Asymptotically Stable Motions of a Gyro in a Spinning Vehicle

An analysis of the motion of a single-axis rate gyroscope mounted in a space vehicle which is spinning with uncertain constant angular velocity xz about the spin axis of the gyro is presented. The nonlinearity in the equation of motion of the gimbal is retained. Using the Lyapunov approach, regions are obtained in the k-xz plane where k is the torsional spring constant, for asymptotic stability and for global asymptotic stability, and an estimate of the region of stability in state space is presented. Analytical relations for the selection of the gyro parameters are derived.     

Gyro Motion Boundedness under Uncertain Vehicle Spin and Acceleration

An analysis is presented of the motion of a single axis rate gyroscope mounted in a space vehicle, which is simultaneously accelerating and spinning about the output and spin axis, respectively, of the gyro. The time-varying acceleration and deceleration ?x(t) and the spin rate ?z(t) of the vehicle are unknown but bounded functions of time t. It is shown that the motion of the gyro remains bounded if the bound ?*2 on the uncertainty in ?z(t) does not exceed some threshold ?*2 and that this threshold depends on the various parameters of the gyro. Furthermore, by a proper selection of the gyro parameters, its motion can be forced to remain in a small neighborhood (called region of ultimate boundedness) of the origin in ?-? plane after a certain finite interval of time for any bounded uncertain ?x(t) and ?z(t). Analytical relations are derived for the selection of gyro parameters to keep the error caused in the measurement of the input rate due to ?x and ?z within any given limit.     

Gyro Motion Boundedness under Uncertain Angular Acceleration about Vehicle Output Axis

An analysis of the motion of a single-axis rate gyroscope mounted in a space vehicle which has uncertain time-varying acceleration and deceleration ?x(t) about the output axis of the gyro is presented. Using a Lyapunov function, a condition for boundedness of the gyro motion is derived. It is shown that by a proper selection of the parameters of the gyro, its motion can be forced to remain in a small neighborhood (called region of ultimate boundedness) of the origin in ? - ? plane after a certain finite interval of time for any bounded uncertain ?x(t). Analytical relations for the selection of gyro parameters to keep the error caused in the measurement of the input rate due to ?x within desirable limits are derived.     

Stability of Gyro in a Vehicle Spinning with Uncertain Angular Velocity

The analysis of a single-axis rate gyroscope mounted in a vehicle which is spinning with uncertain angular velocity about the spin axis of the gyro is presented. The nonlinearity in the equation of motion of the gimbal is retained. Using circle criterion, it is shown that the gimbal motion is globally asymptotically stable if Nyquist plot of the linear transfer function of the gyro lies in the interior of a certain disk. A simple analytical relation for the selection of gyro parameters for stability is derived.     

Asymptotically decoupled discontinuous control of systems andnonlinear aircraft maneuver

The question of control of a class of nonlinear systems that can be decoupled by state-variable feedback is considered. Based on variable-structure system theory, a discontinuous control law is derived that accomplishes asymptotic decoupled output trajectory-following in the presence of uncertainty in the system. In the closed-loop system, the trajectories are attracted toward a chosen hypersurface in the state space and then slide along it. During the sliding phase the motion is insensitive to parameter variations. Based on this result, a control law for asymptotically decoupled control of roll angle, angle of attack, and sideslip in rapid, nonlinear maneuvers is derived. Simulation results are presented to show that large, simultaneous lateral and longitudinal maneuvers can be performed in spite of uncertainty in the stability derivatives     

Nonlinear adaptive and sliding mode flight path control of F/A-18 model

The question of inertial trajectory control of aircraft in the three-dimensional space is discussed. It is assumed that the nonlinear aircraft model has uncertain aerodynamic derivatives. The control system is decomposed into a variable structure outer loop and an adaptive inner loop. The outer-loop feedback control system accomplishes (x,y,z) position trajectory and sideslip angle control using the derivative of thrust and three angular velocity components (p,q,r) as virtual control inputs. Then an adaptive inner feedback loop is designed, which produces the desired angular rotations of aircraft using aileron, elevator, and rudder control surfaces to complete the maneuver. Simplification in the inner-loop design is obtained based on a two-time scale (singular perturbation) design approach by ignoring the derivative of the virtual angular velocity vector, which is a function of slow variables. These results are applied to a simplified F/A-18 model. Simulation results are presented which show that in the closed-loop system asymptotic trajectory control is accomplished in spite of uncertainties in the model at different flight conditions.     

Bifurcation analysis of polynomial models for longitudinal motion at high angle of attack

To investigate the longitudinal motion stability of aircraft maneuvers conveniently, a new stability analysis approach is presented in this paper. Based on describing longitudinal aerodynamics at high angle-of-attack (a < 50 ) motion by polynomials, a union structure of two-order differential equation is suggested. By means of nonlinear theory and method, analytical and global bifurcation analyses of the polynomial differential systems are provided for the study of the nonlinear phenomena of high angle-of-attack flight. Applying the theories of bifurcations, many kinds of bifurcations, such as equilibrium, Hopf, homoclinic (heteroclinic) orbit and double limit cycle bifurcations are discussed and the existence conditions for these bifurcations as well as formulas for calculating bifurcation curves are derived. The bifurcation curves divide the parameter plane into several regions; moreover, the complete bifurcation diagrams and phase portraits in different regions are obtained. Finally, our conclusions are applied to analyzing the stability and bifurcations of a practical example of a high angle-of-attack flight as well as the effects of elevator deflection on the asymptotic stability regions of equilibrium. The model and analytical methods presented in this paper can be used to study the nonlinear flight dynamic of longitudinal stall at high angle of attack.     

Adaptive Sliding Control of Six-DOF Flight Simulator Motion Platform

本文使用Newton-Euler法推导了六自由度飞行模拟器运动平台完整的线性化形式的动力学方程,并以此为基础,提出了一种在任务空间中的非线性自适应滑模控制方法。这种控制方法将系统中的不确定性分为定常不确定参数和时变不确定参数,利用非线性自适应控制对定常不确定参数进行辨识,同时结合滑模控制对时变不确定参数和外部扰动进行补偿。通过数值仿真分析表明,该控制策略能准确识别运动平台的载荷、惯量、重心等参数,同时又能有效地提高系统的鲁棒性能。     

Robust sliding-mode control for the uncertain MIMO aircraft model F-18

Robust flight control laws based on variable structure control (VSC) theory and Lyapunov V-function method are designed for a simplified aircraft model F-18. A min-max control (MMC) and VSC laws are derived, for multi-input multi-output (MIMO) systems with plant uncertainties and input disturbance. Two types of robust feedback controllers MMC and VSC for uncertain MIMO systems are considered. For both cases the existence conditions of a stable sliding mode and the robust asymptotic stability in uncertain MIMO systems by MMC and VSC are investigated. For the design of an MMC and VSC, measurable states and sliding surface are chosen so that the zero dynamics of the system are stable. An application of tracking and positioning of VSC of longitudinal dynamics is presented. Finally, simulation results are presented to show the effectiveness of the design methods.     

Dynamic dissipative compensators for multibody flexible spacestructures

The stability characteristics of dynamic dissipative compensators are investigated for multibody flexible space structures having nonlinear dynamics. The problem addressed is that of proving asymptotic stability of dynamic dissipative compensators. The stability proof uses the Lyapunov approach and exploits the inherent passivity of such systems. For such systems these compensators are shown to be robust to parametric uncertainties and unmodeled dynamics. The results are applicable to a large class of structures such as satellites with multiple payloads and space-based manipulators     

Nonlinear Adaptive Robust Force Control of Hydraulic Load Simulator

This paper deals with the high performance force control of hydraulic load simulator. Many previous works for hydraulic force control are based on their linearization equations, but hydraulic inherent nonlinear properties and uncertainties make the conventional feedback proportional-integral-derivative control not yield to high-performance requirements. In this paper, a nonlinear system model is derived and linear parameterization is made for adaptive control. Then a discontinuous projection-based nonlinear adaptive robust force controller is developed for hydraulic load simulator. The proposed controller constructs an asymptotically stable adaptive controller and adaptation laws, which can compensate for the system nonlinearities and uncertain parameters. Meanwhile a well-designed robust controller is also developed to cope with the hydraulic system uncertain nonlinearities. The controller achieves a guaranteed transient performance and final tracking accuracy in the presence of both parametric uncertainties and uncertain nonlinearities; in the absence of uncertain nonlinearities, the scheme also achieves asymptotic tracking performance. Simulation and experiment comparative results are obtained to verify the high-performance nature of the proposed control strategy and the tracking accuracy is greatly improved.     

Energy-saving and accurate motion control of a hydraulic actuator with uncertain negative loads

Pump controlled hydraulic actuators are wildly used in the aerospace industry owing to the advantages of energy-saving and integrated configurations. Negative loads may occur to actuators due to external force loads or the inertial force when the actuator decelerates significantly. Uncertain negative load working conditions may cause cavitation, actuator vibration, and even instability to the motion control if the actuator is without sufficient meter-out damping. Various types of hydraulic configuration schemes have been proposed to deal with negative loads of hydraulic actuators. However, few of them can simultaneously achieve energy saving and high control accuracy. This study proposes an energy-saving and accurate motion tracking strategy for a hydraulic actuator with uncertain negative loads. The actuator’s motion is driven by a servomotor pump, which gives full play to the advantage of energy-saving. The meter-out pressure is controlled by proportional valves to provide the optimized meter-out damping. The nonlinear adaptive robust control law is designed, which guarantees the control stability and achieve high tracking accuracy. An integrated direct/indirect adaptation law obtains satisfactory parameter estimations and model compensation for asymptotic motion tracking. Comparative experiments under different working conditions were performed to validate the advantages of the proposed control strategy.     

Multiple-Model Probability Hypothesis Density Filter for Tracking Maneuvering Targets

Tracking multiple targets with uncertain target dynamics is a difficult problem, especially with nonlinear state and/or measurement equations. With multiple targets, representing the full posterior distribution over target states is not practical. The problem becomes even more complicated when the number of targets varies, in which case the dimensionality of the state space itself becomes a discrete random variable. The probability hypothesis density (PHD) filter, which propagates only the first-order statistical moment (the PHD) of the full target posterior, has been shown to be a computationally efficient solution to multitarget tracking problems with a varying number of targets. The integral of PHD in any region of the state space gives the expected number of targets in that region. With maneuvering targets, detecting and tracking the changes in the target motion model also become important. The target dynamic model uncertainty can be resolved by assuming multiple models for possible motion modes and then combining the mode-dependent estimates in a manner similar to the one used in the interacting multiple model (IMM) estimator. This paper propose a multiple-model implementation of the PHD filter, which approximates the PHD by a set of weighted random samples propagated over time using sequential Monte Carlo (SMC) methods. The resulting filter can handle nonlinear, non-Gaussian dynamics with uncertain model parameters in multisensor-multitarget tracking scenarios. Simulation results are presented to show the effectiveness of the proposed filter over single-model PHD filters.     

Fuzzy robust nonlinear control approach for electro-hydraulic flight motion simulator

A fuzzy robust nonlinear controller for hydraulic rotary actuators in flight motion simulators is proposed. Compared with other three-order models of hydraulic rotary actuators, the proposed controller based on first-order nonlinear model is more easily applied in practice, whose control law is relatively simple. It not only does not need high-order derivative of desired command,but also does not require the feedback signals of velocity, acceleration and jerk of hydraulic rotary actuators. Another advantage is that it does not rely on any information of friction, inertia force and external disturbing force/torque, which are always difficult to resolve in flight motion simulators. Due to the special composite vane seals of rectangular cross-section and goalpost shape used in hydraulic rotary actuators, the leakage model is more complicated than that of traditional linear hydraulic cylinders. Adaptive multi-input single-output(MISO) fuzzy compensators are introduced to estimate nonlinear uncertain functions about leakage and bulk modulus. Meanwhile, the decomposition of the uncertainties is used to reduce the total number of fuzzy rules. Different from other adaptive fuzzy compensators, a discontinuous projection mapping is employed to guarantee the estimation process to be bounded. Furthermore, with a sufficient number of fuzzy rules, the controller theoretically can guarantee asymptotic tracking performance in the presence of the above uncertainties, which is very important for high-accuracy tracking control of flight motion simulators.Comparative experimental results demonstrate the effectiveness of the proposed algorithm, which can guarantee transient performance and better final accurate tracking in the presence of uncertain nonlinearities and parametric uncertainties.     

陀螺动力学系统计算机仿真

推导出了适于计算机仿真的陀螺完整运动方程式并给出了仿真曲线,可看出在外力矩作用下陀螺仪从起动到稳定这一段时间内的转动角速度和转角的变化规律。通过降低陀螺转速并减小外力矩,使无锁紧机构的陀螺仪消除起动时的剧烈抖动而达到平稳起动的目的。     

弹性飞行器纵向稳定性问题

 本文研究考虑气动弹性时飞行器的纵向稳定性问题。首先由弹性飞行器的纵向扰动运动方程出发,导出了便于计算采用的弹性飞行器纵向扰动方程的标准矩阵形式,作出作为控制对象的弹性飞行器在考虑一阶、二阶及三阶振型时的传递函数;其次分析气动弹性对整个飞行器系统的稳定性的影响,并提出对飞行器自动驾驶仪敏感元件的可能合适位置选择的要求。最后还建立了计算气动弹性对飞行器气动导数值影响的理论式。     

Experimental investigation of influence of strake wings on self-induced roll motion at high angles of attack

The modern high performance air vehicles are required to have extreme maneuverability,which includes the ability of controlled maneuvers at high angle of attack. However, the nonlinear and unsteady aerodynamic phenomena, such as flow separation, vortices interaction, and vortices breaking down, will occur during the flight at high angle of attack, which could induce the uncommanded motions for the air vehicles. For the high maneuverable and agile air missile, the nonlinear roll motions would occur at the high angle of attack. The present work is focused on the selfinduced nonlinear roll motion for a missile configuration and discusses the influence of the strake wings on the roll motion according to the results from free-to-roll test and PIV measurement using the models assembled with different strake wings at a = 60°. The free-to-roll results show that the model with whole strake wings(baseline), the model assembled with three strake wings(Case A)and the model assembled with two opposite strake wings(Case C) experience the spinning, while the model assembled with two adjacent strake wings(Case B), the model assembled with one strake wing(Case D) and the model with no strake wing(Case E) trim or slightly vibrate at a certain "×"rolling angle, which mean that the rolling stability can be improved by dismantling certain strake wings. The flow field results from PIV measurement show that the leeward asymmetric vortices are induced by the windward strake wings. The vortices would interact the strake wings and induce crossflow on the downstream fins to degrade the rolling stability of the model. This could be the main reason for the self-induced roll motion of the model at a = 60°.     

Inertial System Platform Rotation

Differential error equations are derived for the navigation errors of a local level undamped pure inertial platform that continuously rotates in azimuth. From these, the time response equations for the vector position error produced by a constant level gyro drift error, as a function of platform rotation rate, are computed and evaluated. It is shown that platform rotation attenuates the system position error due to level gyro bias and that this attenuation is a nonlinear function of rotation rate.     

Stability of a Magnetic Suspension Device

This paper presents an analysis of a magnetic suspension device which is used in place of mechanical bearings for the gyro rotors of inertial guidance systems. A formula for the suspension device's strength is derived, the criteria for the device's stability is given, and the device's potential instability (when that criteria is violated) is explained. Data are given of an experiment which confirms the analysis of this instability.     

Aeroservoelastic stability analysis for flexible aircraft based on a nonlinear coupled dynamic model

A unified theoretical aeroservoelastic stability analysis framework for flexible aircraft is established in this paper. This linearized state space model for stability analysis is based on nonlinear coupled dynamic equations, in which rigid and elastic motions of aircraft are both considered. The common body coordinate system is utilized as the reference frame in the deduction of dynamic equations, and significant deformations of flexible aircraft are also fully concerned without any excessive assumptions. Therefore, the obtained nonlinear coupled dynamic models can well reflect the special dynamic coupling mechanics of flexible aircraft. For aeroservoelastic stability analysis, the coupled dynamic equations are linearized around the nonlinear equilibrium state and together with a control system model to establish a state space model in the time domain. The methodology in this paper can be easily integrated into the industrial design process and complex structures. Numerical results for a complex flexible aircraft indicate the necessity to consider the nonlinear coupled dynamics and large deformation when dealing with aeroservoelastic stability for flexible aircraft.