace ◽  
2021 ◽  
Vol 8 (9) ◽  
pp. 251
Author(s):  
Shuai Ma ◽  
Xugang Wang ◽  
Zhongyuan Wang
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Field Of View ◽  
Time Varying ◽  
Sliding Surface ◽  
Impact Time ◽  
Mode Control ◽  
Time Control ◽  
Guidance Law ◽  
The Impact

The problem of impact time control guidance with field-of-view constraint is addressed based on time-varying sliding mode control. The kinematic conditions that satisfy the impact time control with field-of-view constraint are defined, and then a novel time-varying sliding surface is constructed to achieve the defined conditions. The sliding surface contains two unknown coefficients: one is tuned to achieve the global sliding surface to satisfy the impact time constraint and zero miss distance, and the other is tuned to guarantee the field-of-view constraint. The guidance law is designed to ensure the realization of the global sliding mode. On this basis, the guidance law is modified to a closed-loop structure, and the maximum detection capability of the seeker is utilized to a greater extent. Under the proposed guidance law, neither the small angle assumption nor time-to-go estimation is needed. The guidance command is continuous and converges to 0 at the desired impact time. Simulation results demonstrate the effectiveness and superiority of the proposed guidance law.

Cooperative guidance law for intercepting a hypersonic target with impact angle constraint

2022 ◽  
pp. 1-19
Author(s):  
S. Liu ◽  
B. Yan ◽  
R. Liu ◽  
P. Dai ◽  
J. Yan ◽  
...  
Keyword(s):  
Measurement Errors ◽  
Sliding Mode ◽  
Impact Angle ◽  
Terminal Sliding Mode ◽  
Guidance Law ◽  
Cooperative Guidance ◽  
Simulation Results ◽  
Twisting Algorithm ◽  
The Impact ◽  
Impact Angle Constraint

Abstract The cooperative guidance problem of multiple inferior missiles intercepting a hypersonic target with the specific impact angle constraint in the two-dimensional plane is addressed in this paper, taking into consideration variations in a missile’s speed. The guidance law is designed with two subsystems: the direction of line-of-sight (LOS) and the direction of normal to LOS. In the direction of LOS, by applying the algebraic graph theory and the consensus theory, the guidance command is designed to make the system convergent in a finite time to satisfy the goal of cooperative interception. In the direction of normal to LOS, the impact angle is constrained to transform into the LOS angle at the time of interception. In view of the difficulty of measuring unknown target acceleration information in real scenarios, the guidance command is designed by utilising a super-twisting algorithm based on a nonsingular fast-terminal sliding mode (NFTSM) surface. Numerical simulation results manifest that the proposed guidance law performs efficiently and the guidance commands are free of chattering. In addition, the overall performance of this guidance law is assessed with Monte Carlo runs in the presence of measurement errors. The simulation results demonstrate that the robustness can be guaranteed, and that overall efficiency and accuracy in intercepting the hypersonic target are achieved.

scholarly journals A Geometry-Based Guidance Law to Control Impact Time and Angle under Variable Speeds

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1029
Author(s):  
Xinghui Yan ◽  
Minchi Kuang ◽  
Jihong Zhu
Keyword(s):  
Inverse Dynamics ◽  
Impact Angle ◽  
Generation Process ◽  
Impact Time ◽  
End Point ◽  
Guidance Law ◽  
Trajectory Length ◽  
Aerial Vehicle ◽  
Adjustable Range ◽  
The Impact

To provide a feasible solution for a variable speed unmanned aerial vehicle (UAV) to home on a target with impact time and angle constraints, this paper presents a novel geometry-based guidance law composed of trajectory reshaping and tracking. A trajectory generation process using Bezier curves is introduced to satisfy the impact time and angle constraints under time-varying speed. The impact angle is satisfied by driving the UAV along a specified ending line. The impact time is satisfied by controlling the trajectory length, which is realized through adjusting one Bezier curve end point along the ending line. The adjustable range of this end point, along with the maximum trajectory curvature, is analyzed to ensure that the trajectory is flyable. Guidance command is generated using inverse dynamics. Numerical simulations under various scenarios are demonstrated to illustrate the performance and validate the effectiveness of the proposed method.

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