Analysis of a Class of Nonlinear Sampled-Data Systems with a Gaussian Input Signal

The problem treated here is the analysis of a class of nonlinear sampled-data systems with a Gaussian input signal. The nonlinear element is a symmetrical limiter (memoryless device) that feeds the linear element. Preceding the limiter is a sampler and zero-order hold unit for data reconstruction. The analysis is predicated on finding an equivalent gain for the nonlinear element such that the mean-square error is a minimum. The nonlinearity is thus replaced by a linear component and the system is then analyzed by conventional techniques. It is also shown that for appropriate sampling rates the sampled-data system is equivalent to a continuous system due to the action of the sampler-hold combination. All calculations pertaining to the limiter input signal require the use of a transfer function that is interior to the feedback loop. However, in developing this transfer function, the overall system is considered so that the system output may be evaluated after the value of equivalent gain has been found.     

Helicopter Motion: Equation Linearization

The nonlinear set of equations which represent helicopter motion is linearized about a prescribed nominal state. Once the linearized system is obtained it is validated by comparing the output of the nonlinear system to that of its linearized counterpart. Having obtained a linear model, linear system theory may then be applied in order to investigate the stability and control characteristics of the aircraft.     

电动静液作动器非线性框图建模与鲁棒控制方法

 阐述了机载电动静液作动器（EHA）的典型工作原理与结构特点,根据其元部件数学方程,建立非线性精确框图模型,完善了EHA补油回路和摩擦特性的描述。通过对系统阻尼、稳态误差及摩擦的仿真分析,设计了一种结合动态压力反馈与变增益控制策略的状态反馈控制器,改善了系统动、静态性能。鲁棒性测试结果反映了系统参数不确定性对性能的影响。     

一种求取发动机状态变量模型的改进拟合法

采用的拟合辨识方法是直接对根据状态变量模型中各变量间的线性关系对系数矩阵进行拟合,并且实现对稳态过程和瞬态过程进行分步拟合,从而消除瞬态误差对稳态精度的影响.本方法有接近传统最小二乘法的精度,并且无需求解状态变量模型微分方程或使用迭代算法,只需要进行简单的矩阵运算即可得到各系数矩阵,因此计算效率远高于传统最小二乘法.同时,该方法也可与其他拟合方法结合使用从而进一步提高拟合精度.最后,应用该方法建立了某涡轴发动机的小偏差状态变量模型,通过与非线性模型仿真结果比较,验证了该方法的有效性,即使对象非线性较强,该方法也能得到精度较高的拟合效果.      

非线性椭球集员滤波及其在故障诊断中的应用

 针对带有未知但有界噪声的非线性系统，提出一种椭球集员滤波算法，并将其应用于保证故障检测与隔离。对非线性状态方程和量测方程进行泰勒展开之后，通过区间分析的方法给出线性化余项存在区域的盒子外界描述。假设过程和量测噪声由盒子限界，在算法的时间更新和量测更新过程中，分别计算包含椭球与线段的向量和及椭球与带的交的次最小容积椭球。在椭球集员滤波算法的基础之上，给出传感器故障检测与隔离的方法。由于集员滤波是保证状态估计，因而基于集员滤波算法的故障检测与隔离方法也具有保证性，即如果发出故障警报，则一定有故障发生。一个二维非线性系统的例子说明了该方法的有效性。     

Interlaced Kalman filtering of 3D angular motion based on Euler'snonlinear equations

A novel Kalman filtering technique is presented that reduces the mean-square-error (MSE) between three-dimensional (3D) actual angular velocity values and estimated ones by an order of magnitude (when compared with the MSE resulting from direct measurements) even under extremely low signal-to-noise ratio conditions. The filtering problem is nonlinear in nature because the dynamics of 3D angular motion are described by Euler's equations. This nonlinear set of differential equations state that the angular acceleration in one axis is proportional to the torque applied to that axis, and to the products of angular velocity components in the other two axes of rotation. Instead of using extended Kalman filtering techniques to solve this complex problem, the authors developed a new approach where the nonlinear Euler's model is decomposed into two pseudolinear models (primary and secondary). The first model describes the time progression of the state vector containing the linear terms, while the other characterizes the propagation of the state vector containing the nonlinearities. This makes it possible to run two interlaced discrete-linear Kalman filters simultaneously. One filter estimates the values of the state vector containing the linear terms, while the other estimates the values of the state vector containing the nonlinear terms in the system. These estimates are then recombined, solving the nonlinear estimation process without linearizing the system. Thus, the new approach takes advantage of the simplicity, computational efficiency and higher convergence speed of the linear Kalman filter form and it overcomes many of the drawbacks typical of conventional extended Kalman filtering techniques. The high performance and effectiveness of this method is demonstrated through a computer simulation case study     

线性拟合法建立航空发动机状态变量模型

针对非线性拟合法建立航空发动机状态变量模型过程中的初值问题,提出了一种能够避免该问题的线性拟合法,即在离散域情况下,利用已知的状态序列来构建系统矩阵与模型响应之间呈线性关系的目标函数,从而使非线性最小二乘问题转化为线性最小二乘问题.应用该方法建立某型涡扇发动机的小偏差状态变量模型,并与非线性拟合法进行了对比研究,结果表...     

Pseudo-linear inertial navigation algorithm

A new method is illustrated for processing the output of a set of triad orthogonal rate gyros and accelerometers to reconstruct vehicle navigation parameters (attitude, velocity, and position). The paper introduces two vectors with dimensions 4 × 1 as velocity and position quaternions. The navigation equations for strapdown systems are nonlinear but after using these parameters, the navigation equations are converted into a pseudo-linear system. The new set of navigation equations has an analytical solution and the state transition matrix is used to solve the linear time-varying differential equations through time series. The navigation parameters are updated using the new formulation for strapdown navigation equations. Finally, the quaternions of velocity and position are converted into the original position and velocity vectors. The combination of the coning motion and a translational oscillatory trajectory is used to evaluate the accuracy of the proposed algorithm. The simulations show significant improvement in the accuracy of the inertial navigation system, which is achieved through the mentioned algorithm.     

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.     

液体火箭发动机燃烧室的一种分区模型

发展了燃烧室的分区模型 :将燃烧室分为两个区 ,一个是燃烧区 ,采用时滞燃烧瞬时均匀混合模型 ,另一个是流动区 ,连同喷管一起 ,采用一维理想气体流动的有限元状态变量模型。给出了一个利用该模型计算发动机起动过程的一个算例 ,计算结果表明该模型可较好地描述液体火箭发动机燃烧室的建压及非稳态流动过程。模型采用状态方程形式 ,具有形式简单、计算简便的特点 ,适用于液体火箭发动机的控制与仿真     

基于LMI极点配置的高空台飞行环境模拟系统PI增益调度控制研究

针对高空台飞行环境模拟系统的温度和压力在整个工作包线内的鲁棒性能控制问题，提出了一种基于LMI极点配置的PI增益调度控制设计方法。在考虑变比热容腔微分方程、管道热传导、调节阀流量特性、液压伺服动态、传感器增益对飞行环境模拟系统造成的建模不确定性的基础上，建立了完整、准确的飞行环境模拟系统非线性模型；对非线性模型进行了线性化，并根据线性模型推导了基于LMI极点配置的PI控制器设计算法；在飞行环境模拟系统的工作包线内选取了36个稳态点设计了基于LMI极点配置的PI增益调度控制器；设计了两种飞行环境模拟试验来验证设计的PI增益调度控制器的鲁棒性能。仿真结果表明，飞行环境模拟系统温度的稳态误差和动态误差均小于0.1%，压力的稳态误差小于0.5%，动态误差小于0.7%。     

Current Injected Equivalent Circuit Approach to Modeling Switching DC-DC Converters

A new current injected equivalent circuit approach (CIECA) to modeling switching dc-dc converter power stages is developed, which starts with the current injected approach and results in either a set of equations which completely describe input and out-put properties or an equivalent linear circuit model valid at small signal, low frequency levels. This approach to modeling switching dc-dc converter power stages has the merits but not the demerits of both the electronic equivalent circuit state space average approach and the current injected control type approach, namely, 1) the modeling is very clear and is simple whether the converter operates in continuous or discontinuous inductor conduction modes, 2) the modeling results in an equivalent circuit which is very close to the actual converter, and 3) the equivalent circuit can be used directly in the computer for theoretical predictions like SPICE, etc.     

航空发动机过渡态最优控制规律设计的新方法

针对航空发动机过渡态最优控制规律的设计问题,提出了一种新的方法——动态稳定法:在发动机动态特性计算模型的基础上,通过额外提取其中所有的状态量变化率,使其共同工作方程组的偏差趋于0,从而让过渡态仿真稳定下来,此时的稳态参数值即为对应过渡态工作点的各项参数;然后分别根据指定的物理约束条件,通过简单的静态迭代优化即可直接建立相应的控制规律;最后将这些控制规律通过取大/小的方式进行合并,从而获得所需过渡态最优控制规律.以某型涡扇发动机最优加速控制规律的改进设计为例,结果表明该方法具有设计精度高、实现简单以及快速直观等优点.      

Limit cycle oscillation control of wing with static output feedback control method

This paper presents a static output feedback controller (SOFC) for aeroelastic control of a cantilevered rectangular wing in low subsonic flow. For this purpose, an optimal formulation of this control method is developed, and a solution method is proposed for the related matrix equation. This optimal solution is obtained by solving combined Lyapunov and Riccati equations. At first these equations are transformed into a set of nonlinear algebraic equations and then are solved with iterative Newton–Raphson?s method. This solution method is applicable to the full state feedback case. The controller is designed to extend flutter boundary and suppress limit cycle oscillation (LCO) of a low aspect ratio rectangular nonlinear structural wing. This structural nonlinearity is given by Von Karman plate theory. Both full and reduced order aerodynamic models are examined based on the modified vortex lattice theory. Results show combination of SOFC with reduced order aerodynamic model would be an effective choice for aeroelastic stabilization, and this controller has a very comparable result with linear quadratic regulator (LQR).     

一种航空发动机的分段实时线性动态模型

针对喷口不可调涡扇发动机实时线性动态模型的建立问题,提出了一种基于粒子群优化算法小偏差状态空间模型的方法.选取高压转子换算转速为增益调度参数,根据发动机相似原理,建立了发动机全飞行包线分段实时线性模型.全飞行包线内所提出的分段实时线性模型与非线性模型仿真对比结果表明:涡扇发动机高压压气机出口总压、低压涡轮出口温度、高压转子转速和低压转子转速的最大相对误差不超过3.5%,仿真结果验证了该方法的有效性.      

直升机飞行动力学高阶线性系统建模

针对常规单旋翼带尾浆直升机,从复杂的飞行动力学非线性数学模型入手,采用数值方法在平衡点处求出线性模型;该线性模型包括传统的６自由度刚性机体模型,还包括主桨和尾浆动力入流、主桨和尾桨挥舞自由度,其状态空间形式具有２５个状态变量（５简称２５状态模型）。以某型直升机为例,对线性模型与非线性模型的时域动态响应,及２５状态高阶线性模型和传统６自由度９状态模型的特征值进行了比较,验证了建模方法的可靠性和精度。     

Flyback Converter Output Voltage Stabilization

The expression of the flyback converter output voltage (output power) is derived as a function of the supply voltage, load resistance, transformer ratios, transistor current gain, and base-circuit resistor value. Switching period and duty cycle are also calculated. A converter circuit is designed having stabilized output voltage, with respect to supply voltage, at constant load. The transistor base current is controlled by the supply voltage, via a nonlinear circuit. This feedforward circuit approximates with logarithmic characteristics the ideal hyperbolic dependence of the transistor base current as a function of the supply voltage. The converter has high performance and low cost. A cheaper circuit variant is presented, in which the high-voltage control transistor was eliminated.     

基于模糊奇偶方程的非线性系统传感器故障诊断

 给出了一种非线性系统传感器的故障诊断方法。该方法将T-S 模糊模型、全解耦奇偶方程和参数估计相结合,同时对非线性系统的多个传感器的故障进行检测、隔离与识别。设计出用于产生残差的线性系统全解耦奇偶方程,并给出了全解耦奇偶向量的存在条件,全解耦奇偶方程产生的残差仅对一个传感器故障敏感,而对系统状态、扰动输入和其它传感器输出解耦。引入T-S 模型将全解耦奇偶方程推广到非线性系统中得到了模糊奇偶方程。传感器的故障模型表示为刻度因子和偏差的形式,根据残差信息应用卡尔曼估计方法可识别出故障模型的参数。最后给出了某型号飞机控制系统传感器的故障诊断仿真实例。     

Gain self-scheduled H_∞ control for morphing aircraft in the wing transition process based on an LPV model

This article investigates gain self-scheduled H 1 robust control system design for a tailless fold- ing-wing morphing aircraft in the wing shape varying process. During the wing morphing phase, the aircraft’s dynamic response will be governed by time-varying aerodynamic forces and moments. Nonlinear dynamic equations of the morphing aircraft are linearized by using Jacobian linearization approach, and a linear parameter varying (LPV) model of the morphing aircraft in wing folding is obtained. A multi-loop controller for the morphing aircraft is formulated to guarantee stability for the wing shape transition process. The proposed controller uses a set of inner-loop gains to provide stability using classical techniques, whereas a gain self-scheduled H 1 outer-loop controller is devised to guarantee a specific level of robust stability and performance for the time-varying dynamics. The closed-loop simulations show that speed and altitude vary slightly during the whole wing folding process, and they converge rapidly after the process ends. This proves that the gain self-scheduled H 1 robust controller can guarantee a satisfactory dynamic performance for the morphing aircraft during the whole wing shape transition process. Finally, the flight control system’s robustness for the wing folding process is verified according to uncertainties of the aerodynamic parameters in the nonlinear model.     

实现复杂控制计划的控制通道增益匹配方法

通过航空发动机控制系统的非线性数字仿真，发现对于同一控制变量制定的复杂控制计划不能由多个控制器实现，这个问题可以通过控制通道的增益匹配得到解决。给出了频域和时域的两种控制通道增益匹配的方法。仿真表明，经过控制通道的增益匹配能够实现所制定的复杂控制计划，同时可以大幅度地简化控制系统的控制逻辑，使得所设计的控制系统更具工程实用性。