Spinning Missile Research Articles

Controller design and stability analysis for spinning missiles via tensor product

In this paper, the controller design and stability analysis for the parameters time-varying model of spinning missiles are investigated. A mathematical model for the spinning missile considering the flight parameters varying with time is proposed. Based on tensor product (TP) model transformation for the spinning missile, the parallel distributed compensation (PDC) state feedback controller is designed, and the stability of the controlled system is analyzed with the tool of linear matrix inequalities (LMIs). Numerical simulations with time-varying parameters are conducted to demonstrate the effectiveness of the proposed controller. The given controller can not only guarantee the steady performance but also the decoupling performance between pitch and yaw channels when used in the flight parameters time-varying spinning missiles.

Numerical Investigation on Transient Effect of Jet Interference Characteristics of Lateral-Jet-Controlled Spinning Missile

At present, there is no publicly published research on the unsteady interference effect in the start-up process of the lateral jet control of the spinning missile. The variation of aerodynamic characteristics during the jet start-up process of the spinning missile is still unclear. Therefore, the unsteady numerical method based on the three-dimensional unsteady compressible Navier–Stokes equations and the sliding mesh method is used to study the unsteady jet interference characteristics of the spinning missile during the starting process of the lateral jet. Based on the verification of the numerical simulation method in this paper, the jet interference flow field under the conditions of non-rotation and rotation is simulated, and the variation of the aerodynamic characteristics of the missile under the two conditions is given. The influence of rotation on the unsteady aerodynamic characteristics of the lateral-jet-controlled spinning missile is analyzed. The flow mechanism resulting in the change of the jet control characteristics and the lateral aerodynamic characteristics of the missile is analyzed through the interference flow field structure at different moments after the jet starts. The results indicate that in the start-up process of pulse jet control, the jet interference characteristics on the fins have a delay effect compared with the projectile body. The duration of the unsteady effect caused by the high-pressure region upstream of the nozzle is shorter than that caused by the low-pressure region downstream of the nozzle. The flow separation and reattachment near the nozzle have strong unsteady characteristics. The jet wake has the most obvious interference effect on Fin1. The pressure on the side of the rotation direction of Fin1 increases, while the opposite side is in contrast.

Single channel digital controller design for a high spinning rate rolling airframe missile

AbstractSpinning/Rolling Airframe Missiles (RAM) mostly use an analog (ON-OFF type) control approach that deflects control surfaces (fins) at minimum and maximum positions continuously, and control is achieved by applying phase shift between the minimum and maximum deflections during a complete roll cycle. Therefore, the control signal shape changes continuously during the roll cycle. In this study, a novel single channel digital controller is designed and tested for a high spinning rate (10–20 Hz) RAM. The digital controller adjusts the amplitude of fin deflections instead of applying a phase shift. In this way, control signal shapes are predetermined in design to completely decouple yaw and pitch dynamics. At the beginning of each roll cycle, the algorithm decides on the control signal shape and amplitude to apply throughout the cycle. Delays on the actuator system and sensor measurements which might lead to instability at high spinning rates are handled effectively thanks to the predetermined control signal shapes that are changing with 90-degree intervals. Detailed geometry of a surface-to-air spinning missile is used to obtain aerodynamic coefficients for the entire flight regime (i.e. from launch to terminal phase) via Missile DATCOM. The 6-DOF flight dynamics model and the controller algorithms are built in MATLAB/Simulink environment. The proposed digital controller is tested systematically for various scenarios and the performance is compared with the conventional analog control approach. The digital controller gives better performance compared to the analog approach under the influence of servo delays and sensor noise.

Magnus Effect over Aerodynamic Components of Spinning Missile

To reveal the flow mechanism of the Magnus effect of the spinning missile, the flow field under supersonic conditions was numerically simulated based on the unsteady Reynolds-time-averaged Navier–Stokes equation, and the implicit dual-time stepping method and sliding mesh method were used. Validation was performed to ensure the reliability of the numerical methods. The results of the numerical simulation and the wind-tunnel experimental data coincided quite well. The aerodynamic characteristics of various configurations while spinning were calculated. The effect of aerodynamic components and aerodynamic interference between components on the Magnus effect were analyzed. The results indicate that for the projectile body, the interference of the canard enlarges the time-averaged side force; when the slenderness ratio becomes large, from the view of the base, the left leeward separation vortex is close to the surface, resulting in a low-pressure region, and the direction of the side force and yawing moment are changed. The fin installation angle can weaken the body Magnus effect to some extent. For the projectile fin, the influence of leeward separation vortices on the fin depends on their relative positions. The fin installation angle can weaken and even cause the reversal of the side force direction.

The aerodynamic characteristics and its estimation method of finned missile experiencing spin-deformation coupling motion

The coupling of rolling motion and bending deformation of a finned missile can significantly affect its lateral force and yawing moment, thus threatening flight stability and maneuverability. By solving the unsteady Reynolds-averaged Navier-Stokes (URANS) equations with a dual-time stepping method and a previously proposed coupling motion mode, flow over the Air Force Modified Basic Finner Missile (AFF) experiencing spin and spin-deformation coupling motion were simulated, and the aerodynamic characteristics were obtained. The relationship between the variation tendency of aerodynamic characteristics and different motion modes was analyzed. On this basis, an aerodynamic model previously proposed by Murphy was revised and a modified model suitable for the aerodynamic prediction of spin-deformation coupling missiles was developed and verified. The results indicate that as angle of attack (AoA) increases, the total time-averaged lateral force induced by spin-deformation coupling motion alters direction and increases by an order of magnitude compared with that induced by spin, and the time-averaged body lateral force becomes dominant. Combining the three aerodynamic components, including that of rigid spinning missile at non-zero AoA, that produced by bending deformation and spin-deformation coupling effect at zero AoA, and that account for the aerodynamic interference effect at non-zero AoA, the accuracy of the modified aerodynamic model can be greatly improved. At forebody cross sections, the results of the modified aerodynamic model and the computational fluid dynamic (CFD) method match well. While at aftbody cross sections, the transient results have certain deviation, while the relative differences for the time-averaged normal force and lateral force are within 10% and 20%, respectively.

Numerical investigation on aerodynamic and inertial couplings of flexible spinning missile with large slenderness ratio

There are aerodynamic and inertial couplings in rigid-body motion and structural vibration of a flexible spinning missile in flight, and when slenderness ratio is larger, the couplings are more obvious. As for the flexible spinning missile with large slenderness ratio, aerodynamic and inertial couplings should be considered. Based on rigid-motion mesh and radial-basis-function (RBF) mesh deformation techniques, unsteady Reynolds-averaged Navier-Stokes (URANS) Equations and flight dynamics equations of flexible spinning missile derived from Lagrange equation are coupled simultaneously to simulate the dynamic response of flexible spinning missile with large slenderness ratio. The URANS equations are solved by Computational Fluid Dynamics (CFD) technique with the in-house code. Not only the aerodynamic coupling between rigid-body six degree of freedom (DOF) motion and structural vibration are included in the flight dynamics equations of flexible spinning missile, but also the variation of inertia tensor and extra moment terms caused by structural vibration are included, too. More importantly, the extra force term caused by angular acceleration of rigid-body motion, Coriolis and centrifugal loading terms caused by angular velocity of rigid-body motion are included. The rigid-motion mesh and RBF mesh deformation techniques are both based on unstructured mesh. The rigid-motion mesh is adopted to treat the large rigid-body motion due to flight dynamics, while the RBF mesh deformation is employed for flexible structural deformation caused by aeroelasticity. Numerical results of free flight case and aeroelastic case are well agreed with the experimental results, which validates the numerical method. A missile model with X-X configuration is constructed to quantitatively investigate the aerodynamic and inertial couplings between rigid-body motion and structural elastic vibration, and aerodynamic force, extra generalized force terms caused by rigid-body motion and extra moment terms caused by structural vibration are all investigated. Final results show that for the critical stable case studied in this paper, the aerodynamic force plays a major role in coupling effects between rigid-body motion and structural vibration, and the inertial coupling terms in rigid-body motion caused by structural vibration are negligible compared with the aerodynamic force. However, the inertial coupling terms in structural vibration due to rigid-body motion are not negligible compared with the aerodynamic force.

Effects of rotational motion on dynamic aeroelasticity of flexible spinning missile with large slenderness ratio

Abstract The structural rigidity of a spinning missile with large slenderness ratio is usually small, and the structural deformation and rate should not be ignored. Furthermore, rotational motion makes the aeroelasticity more complicated. Therefore, unsteady Euler equations and generalized dynamic aeroelastic equations are coupled simultaneously to simulate the dynamic aeroelastic response of a spinning missile with large slenderness ratio using rigid-motion mesh and radial-basis-function (RBF) morphing mesh techniques. The unsteady Euler equations are solved by computational fluid dynamics (CFD) technique by the in-house code. The Coriolis term and centrifugal loading term due to rotational motion are both considered in the generalized dynamic aeroelastic equations. The rigid-motion mesh and RBF morphing mesh techniques are both based on unstructured mesh, and the rigid-motion mesh is adopted to treat the rigid motion due to rotational motion, while the RBF morphing mesh is employed for flexible structural deformation caused by aeroelasticity. Numerical results of aeroelastic case are well agreed with the experimental results, which validates the numerical method. A missile model with X-X configuration is constructed to investigate the effects of rotational motion on dynamic aeroelasticity. The dynamic aeroelastic responses of the missile with and without rotational motion are simulated, respectively. Comparison results show that the lateral modes and longitudinal modes are coupled together because of rotational motion. In addition, the structural natural frequencies are changed due to rotational motion. In the end, detailed numerical analysis of the generalized dynamic aeroelastic equations used in this paper indicates the mechanism by which the rotational motion leads to the coupling of lateral modes and longitudinal modes and changes the structural natural frequencies.

Stability analysis of spinning missiles induced by seeker disturbance rejection rate parasitical loop

This paper focuses on the dynamic stability of spinning missiles equipped with two-loop autopilot considering the seeker disturbance rejection rate parasitical loop (DRRPL) effect induced by attitude disturbance of projectile. The representative mathematical model of spinning missiles in the non-spinning coordinate system is established, and the cross-coupling effect between the pitch and yaw induced by the rotation motion of missile body is analyzed and decoupled. The two-loop acceleration autopilot for each channel is designed with the conventional design method, and the relationship between the autopilot gains and the expected design indexes is deduced. A proportional navigation guidance (PNG) system model with consideration for the seeker DRRPL is further proposed in the form of complex summation. After strict mathematic deduction, the sufficient and necessary condition of the dynamic stability for spinning missiles is obtained. Numerical simulations and discussions under different cases are conducted to demonstrate the validity of stability condition. The results indicate that the stability of a spinning missile is closely related to the amplitude of the seeker DRR, the rolling rate, and the autopilot design indices. The stable region of the autopilot design frequency is obtained by solving the dynamic stability condition. To meet the requirement of stable controlling at a constant spinning rate, it was found to be effective to decrease the amplitude of the seeker DRR for spinning missiles, employ the lead angle decoupling approach to the commands for the servo system, and guarantee that the autopilot design frequency is lower than the critical value. The dynamic stability condition derived in this paper is useful for evaluating the stability of a spinning missile with consideration for the seeker DRRPL, and the conclusions obtained can provide guidance for the autopilot design of spinning missiles.

Nonsingular Fast Terminal Sliding Mode Control for Spinning Missiles Based on Extended State Observer

A backstepping nonsingular fast terminal sliding mode control with the extended state observer (ESO) is proposed for the uncertain factors of nonlinear spinning missile. Based on Lyapunov stability theory, the virtual control as sliding mode is taken in the backstepping design and then the tracking differentiator (TD) is employed to eliminate the “explosion of terms”. In the last step of the backstepping design, nonsingular fast terminal sliding mode control is utilized to drive the angular velocity tracking error to converge to the origin in a finite period of time. To estimate the chattering phenomenon caused by disturbance influence variable in the system, an ESO is applied to estimate and compensate the impact from uncertainties and disturbances. The stability of the closed-loop system is proved. The simulation results show the effectiveness of the proposed control method and the stability of the controller.

Canards interference on the Magnus effect of a fin-stabilized spinning missile

Reynolds-averaged simulations of flow over spinning finned missiles with and without canards were carried out at Ma = 0.6, 0.9, 1.5, and 2.5; α = 4°, 8°, and 12.6°; and [Formula: see text] to investigate different mechanisms of the Magnus effect. An implicit dual-time stepping method and the [Formula: see text] transition model were combined to solve the unsteady Reynolds-averaged Navier–Stokes equations. Grid independence study was conducted, and the computed results were compared with archival experimental data. The transient and time-averaged lateral force coefficients were obtained, and the flow field structures were compared at typical rolling angles. The results indicate that in subsonic conditions, the canards interference intensifies the asymmetrical distortion of the body surface boundary layer and flow separation at different angles of attack, doubling the absolute value of the time-averaged body lateral force; the wash flow effect strengthens on the leeward tail due to the canards interference, increasing its time-averaged lateral force; in supersonic conditions, the shock and expansion waves induced by canards, the vortex system, and the flow separation are responsible for the fluctuation of the body lateral force; the direction of the canard induced wash flow alters as angle of attack increases, increasing first and then decreasing the time-averaged tail lateral force.

Stability of spinning missile with homing proportional guidance law

The terminal proportional guidance loop has been employed by spinning missiles to improve the attacking accuracy. However, it has been observed that the miss distance increases dramatically during the design of the spinning missile with only a guidance loop. Meanwhile, the conventional stability criteria of the guidance loop applicable to the non-spinning missile are no longer valid in the event of the spinning. To address this problem, in this paper, the stability of the spinning missiles with only a 3D proportional guidance loop is analytically derived from system equations in a form of complex summation and the suitable design criteria for the whole proportional guidance loop are also established. Numerical simulations show that during the terminal guidance phase the stable region for the proportional navigation coefficient is reduced with the increase of flight time, which is also shrunk dramatically due to spinning, and the decrease of the critical stable time of spinning missiles results in the increase of miss distance, which exhibit great agreements to those derived from the analytical stability criteria.

Dynamic modeling and stability analysis of a flexible spinning missile under thrust

The general equations of motion of a flexible spinning missile under thrust in the powered flight phase are established and the stability of the motion of the missile is analyzed. The spinning missile is approximated to the unconstrained flexible rotor. Moreover, the thrust in the powered flight phase is deemed as a follower load when the factors of gyroscopic effect, aeroelastic effect, and axial force are considered under the mean axis condition. The equations of motion and stability of the flexible spinning missile in the powered flight phase are then deduced. The stability and dynamic response of the flexible spinning missile under thrust is analyzed through numerical calculation. Calculation results show that thrust, spinning speed, and dynamic pressure exert different influences on the stability of the spinning missile. These factors should be considered and analyzed comprehensively.

Effects of aeroelasticity on coning motion of a spinning missile

The coning motion is a basic angular behavior of spinning missiles. Research on the stability of coning motion is always active. In this paper, the integrated nonlinear governing equations of rigid-elastic angular motion for a spinning missile with high fineness ratio are derived firstly following the Lagrangian approach. Secondly, a set of linear equation is obtained under some assumptions considering the first order vibration mode in the form of complex summation for theoretical analysis. Finally, the sufficient and necessary conditions of coning motion dynamic stability for spinning missile with and without an acceleration autopilot are analytically derived and verified by numerical simulations based on the linear equation. It is concluded that the aeroelasticity can shrink the stable region of the design parameters, even lead to a divergent coning motion.

Coning motion instability of spinning missiles induced by hinge moment

In the flight trials of a spinning missile, it was observed that an unexpected and unstable coning motion occurred after burnout. The missile was still in the free flight phase while the canards kept their original positions by servomechanisms. To address this unstable motion, the governing equation of the coning motion is derived and the dynamics of the fin actuators under the associated hinge moment is taken into account. The necessary and sufficient conditions of the coning motion stability are then analytically derived and further validated through nonlinear six degrees-of-freedom simulations for a representative scenario. It is demonstrated that the hinge moment may lead to the instability of spinning missiles under specific conditions. Finally, the effects of design parameters on the dynamic stability limit are discussed.

Multiple-input describing function technique applied to design a single channel ON-OFF controller for a spinning flight vehicle

In this study, the guidance and control problem of a single-channel spinning missile is investigated. The missile utilizes a single ON-OFF actuator to drive a pair of control surfaces (e.g. elevators) and consequently to perform all required lateral maneouvers. An approximated linear response of the so-called non-rotating frame to ON-OFF input, applied to the rotating frame, is derived using the multiple-input describing function technique. It is shown that there is a relationship between the response of the non-rotating frame and that of the equivalent non-rotating body. It is also shown that the two-channel flight controller, designed for the equivalent non-rotating body, can be reduced to a single-channel controller, the output of which is applied to the rotating body. A necessary condition is introduced for this purpose. A proportional navigation guidance law for such a spinning missile is also introduced that generates an angular rate command instead of the acceleration command. Finally, the performance of the proposed controller in the presence of noise and uncertainties is validated through flight simulations.

Controller Design for Spinning Missile with the Actuator Limit

A nonlinear two time-scale dynamic inversion controller is designed. Actuator saturation in the spinning missile will limit the control commands responses. And the periodic motion and the physical limits of the actuator’s angle and angular velocity would make the respondent pseudo fin deflection angles much different from the desired dynamics. So a kind of command shaping method which limits the fin deflection angle commands in the pseudo body coordinates before the actuator’s limiter is proposed. Meanwhile, a feedback compensation method is applied to eliminate the cross coupling between the pitch and yaw channels in the actuator due to the spinning of the missile. Finally the performance of the controller with the command shaping and decoupling treatment is analyzed.

Ballistic missile detection via micro-Doppler frequency estimation from radar return

The spinning motion of a ballistic missile (BM), which is a kind of micro-Doppler motion, induces additional frequency modulation on the returned radar signal. This modulation period in frequency, called the micro-Doppler modulation frequency, is a stable and unique parameter in radar target recognition. This paper first establishes the radar signal model of the spinning missile during flight, and then extracts the micro-Doppler modulation frequency through analysis of the periodic structure of the resulting spectrogram (short-time Fourier transform (STFT)) - i.e., the time-frequency distribution (TFD). In order to be used for BM target recognition we implemented a data-dependent optimal window length for the STFT. We treated the resultant TFD as an image and then used the 2-D DFT/FFT for feature extraction. Experimental results illustrate the validity of the proposed method.

Feature‐based adaptive mesh refinement for wingtip vortices

AbstractFeature‐based solution‐adaptive mesh refinement is an attractive strategy when it is known a priori that the resolution of certain key features is critical to achieving the objectives of a simulation. In this paper, we apply vortex characterization techniques, which are typically employed to visualize vortices, to identify regions of the computational domain for mesh refinement. We investigate different refinement strategies that are facilitated by these vortex characterization techniques to simulate the flow past a wing in a wind tunnel. Our results, which we compare with experimental data, indicate that it is necessary to refine the region within and near the vortex extent surface to obtain an accurate prediction. Application of the identified mesh refinement strategy also produced observed improvement in the results predicted for a spinning missile with deflected canards. Copyright © 2010 John Wiley & Sons, Ltd.

Critical assessment of hybrid and zonal wall functions for missile aerodynamics simulations

A state-of-the-art wall function near-wall modelling capability was implemented into a general-purpose computational fluid dynamics solver to assess its performance in viscous missile aerodynamics simulations. Test cases included a simple two-dimensional boundary layer, a complex missile configuration with fixed control surfaces, and a spinning missile with dithering canards. Results indicate that judicious use of wall functions may provide a useful compromise between economy and accuracy for viscous missile aerodynamics simulations. However, the results do not indicate a substantial advantage to using any particular version of the wall functions, at least for the test cases addressed in this study.

Coning Motion of Spinning Missiles Induced by the Rate Loop

Rate loops are commonly employed to compensate damping for missiles due to their great effectiveness. However, unexpected coning instability could be induced when the missile is subjected to spinning. The stability condition of coning motion as well as suitable design criteria for spinning missiles with rate loop feedback is established in this paper. Based on the theory of nutation movement, nonlinear equations of motion in terms of the nutation and precession angles are created. The mathematic model of the actuator acting on spinning missiles is also derived. After introducing the complex angle of attack into the system, the governing equations can be simplified to an analytically solvable second-order differential equation with respect to this variable. The proposed method is demonstrated by numerical simulations. It is also found that the upper limit of the critical gain in the damping loops' feedback for the stability decreases dramatically with a spinning missile. The dynamic inverse technique is employed as a remedy and it shows great effectiveness and applicability for the problem discussed in this paper.