Liangyu Zhao

Stability of Spinning Missiles with an Acceleration Autopilot

noticed that the stable region of the design parameters for the autopilot shrinks significantly under the spinning condition. It is also observed that the stable region for design parameters is further narrowed when an integrator is introduced into the acceleration loop while the steady-state accuracy is dramatically improved. A simple decoupling method of setting a lead angle for the commands to the servosystem is demonstrated to be effective to correct the crosscoupling and to extend the stability region for design parameters of the autopilot.

Three-loop autopilot of spinning missiles:

The three-loop autopilot is employed by spinning missiles as well as by many high-performance command or homing guidance missiles currently because it performs well in stabilizing airframe and implementing guidance commands. However, for spinning missiles, the closed-loop system may be dynamically unstable in the form of a divergent coning motion due to the existence of cross-coupling effects. And the stability criteria of the autopilot applicable to the nonspinning missile are no longer valid in the event of the spinning. To address this issue, the structure of a three-loop autopilot of spinning missiles is introduced in this study, for which the sufficient and necessary condition of coning motion stability is analytically derived from the equations in the form of complex summation. The stability criteria are further illustrated by numerical simulation. It is noticed that spinning shrinks the stable region of the design parameters significantly. And the higher the spinning rate, the smaller the stable region becomes.

Modeling and Attitude Control of a Spinning Spacecraft with Internal Moving Mass

An attitude control system of a spinning spacecraft with internal moving mass is presented in this paper. This system consists of a rigid body and two internal radial moving masses. The mathematical model, including attitude kinematics and nonlinear dynamics equations, is established based on Newtonian mechanics. The control law is designed based on the linear-quadratic-regulator (LQR) theory. The performance of the controller is demonstrated in numerical simulation, and the response shows that the attitude control system is stable and effective.

Uncertainty Quantification of a Flapping Airfoil with a Stochastic Velocity Deviation Based on a Surrogate Model

A practical flapping wing micro aerial vehicle should have ability to withstand stochastic deviations of flight velocities. The responses of the time-averaged thrust coefficient and the propulsive efficiency with respect to a stochastic flight velocity deviation under Gauss distribution were numerically investigated using a classic Monte Carlo method. The response surface method was employed to surrogate the high fidelity model to save computational cost. It is observed that both of the time-averaged thrust coefficient and the propulsive efficiency obey a Gauss-like but not the exact Gauss distribution. The effect caused by the velocity deviation on the time-averaged thrust coefficient is larger than the one on the propulsive efficiency.

Retuning the actuator proportional–integral–derivative controller of spinning missiles:

The hinge moment acting on the actuator will cause an out-of-plane moment, which is a destabilizing factor to the angular motion of spinning missiles. A new tuning criterion for the actuator controller is proposed to decrease the out-of-plane moment. It is noted that the integral element does not decrease the out-of-plane moment. A carefully designed proportional–derivative controller with some compromises can ensure the stability of the missile and provide good performance for the actuator.

Transient energy growth in flow past a rotating cylinder

After devoting to asymptotical instability for decades, the hydrodynamic community noticed that non-normality of the evolution operator for perturbations may have dominant effects over limited time horizons by inducing significant transient energy growth, especially in linearly stable/weakly unstable flows. In flow past a rotating cylinder, it has been observed that the unsteadiness and asymptotical instability associated with vortex shedding are suppressed over a wide range of the ratio between the rotating velocity and free stream velocity. In this work, we investigate the transient energy growth of initial perturbations in this stabilized flow and the physical relevance of the optimal initial perturbation. The nonlinear development of the initial perturbations is further studied by evolving the base flow initially perturbed by the optimal initial perturbation in DNS (Direct Numerical Simulation). As the initial perturbation is convected downstream, it is observed that the vortex shedding reassumes transiently.

Adaptive Acceleration Autopilot Design for Terminal Guidance of a Spinning Rocket Projectile

With extending range of modern unguided rocket projectiles, the dispersion is also becoming larger. An acceleration autopilot during terminal guidance is able to reduce the dispersion, improve the accuracy and comprehensive performance of a spinning rocket projectile. However, an autopilot designed at a given point can not reach good performance because the aerodynamic forces\moments and Mach number vary greatly during the terminal guidance. Via gain scheduling, an adaptive acceleration autopilot of the spinning rocket projectile is designed with considering the coupling of the servo system. The numerical simulations show that this acceleration autopilot is effective and adaptable.

Coning Motion Instability of a Spinning Missile Induced by Aeroelasticity

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 governing equations of rigid and flexible angular motions of a spinning missile with high fineness ratio are derived following the Lagrangian approach and the assumed mode method. The aeroelastic stability of the coning motion is comprehensively investigated by means of numerical simulations with taking the spinning rate as the key parameter. In case of the same dynamical coefficients, the coning motion is stable if the spinning missile is considered as a rigid body. However, it is observed that the aeroelasticity can slow down the convergent speed even pull the angular motion to be divergent, whether the spinning missile is uncontrolled or controlled.

Uncertainty Quantification for a Flapping Airfoil with Chordwise Flexure

The uncertainty quantification for a flexible flapping airfoil was investigated using the point-collocation non-intrusive polynomial chaos method. The chordwise flexible amplitude was assumed to obey a normal distribution. It is observed that the time-averaged thrust coefficient obeys a Gauss-like but not the exact Gauss distribution, while the probability of the propulsive efficiency is much different from the exact Gauss distribution. The effect of the chordwise flexure on the time-averaged thrust coefficient is much larger than the effect on the propulsive efficiency. This work could be a preparation for the robust design of a flexible flapping wing with respect to a stochastic chordwise flexure.

Topology Optimization of a Flapping Wing using Equivalent Static Loads

The flapping wing of a micro air vehicle is optimized to enhance performance while some rigidity is kept with minimum mass. A work flow for the design of the flapping wing is defined. The performances to be enhanced are thrust coefficient and propulsive efficiency. The flapping kinematics of the flapping wing is determined by solving a path optimization problem which maximizes the performances. The optimization process is carried out based on a well defined surrogate model. The surrogate model is made from the results of two-dimensional fluid dynamic analysis. The Kriging method is employed to establish the surrogate model and a genetic algorithm is utilized for the multi-objective function problem. Dynamic topology optimization is performed to find the distribution of reinforcement. Certain rigidity can be kept by the results of topology optimization. A dynamic topology optimization method is developed by modification of the equivalent static loads method for non linear static response structural optimization. Three-dimensional computational fluid dynamic analysis is performed based on the optimum values of the path optimization to evaluate the external loads for the topology optimization process. It is found that the topology results are quite similar to the practical product. The process of the defined work flow is materialized by interfacing various software systems.