Integrated guidance and control design for missile with terminal impact angle constraint based on sliding mode control

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.

Design and Analysis of Terminal Guidance Law for Kinetic Interceptors based on Pulse Engine

A new terminal guidance law is proposed based on a solid propellant pulse engine and an improved proportional navigation method to address the terminal guidance issue for kinetic interceptors.On this basis,the start-stop curve of the pulse motor during the terminal guidance process is designed,along with its start-up logic.The effectiveness of the proposed guidance strategy is verified through simulation.

Integrated guidance and control design of the suicide UCAV for terminal attack

A novel integrated guidance and control (IGC) design method is proposed to solve problems of low control accuracy for a suicide unmanned combat aerial vehicle (UCAV) in the terminal attack stage. First of all, the IGC system model of the UCAV is built based on the three-channel independent design idea, which reduces the difficulties of designing the controller. Then, IGC control laws are designed using the trajectory linearization control (TLC). A nonlinear disturbance observer (NDO) is introduced to the IGC controller to reject various uncertainties, such as the aerodynamic parameter perturbation and the measurement error interference. The stability of the closed-loop system is proven by using the Lyapunov theorem. The performance of the proposed IGC design method is verified in a terminal attack mission of the suicide UCAV. Finally, simulation results demonstrate the superiority and effectiveness in the aspects of guidance accuracy and system robustness.

Optimal Guidance Law to Maximize Terminal Velocity for Missiles with Impact Angle Constraint

In this paper,an optimal guidance law for missiles with impact angle and miss distance constraints is proposed to achieve the maximal terminal velocity. The normal acceleration command that includes the timevarying coefficients is introduced to satisfy the desired impact angle as well as zero miss distance according to the geometric relation and relative motion parameters between missile and target. The problem is formulated as an optimal control problem by defining the angle of velocity error and flight-path angle as state variables and maximizing a performance index of the terminal velocity. The analytical form of the proposed guidance law is obtained as the solution of the optimal control problem combining optimal control theory and numerical value computation method. Nonlinear simulations of various situations demonstrate the performance and feasibility of the proposed optimal guidance law.

Terminal Angular Constraint Integrated Guidance and Control for Flexible Hypersonic Vehicle with Dead-Zone Input Nonlinearity

This paper presents an integrated guidance and control model for a flexible hypersonic vehicle with terminal angular constraints.The integrated guidance and control model is bounded and the dead-zone input nonlinearity is considered in the system dynamics.The line of sight angle,line of sight angle rate,attack angle and pitch rate are involved in the integrated guidance and control system.The controller is designed with a backstepping method,in which a first order filter is employed to avoid the differential explosion.The full tuned radial basis function(RBF)neural network(NN)is used to approximate the system dynamics with robust item coping with the reconstruction errors,the exactitude model requirement is reduced in the controller design.In the last step of backstepping method design,the adaptive control with Nussbaum function is used for the unknown dynamics with a time-varying control gain function.The uniform ultimate boundedness stability of the control system is proved.The simulation results validate the effectiveness of the controller design.

Optimum Design of the Control System for a Laser Beam Riding Guidance Anti-Tank Missile

The optimum theory and methods were adopted to design the laser beam riding guidance anti tank missile's control system in the short run. Through building the mathematical model of system, selecting a proper method and taking advantage of computer's high speed calculation and logic traits, an optimal controller was designed. Simulation results showed that the designed control system has fair performance and it satisfies the tactical and technical requirements. The results also demonstrate that by the combination of the optimizing methods and the computer the control system could be designed as soon as possible.

STUDY OF OPTIMAL SLIDING-MODE GUIDANCE LAW

An optimal guidance law based on missile-target line-of-sight (LOS) angular rate is presented for intercepting a nonmaneuvering target. It is then integrated with sliding-mode control theory by using reaching-law of sliding-mode, in order to derive an optimal sliding-mode guidance law for intercepting a maneuvering target. The new guidance method's robustness against target maneuvers and good miss distance performance are proved by the second method of Lyapunov and simulation results. The presented guidance law is simple to implement in practical applications.

Time-to-go weighted optimal trajectory shaping guidance law

For maneuvering target, the optimal trajectory shaping guidance law which can simultaneously achieve the designed specifications on miss distance and final impact angle was deduced using optimal control theory based on the time-to-go weighted function. Based on the same cost function, the closed-form solutions of the guidance law were derived when the initial displacement of missile, final impact angle, heading error and target maneuver was introduced into the lag-free guidance system. To validate the closed-form solutions, the simulation of the lag-free system was done and the simulation results exactly matched the closed-form solutions and only when the exponent is greater than zero, the final acceleration approaches to zero.

Integrated guidance and control of guided projectile with multiple constraints based on fuzzy adaptive and dynamic surface

Based on fuzzy adaptive and dynamic surface(FADS),an integrated guidance and control(IGC)approach was proposed for large caliber naval gun guided projectile,which was robust to target maneuver,canard dynamic characteristics,and multiple constraints,such as impact angle,limited measurement of line of sight(LOS)angle rate and nonlinear saturation of canard deflection.Initially,a strict feedback cascade model of IGC in longitudinal plane was established,and extended state observer(ESO)was designed to estimate LOS angle rate and uncertain disturbances with unknown boundary inside and outside of system,including aerodynamic parameters perturbation,target maneuver and model errors.Secondly,aiming at zeroing LOS angle tracking error and LOS angle rate in finite time,a nonsingular terminal sliding mode(NTSM)was designed with adaptive exponential reaching law.Furthermore,combining with dynamic surface,which prevented the complex differential of virtual control laws,the fuzzy adaptive systems were designed to approximate observation errors of uncertain disturbances and to reduce chatter of control law.Finally,the adaptive Nussbaum gain function was introduced to compensate nonlinear saturation of canard deflection.The LOS angle tracking error and LOS angle rate were convergent in finite time and whole system states were uniform ultimately bounded,rigorously proven by Lyapunov stability theory.Hardware-in-the-loop simulation(HILS)and digital simulation experiments both showed FADS provided guided projectile with good guidance performance while striking targets with different maneuvering forms.

Iterative Learning Control for homing guidance design of missiles

This paper presents an Iterative Learning Control design applied to homing guidance of missiles against maneuvering targets. According to numerical experiments, although an increase of the control energies is appreciated with respect to a previous published base controller for comparison, this strategy, which is simple to realize, is able to reduce the time to reach the head-on condition to target destruction. This fact is important to minimize the missile lateral force-level to fulfill engaging in hyper-sonic target persecutions.

Design methodology of a mini-missile considering flight performance and guidance precision

The design of mini-missiles(MMs)presents several novel challenges.The stringent mission requirement to reach a target with a certain precision imposes a high guidance precision.The miniaturization of the size of MMs makes the design of the guidance,navigation,and control(GNC)have a larger-thanbefore impact on the main-body design(shape,motor,and layout design)and its design objective,i.e.,flight performance.Pursuing a trade-off between flight performance and guidance precision,all the relevant interactions have to be accounted for in the design of the main body and the GNC system.Herein,a multi-objective and multidisciplinary design optimization(MDO)is proposed.Disciplines pertinent to motor,aerodynamics,layout,trajectory,flight dynamics,control,and guidance are included in the proposed MDO framework.The optimization problem seeks to maximize the range and minimize the guidance error.The problem is solved by using the nondominated sorting genetic algorithm II.An optimum design that balances a longer range with a smaller guidance error is obtained.Finally,lessons learned about the design of the MM and insights into the trade-off between flight performance and guidance precision are given by comparing the optimum design to a design provided by the traditional approach.

Design of Closed Loop Optimal Guidance Law Using Neural Networks

It is generally impossible to obtain the analytic optimal guidance law for complex nonlinear guidance systems of homing missiles,and the open loop optimal guidance law is often obtained by numerical methods,which can not be used directly in practice.The neural networks are trained off line using the optimal trajectory of the missile produced by the numerical open loop optimal guidance law,and then,the converged neural networks are used on line as the feedback optimal guidance law in real time.The research shows that different selections of the neural networks inputs,such as the system state variables or the rate of LOS(line of sight),may have great effect on the performances of the guidance systems for homing missiles.The robustness for several guidance laws is investigated by simulations,and the modular neural networks architectures are used to increase the approximating and generalizing abilities in the large state space.Some useful conclusions are obtained by simulation results.

Design of Guided Air Ammunition's Optimal Guidance Law

Some long distance air ammunition can be used to attack large still target. According to this character and according to the mathematical description of target-missile relative motion built by the message supplied by the strapdown inertial navigation system/global position system （SINS/GPS） of air ammunition, optimal guidance law is designed by applying optimal control theory. The simulation is provided to indicate that when the air ammunition reaches the target, its line-of-sight （LOS） and LOS angular rate can nearly equal zero. So the air ammunition can get good terminal attitude, and the air ammunition reaches the target at the expected velocity and heading.

Kinetic Optimal Midcourse Guidance Law for Air-to-Air Missiles

A new kinetic optimal midcourse guidance law is derived based on optimal control formulation. A new simplified Runge-Kutta grade numerical method is proposed to find the optimal trajectory. Real data of an Mr-to-air missile is referred to for comparing results using the kinetic optimal midcourse guidance law with those under both the kinematic optimal guidance law and singular perturbation sub-optimal guidance law, wherein the latter two laws are modified in this paper by adding a vertical g-bias command to each law for the sake of trajectory shaping. Simulation results show that using the new kinetic optimal mideourse guidance law can help save energy and maximize terminal velocity effectively.

Optimal Gliding Guidance of Vertical Plane for Standoff Released Guided Bomb Unit

Optimal gliding guidance for a guided bomb unit in the vertical plane is studied based on nonlinear dynamics and kinematics.The guidance law is designed under minimum energy loss index.To avoid the complexity in solving two-point-boundary-value problems,the steady-state solutions of the adjoint states in regular equations are suggested to be used.With these considerations,a quasi-closed,optimal gliding guidance law is obtained.The guidance law is described by the angle of attack in a simple nonlinear equation.An iterative computation method can be easily used to get the optimal angle of attack.The further simplified direct computation algorithm for the optimal angle of attack is also given.The guidance properties are compared with those of maximum lift-to-drag angle of attack control.The simulation results demonstrate that the quasi-closed,optimal gliding guidance law can improve the gliding phase terminal performance with significant increase in the altitude and much little decrease in the speed.

Use of the Method of Guidance by a Required Velocity in Control of Spacecraft Attitude

We apply the method of guidance by a required velocity for solving the optimal control problem over spacecraft’s reorientation from known initial attitude into a required final attitude.We suppose that attitude control is carried out by impulse jet engines.For optimization of fuel consumption,the controlling moments are calculated and formed according to the method of free trajectories together with principle of iterative control using the quaternions for generating commands to actuators.Optimal solution corresponds to the principle“acceleration-free rotation-separate corrections-free rotation-braking”.Rotation along a hitting trajectory is supported by insignificant correction of the uncontrolled motion at discrete instants between segments of acceleration and braking.Various strategies of forming the correction impulses during stage of free motion are suggested.Improving accuracy of achievement of spacecraft's final position is reached by terminal control using information about current attitude and angular velocity measurements for determining an instant of beginning of braking(condition for start of braking based on actual motion parameters is formulated in analytical form).The described method is universal and invariant relative to moments of inertia.Developed laws of attitude control concern the algorithms with prognostic model,the synthesized control modes are invariant with respect to both external perturbations and parametric errors.Results of mathematical modeling are presented that demonstrate practical feasibility and high efficiency of designed algorithms.

Inverse Optimal Control for Speed-varying Path Following of Marine Vessels with Actuator Dynamics

A controller which is locally optimal near the origin and globally inverse optimal for the nonlinear system is proposed for path following of over actuated marine crafts with actuator dynamics. The motivation is the existence of undesired signals sent to the actuators, which can result in bad behavior in path following. To attenuate the oscillation of the control signal and obtain smooth thrust outputs, the actuator dynamics are added into the ship maneuvering model. Instead of modifying the Line-of-Sight (LOS) guidance law, this proposed controller can easily adjust the vessel speed to minimize the large cross-track error caused by the high vessel speed when it is turning. Numerical simulations demonstrate the validity of this proposed controller.

Multiconstraint adaptive three-dimensional guidance law using convex optimization

The traditional guidance law only guarantees the accuracy of attacking a target. However, the look angle and acceleration constraints are indispensable in applications. A new adaptive three-dimensional proportional navigation(PN) guidance law is proposed based on convex optimization. Decomposition of the three-dimensional space is carried out to establish threedimensional kinematic engagements. The constraints and the performance index are disposed by using the convex optimization method. PN guidance gains can be obtained by solving the optimization problem. This solution is more rapid and programmatic than the traditional method and provides a foundation for future online guidance methods, which is of great value for engineering applications.

Three-dimensional impact angle constrained distributed cooperative guidance law for anti-ship missiles

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.

Strapdown Homing Guidance System Design for Some Ammunition

The strapdown homing guidance system for some ammunition was mainly studied. A strong tracking Kalman filter was designed for the strapdown homing guidance system using the information measured by the strapdown homing seeker to estimate relative movement variables between the ammunition and target. Then the optimal proportional law, which using the estimated information, guided the ammunition. Simulation results show that the designed strapdown homing guidance system with strong tracking Kalman filter can attack the maneuvering target effectively, and satisfy the performance index for the guided ammunition system.