Bank-to-turn Research Articles

Prescribed-time integrated guidance and control for bank to turn reentry vehicle

In this paper, a novel prescribed-time integrated guidance and control (IGC) with spiral maneuvering deceleration (SMD) method is developed for bank to turn (BTT) reentry vehicle with the consideration of elevation angle and terminal velocity constraints. First, a strict feedback form IGC model is established for BTT reentry vehicle under multiple constraints. Second, a prescribed-time sliding mode controller (SMC) based on prescribed-time extended state observer (ESO) is designed to hit the ground fixed target with the desired line of sight (LOS) elevation angle. Then in order to make the reentry vehicle achieve a better strike effect, it is necessary to constrain the terminal velocity of the reentry flight, a SMD scheme is proposed to achieve the desired terminal velocity. Finally, the efficiency of the proposed scheme is verified by six–degree–of–freedom (6DoF) numerical simulations.

Qualitative indicator-based guidance scheme for bank-to-turn missiles against couplings and maneuvering targets

This paper deals with the design of a three-dimensional (3-D) robust guidance scheme for bank-to-turn (BTT) missiles against couplings and target maneuver. Firstly, the missile-target coupled relative dynamics are established. Then, a qualitative indicator (QI) is designed based on Lyapunov stability theory for both coupling and target maneuver terms to indicate whether they strengthen or weaken the system stability. Moreover, a nonlinear disturbance observer (NDOB) with fixed-time convergence is introduced to estimate the unknown target acceleration. A robust guidance scheme is proposed by synthesizing QI, sliding mode control (SMC) and NDOB. The stability of guidance system is proven via Lyapunov stability theory. Finally, numerical simulations are executed to validate the effectiveness of proposed guidance scheme.

A novel reduced-order guidance and control scheme for hypersonic gliding vehicles

A novel analytical model between roll, pitch rates and components of acceleration of the hypersonic vehicle is established, and a reduced-order gliding guidance and control (G&C) design approach for the hypersonic vehicle is proposed in this paper. The six-degree-of-freedom (6DOF) dynamical and kinematic equations of the hypersonic vehicle in the gliding phase are described. An analytical model suitable for the bank to turn (BTT) control strategy is derived by connecting body rates with components of acceleration in the ballistic coordinate system. A novel reduced-order guidance and control design model with respect to quasi-equilibrium gliding flight is deduced and converted into the strict feedback form. The three channel body rates are treated as pseudo-inputs for tracking errors of flight path angle and heading angle of the hypersonic vehicle. Then, the commanded control surface fin deflections of the hypersonic vehicle are obtained by controlling tracking errors of the flight path angle, heading angle, and the body rates by adopting the block dynamic surface control method. In this paper, the aerodynamic coefficient interpolation process for obtaining the commanded angle of attack and bank angle based on expectant guidance overload is avoided. Meanwhile, the control loop of tracking Euler angles for getting the desired body rates is also elided. Finally, effectiveness and robustness of the novel G&C design method are verified and investigated. Moreover, the feasibility of entering quasi-equilibrium gliding phase only depending on the aerodynamic control mechanism is discussed.

Design and Simulation of Air to Air Missile Homing System

This paper will talk about AIM 120 AMRAAM missile guidance for pursuing a moving target. The missile guidance system itself consists of missile dynamics, control system, seeker, and guidance methods. For general purpose, the missile dynamics approach will use non-linear equation of motions. The control surface that will be discussed follow the rule BTT (Bank-to-Turn) and control system that will be used is PID control system that widely used for control design. Lastly, the guidance method that will be studied here is proportional navigation and constant bearing course approach. The simulation will be conducted using MATLAB Simulink. The Simulink model consist of target dynamics, and guidance system. From the result of simulation, it will be shown that the missile can pursue its target quite well. Hence, the simulation system can be used well for preliminary design purpose.Keywords—Homing System, Control System, Proportional Navigation, Missile Dynamics, Seeker, Bank-to-Turn, Constant Bearing Course.

Longitudinal Aerodynamic Coefficients Estimation and Identifiability Analysis for Hypersonic Glider Controlled by Moving Mass

This paper presents a composite Bank-To-Turn (BTT) control mode with a moving mass and non-redundant Reaction Control System (RCS) for a hypersonic unpowered glider vehicle. This type of control mode can not only preclude the aerodynamic control surfaces ablation, but also optimize the internal space of flight vehicle. The identification of the aerodynamic coefficients for gliders under the novel control mode remains an important research focus. As a key part of system identification, input design greatly affects the identification results. Taking into account the flight characteristics and composite control strategy, the longitudinal dynamic characteristics considering the cubic nonlinearities of hypersonic glider are analyzed and the motion form of internal moving mass is designed based on multi-sine input method. The identifiability and identifiability degree of each longitudinal parameter are evaluated using singular value decomposition of the measure matrix. Simulation results demonstrate that the designed input form improves the accuracy of the estimated parameters, and show the identification order from the most identifiable parameter to the least identifiable parameter.

Integrated 3‐D Flight Trajectory Tracking Control with Aerodynamic Constraints on Attitude and control Surfaces

AbstractIn this paper, a new 3‐D trajectory tracking problem for an uncertain high fidelity six‐degree‐of‐freedom (6‐DOF) aerodynamic system is considered. Instead of designing controllers for each subsystem separately, an integrated trajectory tracking control algorithm is proposed to exploit beneficial relationships among interacting subsystems. The high‐order aerodynamic model is first transformed into a quasi‐strict‐feedback form. Then, backstepping technique is utilized to resolve the coupling effect problem of three control channels resulting from the bank‐to‐turn (BTT) control mode. In addition, command filters are introduced to handle state and actuator constraints caused by the physical limitations and the coordinated turn requirement. Furthermore, the uncertain aerodynamic force and moment coefficients are reconstructed by using the B‐spline neural network approximation and adaptive learning approaches. With Lyapunov stability analysis, all the states in the closed‐loop system are shown to be semi‐globally uniformly ultimately bounded (SUUB), and the tracking errors will asymptotically converge into a small compact set around zero by properly adjusting the control parameters. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed algorithm.

Hybrid BTT/STT missile autopilot design

PurposeTraditional skid-to-turn (STT) missile control mode is adopted mostly, but with the improvement of requirements for mobility and the emergence of new aerodynamic layout, a bank-to-turn (BTT) control mode gradually shows a greater advantage. However, the BTT missile also has certain defects, for example, when attacking against a maneuvering target and at the last section of guidance, the maximum lifting surface position of the missile needs to be adjusted frequently, thereby increasing the difficulty of control as well as introducing high-frequency noise.Design/methodology/approachBased on respective characteristics of the two control modes, this paper puts forward a hybrid autopilot design method based on nonlinear dynamic inversion. Firstly, the method converts overload instructions into corresponding angle instructions through the design of hybrid control guidance logic; secondly, based on the nonlinear dynamic inversion algorithm and combined with the fast-changing circuit/slowly changing circuit, a hybrid controller is designed; finally, combined with the missile mathematical model and actuator, it forms a autopilot design closed loop.FindingsThe simulation result shows that the non-linear dynamic inverse-based BTT/STT hybrid controller can input a track command well, normal overload and roll angle tracking performance have more advantages than the hybrid controller designed on the basis of classical control method in terms of overshooting and hysteretic characteristics.Originality/valueThe paper puts forward a new BTT/STT hybrid control method which has both the high mobile ability of the BTT missile and the precise control ability of the STT missile, which can adapt to the more complicated fighting environment. And, the method can effectively weaken the impact of the transformation of the control mode on the system.

Adaptive Self-Learning Fuzzy Autopilot Design for Uncertain Bank-to-Turn Missiles

This paper proposes an adaptive self-learning fuzzy autopilot design for uncertain bank-to-turn (BTT) missiles due to external disturbances and system errors from the variations of the aerodynamic coefficients and control surface loss. The self-learning fuzzy systems called extended sequential adaptive fuzzy inference systems (ESAFISs) are utilized to compensate for these uncertainties in an adaptive backstepping architecture. ESAFIS is a real‐time self-learning fuzzy system with simultaneous structure identification and parameter learning. The fuzzy rules of the ESAFIS can be added or deleted based on the input data. Based on the Lyapunov stability theory, adaptation laws are derived to update the consequent parameters of fuzzy rules, which guarantees both tracking performance and stability. The robust control terms with the adaptive bound-estimation schemes are also designed to compensate for modeling errors of the ESAFISs by augmenting the self-learning fuzzy autopilot control laws. The proposed autopilot is validated under the control surface loss, aerodynamic parameter perturbations, and external disturbances. Simulation study is also compared with a conventional backstepping autopilot and a neural autopilot in terms of the tracking ability. The results illustrate that the designed fuzzy autopilot can obtain better steady‐state and transient performance with the dynamically self-learning ability.

Robust autopilot design for bank-to-turn missiles using adaptive dual-layer sliding mode control

This paper focuses on robust autopilot design for bank-to-turn (BTT) missiles by using adaptive dual-layer sliding mode control (ADSMC) under model uncertainties and external disturbances. This adaptive sliding mode scheme has a dual-layer structure. One layer drives the system reach the sliding surface in finite time, and the other minimizes the size of the control gains, whilst still guaranteeing the existence of a sliding motion. Therefore, the resulting adaptation law enables reducing the chattering magnitude compared with the traditional super-twisting method. The relationship between the gains and how to obtain them are also given in detail in this paper. Autopilot design progress for three channels is conducted and the closed-loop stability of bank-to-turn missile dynamics is guaranteed. Promising dynamic performance and strong robustness have been achieved for the bank-to-turn missile dynamics as shown in the simulation.

On a novel equivalent control-based adaptive sliding mode approach for autopilot design of BTT missiles

This paper presents a novel equivalent control-based adaptive sliding mode control (EASMC) approach for designing the autopilot of a bank-to-turn (BTT) missile under model uncertainties and external disturbances. The sliding surface is constructed with a tracking error between the real attitude angle and the reference command. The equivalent control technique works as a mechanism for the gains over-bounded by uncertainties and this information is implemented in the adaption progress. The method guarantees that the sliding surface reaches zero in finite time and the error tracks the command value asymptotically. The advantage of this method is that the gains will be adapted to counteract uncertainties and enable the control deflection magnitude to be reduced to the minimum value, keeping the property of a finite-time convergence. The skill in choosing the gains is also given in this paper. Simulation results demonstrate that the approach proposed is able to improve the dynamic performance and robustness of a BTT missile system.

Three dimensional impact angle constrained integrated guidance and control for missiles with input saturation and actuator failure

A three dimensional integrated guidance and control law with impact angle constraint is developed, using the dynamic surface control and extended state observer techniques, for the bank to turn (BTT) missile attacking a ground fixed target in the presence of input saturation and actuator failure. Firstly, a novel three dimensional integrated guidance and control model based on Coriolis theorem is built without assuming the angle between line of sight and missile velocity is small or almost constant. Then, to analyze the effect of input saturation on missile's integrated guidance and control system, a smooth tangent function, a Nussbaum function, and an auxiliary system are introduced. The actuator failure, modeling error, and aerodynamic parameters perturbation are viewed as the lumped system uncertainty. Three extended state observers are designed to estimate uncertainty. With the signal generated by the auxiliary system and uncertainty estimate from extended state observer, a robust controller is designed using dynamic surface control technique to track the desired impact angle. The stability of system is proved using Lyapunov theory. Numerical simulations are implemented to demonstrate the effectiveness and robustness of the integrated guidance and control law.

Distributed composite autopilot design for bank-to-turn missiles with optimized tracking based on disturbance observers

Robust autopilot design for bank-to-turn (BTT) missiles under time-varying aerodynamic parameters, heavy nonlinear crossing couplings and external disturbances is investigated in this article by employing a distributed composite control framework. The dynamics of the BTT missiles are separated into three subsystems from the roll, yaw and pitch channels. For each subsystem, a composite control framework consists of a low-level state feedback stabilizer, a high-level model predictive controller and a feedforward compensator based on a disturbance observer. Simulation results demonstrate that compared with the baseline control and traditional integral control approaches, the proposed control strategy exhibits promising guidance command tracking and robustness against external disturbances, nonlinear crossing couplings and aerodynamic parameter perturbations.

Bank-to-Turn Guidance Law with Terminal Impact-Angle Constraint

AbstractTo avoid the mathematical singularity of polar converting in bank-to-turn (BTT) guidance and to provide the specified terminal impact angle, a BTT guidance law with impact-angle constraint (BTT-GL/IA) is presented. Considering the influence of the impact-angle control and target maneuver to the miss-distance, a new form zero-effort miss-distance with impact angle (ZEM/IA) is introduced. Referring to the Lyapunov-like approach used to drive the guidance law in the prior literature, a Lyapunov function is constructed in terms of ZEM/IA. Based on the Lyapunov stability theorem, a negative definite function is designed, and the BTT-GL/IA is derived. Next, BTT-GL/IA is implemented in another form with the variables as the line-of-sight angle and its rate, which are easily measured by the seeker. When using BTT-GL/IA, the guidance law tends to maintain smooth and continuously-varied body acceleration and roll-angle commands while satisfying the impact position and angle constraints. The problem of a mat...

Control System Optimization Design and Simulation for BBT Missile Based on Kriging Meta-model

The backstepping design method has been used to design the control system of the Bank-to-turn (BTT) missile, which depends on the designer’s personal experience and a large number of complicated iterative calculation, and needs to consume a lot of time throughout the design process. To solve this problem, a missile control system surrogate model is established by using Kriging meta-model. After establishing the surrogate model, the genetic algorithm is applied to the control system optimal solution. The proposed method can obtain a set of control parameters that minimizes the performance function by searching the given control parameters space. The simulation results show that the method can reduce the amount of calculations and achieve the desired control parameters effectively.

On decoupled or coupled control of bank-to-turn missiles

In this paper, the differences between decoupled and coupled control of bank-to-turn (BTT) missiles have been studied in detail from three aspects: stabilizability, linear quadratic regulator (LQR) control and tracking control. It is found that for some parameters the BTT missile can be controlled by a decoupled way, especially for stabilizability and LQR control. However, for some others, the BTT missile cannot be decoupled and a coupled control method is needed. Therefore, for a practical flight control system, the decouplability should be studied before giving a decoupled control method. In addition, in order to avoid the disadvantages of LQR control method, an improved H∞ controller design method is given. Combined with tracking control problem, a new H∞ control method is established for trajectory tracking.

Singular perturbationlike approach to compensation of actuator dynamics effect in missile control

Our recently developed nonlinear autopilot controller can make the input-output (I/O) dynamic characteristics of the nonlinear bank-to-turn (BTT) missile system linear and independent of flight conditions. However, relatively slow actuator dynamics can degrade its performance significantly. The proposed compensation method can nearly eliminate the effect of slow actuator dynamics while maintaining the desired linear I/O dynamic characteristics. It considers fully the nonminimum-phase nonlinear BTT missile dynamics but requires no differentiations of noisy variables, unlike other existing control methods.

Trajectory Tracking Control for Micro Unmanned Aerial Vehicles

This article considers the problem of trajectory tracking control for a micro fixed-wing unmanned air vehicle (UAV). With Bank-to-Turn (BTT) method to manage lateral deviation control of UAV, this paper discusses the outer loop guidance system, which separates the vehicle guidance problems into lateral control loop and longitudinal control loop. Based on the kinematic model of the coordinated turning of UAV, the aircraft can track a pre-specified flight path with desired error range. Flight test results on a fixed-wing UAV have indicated that the trajectory tracking control law is quite effective.

Robust Autopilot Design for Bank-to-Turn Missiles using Disturbance Observers

A decoupling control strategy consisting of robust feedback and feedforward compensation based on disturbance-observers is proposed for bank-to-turn (BTT) missile autopilot. For each of the three channels, the lumped disturbances, which consist of nonlinear couplings and external disturbances, are estimated by a disturbance observer and then feedforward compensated. Three distributed robust state feedback controllers are designed to stabilize the rest linear parts of three channels, respectively. Simulation studies demonstrate the effectiveness of the proposed method.

Robust autopilot design of uncertain bank-to-turn missiles using state-space disturbance observers

Robust autopilot design for bank-to-turn (BTT) missiles under disturbances and uncertainties is investigated in this article using the disturbance observer concept. It is well known that the BTT missile dynamics undergo substantial change during its flight. In this disturbance observer-based control (DOBC) setting, the influences caused by parameter variations are merged into disturbance terms and regarded as parts of the lumped disturbances. Disturbance observers are employed to estimate the lumped disturbances, and then a disturbance observer-based robust control (DOBRC) method is proposed in this article to compensate the influences of parameter variations and the disturbances from the output channels. Similar to the baseline linear quadratic regulator design, the DOBRC is analysed and designed using linear techniques. Very promising performance has been achieved for the BTT missile as shown in simulation. It is demonstrated that DOBC approach provides a simple, intuitive, and practical solution for many challenging control problems where systems are subject to significant external disturbances, and uncertainties such as BTT missiles.

New three-dimensional guidance law for BTT missiles based on differential geometry and Lie-group

A new non-decoupling three-dimensional guidance law is proposed for bank-to-turn (BTT) missiles with the motion cou- pling problem. In this method, the different geometry is taken for theoretically modeling on BTT missiles' motion within the three- dimensional style without information loss, and meanwhile, Lie- group is utilized to describe the line-of-sight (LOS) azimuth when the terminal angular constraints are considered. Under these cir- cumstances, a guidance kinematics model is established based on differential geometry. Then, corresponding to no terminal angular constraint and terminal angular constraints, guidance laws are re- spectively designed by using proportional control and generalized proportional-derivative (PD) control in SO(3) group. Eventually, simulation results validate that this developed method can ef- fectively avoid the complexity of pure Lie-group method and the information loss of the traditional decoupling method as well.