Tail-controlled Missile Research Articles

Robust missile autopilot design based on dynamic surface control

Since the dynamical system and control system of the missile are typically nonlinear, an effective acceleration tracking autopilot is designed using the dynamic surface control (DSC) technique in order to make the missile control system more robust despite the uncertainty of the dynamical parameters and the presence of disturbances. Firstly, the nonlinear mathematical model of the tail-controlled missile is decomposed into slow acceleration dynamics and fast pitch rate dynamics based on the naturally existing time scale separation. Secondly, the controller based on DSC is designed after obtaining the linear dynamics characteristics of the slow and fast subsystems. An extended state observer is used to detect the uncertainty of the system state variables and aerodynamic parameters to achieve the compensation of the control law. The closed-loop stability of the controller is derived and rigorously analyzed. Finally, the effectiveness and robustness of the design is verified by Monte Carlo simulation considering different initial conditions and parameter uptake. Simulation results illustrate that the missile autopilot based DSC controller achieves better performance and robustness than the other two well-known autopilots. The method proposed in this paper is applied to the design of a missile autopilot, and the results show that the acceleration tracking autopilot based on the DSC controller can ensure accurate tracking of the required commands and has better performance.

Integrated Autopilot Guidance Based on Zero-Effort-Miss Formulation for Tail-Controlled Missiles

This paper presents a control structure integrating guidance and control loops for tail-controlled missile systems. Motivated by the fact that common tail-controlled missiles involve non-minimum phase dynamics, the proposed controller is designed to prevent the internal dynamics from diverging, as well as achieving homing against the intended target. To minimize the miss distance at the end of homing, we derive a formulation of a zero-effort-miss using engagement kinematics that contain the rotating dynamics of the missile, which is different from existing approaches. Subsequently, to nullify the zero-effort-miss, a nonlinear controller is designed based on the Lyapunov stability theory. Since the derived controller has a similar structure to the conventional three-loop topology that has been utilized for various tail-controlled flight systems, it is expected that the proposed method can be applied to the actual system from a practical point of view. Numerical simulation results also show that the proposed method achieves target interception while possessing stable internal dynamics.

Missile Angle of Attack Tracking Using Integrator Backstepping

This paper deals with missile longitudinal dynamics control. The angle of attack tracking problem is considered for an unpowered flight phase of a short range tail-controlled missile with the zero engine thrust. For the control synthesis, a simplified missile dynamics model that includes the actuator dynamics is used. The tracking control law is designed using the integrator backstepping approach. The aerodynamic polynomials dependence on absolute values of the angle of attack is considered from the perspective of applying the integrator backstepping technique.

Numerical simulation of aerodynamic characteristics and heating for grid fin missiles

A grid fin is an unconventional missile control surface comprising an outer frame supporting an inner grid of lifting surfaces. Although the topic of grid fin aerodynamics has been studied by many researchers, only a few have considered aerodynamic heating, generating a high-quality structured grid that remains to be a difficult task. An effective method of grid partition and an aerodynamic prediction method to simulate the viscous flow fields of grid-fin configurations at supersonic Mach numbers have been developed. Multi-block and H-O-type grid treatments are developed for complex grid fin configurations. The viscous flow over a tail-controlled missile with grid fins at a Mach number of 2.5 and several angles of attack is calculated using computational fluid dynamics. Additionally, the heat flux distribution of grid fins is investigated, and the effects of shock wave interaction on heat flux are analyzed. The numerical results show good agreement with the measured data, and confirm that this method is an effective way to numerically simulate viscous grid fin flow fields. Furthermore, the aerodynamic heating results show that, because the peak heat flux on the shock wave interaction region is lower than that on the leading edge of the grid fin, it does not affect the thermal protection of the grid fin.

꼬리날개 조종 유도무기의 주날개-꼬리날개 간섭 현상

꼬리날개 조종 유도무기의 주날개-꼬리날개 간섭 현상에 대한 연구를 수행하였다. 풍동시험 데이터를 이용하여 주날개-꼬리날개 간섭 정도를 산출하였으며 날개간의 간섭 현상이 전체 공력에 미치는 영향을 분석하였다. 성분 시험 결과를 이용하여 downwash angle을 산출하였으며 날개간의 간섭 영향을 받음각에 대한 비율로 나타내었다. 날개간의 간섭 현상 발생 시 유동 특성을 살펴보기 위해 수치해석을 실시하였으며 받음각에 대한 vorticity 특성을 비교하였다. 실험적, 수치적 연구를 통해 주날개-꼬리날개 간섭현상이 유도무기의 정안정성에 큰 영향을 미침을 확인하였다.

Multi-Mode Electric Actuator Dynamic Modelling for Missile Fin Control

Linear first/second order fin direct current (DC) actuator model approximations for missile applications are currently limited to angular position and angular velocity state variables. Furthermore, existing literature with detailed DC motor models is decoupled from the application of interest: tail controller missile lateral acceleration (LATAX) performance. This paper aims to integrate a generic DC fin actuator model with dual-mode feedforward and feedback control for tail-controlled missiles in conjunction with the autopilot system design. Moreover, the characteristics of the actuator torque information in relation to the aerodynamic fin loading for given missile trim velocities are also provided. The novelty of this paper is the integration of the missile LATAX autopilot states and actuator states including the motor torque, position and angular velocity. The advantage of such an approach is the parametric analysis and suitability of the fin actuator in relation to the missile lateral acceleration dynamic behaviour.

Nonlinear Autopilot Design for an Asymmetric Missile Using Robust Backstepping Control

This paper deals with the design of a robust nonlinear controller for a highly maneuverable missile. Stabilization and tracking are achieved, exploiting a detailed nonlinear model of the six-degree-of-freedom, nonminimum phase, uncertain, and time-varying dynamics of a non-axial-symmetric air-to-air tail-controlled missile. A robust backstepping approach is applied to the multi-input/multi-output model to achieve both bank-to-turn and skid-to-turn maneuvers. Control objectives consist of following the reference signals in angle of attack, sideslip, and bank angle produced by the external guidance system, in order to pursue highly agile maneuvers. Uncertain terms, mostly due to aerodynamic coefficients and dynamic pressure, are suitably limited by bounding functions constructed using experience, a priori knowledge on system behavior, and a bit of conservatism. Robust sigmoidlike control functions are then used to dominate in size the uncertain terms. The whole control system is shown to be practically-robustly uniformly asymptotically stable and control objectives are met within a prescribed level of performance, in both bank-to-turn and skid-to-turn maneuvers. Simulation results validate the quality of the proposed controller.

Missile two-loop acceleration autopilot design based on 𝓛1adaptive output feedback control

This article documents the design of a novel two-loop acceleration autopilot based on L1 adaptive output feedback control for tail-controlled missiles. The inner loop is an adaptive angle-of-attack tracking loop and the outer loop is the traditional PI controller for error compensation. A systematic low-pass filter design procedure is provided for minimum phase system and is applied to the inner loop design while the parameters of the outer loop are obtained from the multi-objective optimization problem. The effectiveness of the proposed autopilot is verified through numerical simulations under various conditions.

Outer-Loop Sliding Mode Control Approach to Longitudinal Autopilot Missile Design

AbstractThis paper presents a new feedback control methodology to design robust Outer-Loop Sliding Mode (OLSM) controllers for systems with nonlinear rapidly time varying and highly uncertain dynamics such as tactical missiles. Within Sliding Mode Control (SMC) framework and based on relative degree and local diffeomorphic coordinate transformation concepts, OLSM controllers that feature short finite time convergence, heavy modeling uncertainties robustness, and chattering extinction and suppression are designed. Two OLSM pitch-axis autopilots for tail-controlled missile are designed and implemented in computer-simulation environment. Simulation results demonstrate the capabilities of OLSM approach in providing high performance levels while maintaining robustness against heavy uncertainties.

Quasilinear Parameter-Varying Autopilot Design Using Polynomial Eigenstructure Assignment with Actuator Constraints

In this paper, eigenstructure assignment is used in a polynomial matrix framework. In particular, such eigenstructure assignment does not impose any particular eigenvalues and the assignment is done in one-single pass over the flight envelope of a nonlinear missile. The eigenspace of the system is manipulated in polynomial matrix form and the closed-loop transfer function is expressed as a coprime factorization. The designer is left to choose the controller structure producing a flexible design approach. The approach enables the design to consider both static and dynamic controllers alike. In this paper, the approach is applied to a quasilinear parameter-varying missile and it is simple, attractive and comparable to other approaches while leading to a closed-loop system independent of the operating point. The approach is thus similar to dynamic inversion with a self-scheduled controller, but without the need to consider zero dynamics. A tail-controlled missile in the cruciform fin configuration is modeled as a second-order quasilinear parameter-varying system. A lateral velocity controller is designed for the nonlinear model of a tactical missile. The actuator dynamics are included and successively, the actuator dimensioning and the actuator dynamics effects are traded off against performance using the matching conditions developed herein.

Polynomial approach for design and robust analysis of Lateral missile control

A polynomial approach is presented for the design and analysis of a sideslip velocity missile autopilot. The controller is designed using polynomial eigenstructure assignment (PEA). The missile model is described by linear parameter varying (LPV) matrices. The design renders to a closed-loop system independent of the choice of equilibria. Thus, if the operating points are in the vicinity of the equilibria, then only one linear model will describe closed-loop dynamics, regardless of the rate of change of the operating points. Parametric stability margins for uncertainty in the controller parameters and aerodynamic derivatives are analysed using a finite version of the Nyquist Theorem. The Finite Nyquist Theorem (FNT) exploits the polynomial framework to assess robustness for a parametric uncertain system with the Finite Inclusion Theorem (FIT). The design and analysis approach is applied to a single-input single-output (SISO) tail-controlled missile in the cruciform fin configuration. Simulations show good tracking of sideslip velocity with closed-loop system, fast responses and good parametric robustness against six uncertain parameters.

Adaptive control based on a parametric affine model for tail-controlled missiles

An adaptive control against uncertainties in tail-controlled STT (skid-to-turn) missiles is presented. First, we derive an analytic uncertainty model from a parametric affine missile model developed by the authors. Based on this analytic model, an adaptive feedback linearizing control law accompanied by a sliding mode control law is proposed. We provide analyses of stability and output tracking performance of the overall adaptive missile system. The performance and validity of the proposed adaptive control scheme are demonstrated by simulation.

Robust Analysis for Missile Lateral Acceleration Control Using Finite Inclusion Theorem.

In this paper, polynomial eigenstructure assignment design approach is applied to the lateral acceleration control for a tactical missile model. The tail-controlled missile in the cruciform n conguration is modelled as a second-order quasi-linear parameter-varying system. Polynomial eigenstructure assignment is seen as an approach to perform dynamic inversion where the controller has a chosen structure. Although developed primarily for LTI systems, the design approach uses here the explicit parametrisation of the LPV system and thus lead to a LPV controller. Keeping the polynomial framework, robustness to parametric uncertainties is then assessed based on a nite version of the Nyquist Theorem, the Finite Nyquist Theorem and its extension to polynomial families, the Finite Inclusion Theorem. Simplifying the value set using the Mapping Theorem, the multi-linear polynomial family is captured and its D-stable robustness assessed. Finally, simulations show good tracking of lateral acceleration with fast response time and lead to discussion on the robust properties of the closed-loop system.

Robust augmented lateral acceleration flight control design for a quasi-linear parameter-varying missile

An augmented lateral acceleration autopilot is designed for a model of a tactical missile and robust stability of the closed-loop system investigated. The tail-controlled missile in the cruciform fin configuration is modelled as a second-order quasi-linear parameter-varying system. This non-linear model is obtained from the Taylor linearized model of the horizontal motion by including explicit dependence of the aerodynamic derivatives on a state (side-slip velocity) and external parameters (longitudinal velocity and roll angle). The autopilot design is based on input-output pseudolinearization, which is a restriction of input-output feedback linearization to the set of equilibria of the non-linear model. The design makes Taylor linearization of the closed-loop system independent of the choice of equilibria. Thus, if the operating points are in the vicinity of the equilibria, then only one linear model will describe closed-loop dynamics, regardless of the rate of change in the operating points. Simulations for constant lateral acceleration demands show good tracking with fast response time. Robust autopilot design taking into account parametric stability margins for uncertainty aerodynamic derivatives is implemented using convex optimization and linear matrix inequalities.

Robust Lateral Augmented Acceleration Flight Control Design

A lateral augmented acceleration autopilot is designed for a model of a tactical missile. The tail-controlled missile in the cruciform fin configuration is modelled as a second-order quasi-linear parameter-varying system. The autopilot design is based on input-output pseudolinearisation, which is a restriction of input-output feedback linearisation to the set of equilibria of the nonlinear model. Robust autopilot design taking account parametric stability margins for uncertainty aerodynamic derivatives is implemented using convex optimisation and linear matrix inequalities - LMI. Simulations for constant lateral acceleration demands including uncertainties show satisfactory robust performance.

Flight Control Design for Quasi-Linear Parameter Varying Missile via Pseudolinearisaton

An autopilot is designed for a model of a tactical missile and stability of the closed-loop system investigated. The tail-controlled missile in the cruciform fin configuration is modelled as a quasi-linear parameter-varying system. This nonlinear model is obtained from the Taylor linearised model of the lateral and longitutinal motion by including explicit dependence of the aerodynamic derivatives on a states (incidence angle and roll angle) and external parameter (Mach number). The autopilot design is based on input-output pseudolinearisation, which is the restriction of inputoutput feedback linearisation to the set of equilibria of the nonlinear model. The design makes Taylor linearisation of the closed-loop system independent of the choice of equilibria. Thus, if the operating points are in the vicinity of the equilibria, then only one linear model will describe closed-loop dynamics, regardless of the rate of change of the operating points. Simulations for constant lateral acceleration demands show good tracking with fast response time. Parametric stability margins for uncertainty in the controller parameters and aerodynamic derivatives are analysed using Quadratic Lyapunov approach.

Robust Autopilot for a Quasi-Linear Parameter-Varying Missile Model

A sideslip velocity autopilot is designed for a model of a tactical missile, and robust stability of the closed-loop system is investigated. The tail-controlled missile in the cruciform e n cone guration is modeled as a second-order quasi-linear parameter-varying system. This nonlinear model is obtained from the Taylor linearized model of the horizontal motion by including explicit dependence of the aerodynamic derivatives on a state (sideslip velocity ) and external parameters (longitudinal velocity and roll angle ). The autopilot design is based on input ‐output pseudolinearization, which is the restriction of input ‐output feedback linearization to the set of equilibria of the nonlinear model. The design makes Taylor linearization of the closed-loop system independent of the choice of equilibria. Thus, iftheoperating points are in thevicinity of the equilibria, then only onelinear model will describe closed-loop dynamics, regardless of the rate of change of the operating points. Simulations for constant lateral acceleration demands show good tracking with fast response time. Parametric and H1 stability margins for uncertainty in the controller parameters and aerodynamic derivatives are analysed using Kharitonov’ s approach. The analysis shows that the design is fairly robust with respect to both kinds of uncertainty.

Lateral Acceleration Flight Control for a Quasi-Linear Parameter Varying Missile Model Via Pseudolinearisation

A lateral augmented acceleration autopilot is designed for a model of a tactical missile and robust stability of the closed-loop system investigated. The tail-controlled missile in the cruciform fin configuration is modelled as a second-order quasi-linear parameter-varying system. This nonlinear model is obtained from the Taylor linearised model of the horizontal motion by including explicit dependence of the aerodynamic derivatives on a state (sideslip velocity) and external parameters (longitudinal velocity and roll angle). The autopilot design is based on input-output pseudolinearisation, which is the restriction of input-output feedback linearisation to the set of equilibria of the nonlinear model. The design makes Taylor linearisation of the closed-loop system independent of the choice of equilibria. Thus, if the operating points are in the vicinity of the equilibria, then only one linear model will describe closed-loop dynamics, regardless of the rate of change of the operating points. Simulations for constant lateral acceleration demands show good tracking with fast response time. Parametric stability margins for uncertainty in the controller parameters and aerodynamic derivatives are analysed using Quadratic Lyapunov approach.