基于改进sigmoid函数的非线性跟踪微分器

本文受神经网络中常用的sigmoid激励函数特性的启发,提出了一种形式简单、调参相对容易的非线性跟踪微分器(STD).首先,在sigmoid函数的基础上引入指数和幅度因子,利用改进后的sigmoid函数构造加速度函数,接着,借助Lyapunov直接法证明了所设计的跟踪微分器的非摄动形式具有全局渐近稳定性,随后利用系统等价性给出了跟踪微分器的具体形式并通过扫频测试分析了其频域特性;最后,与线性微分器(LD)、全程快速跟踪微分器(HSTD)以及改进的跟踪微分器(ITD)、反正切形式的跟踪微分器(ATD)分别进行对比仿真分析.结果表明,基于sigmoid函数设计的跟踪微分器可以兼顾响应的快速性以及平稳性、全程无抖振,对信号的广义导数具有良好的逼近能力和滤波效果.     

快速高阶滑模微分器

首先利用Terminal吸引子函数代替高阶滑模微分器中的不连续函数,以避免抖振;然后在高阶滑模微分器每一层滑模面中增加快速收敛项,以提高收敛速度,并分别针对不同情况证明了快速高阶滑模微分器的稳定性,给出了估计误差的具体表达式,提出了一种抑噪设计方法;最后比较了快速高阶滑模微分器与标准高阶滑模微分器的收敛时间和误差,总结了快速高阶滑模微分器的一般设计方法,并通过仿真结果表明了所得结论的正确性和有效性.     

跟踪微分器在航空发动机控制系统中的应用研究

对自发动机转速信号提取转速加速度信息的微分算法进行了研究,对比、分析了跟踪微分器和传统一阶差分算法的性能差异.在此基础上,提出了基于转速补偿的双跟踪微分器算法.仿真研究表明,这一双跟踪微分器的跟随性和稳定性均较为理想.     

基于集成光波导的超快光子微积分运算研究进展

为了克服电子计算的速率瓶颈,采用全光计算可以有效释放光子的巨大带宽资源,同时全光计算在全光通信网络中有着举足轻重的作用,集成光波导器件以其尺寸小、质量轻、功率代价小等优势已经成为最受关注的光子计算芯片资源之一。光子微积分运算是指在光域中直接对输入信号进行微积分数学运算。本文回顾了几种 常见的硅基光波导器件用于光子微积分运算的实现方案,包括高阶光子微分运算、分数阶微分运算、高阶常系数微分方程求解、可重构的一阶常系数微分方程求解,分别采用的硅基集成光子器件包括级联马赫增德尔干涉仪、掺杂型马赫增德尔干涉仪、级联微环谐振器和掺杂型微环谐振器。本文指出利用集成光波导器件来实现光子微积分器势必会成为光子微积分运算的重要发展方向。     

一种非线性系统直接控制方法的分析与改进

本文对文［１］提出的非线性ＰＩＤ控制系统进行了深入的分析，探讨了系统鲁棒性的原因，并在理论分析的基础上提出了一种新的非线性微分器。仿真结果表明，由改进微分器构成的非线性ＰＩＤ控制系统比采用文［１］的办法具有更强的鲁棒性和适应性，而且对反馈回路的噪声有更强的抑制能力。     

带有跟踪微分器的无模型控制器的控制仿真研究

本文介绍了带有跟踪微分器的无模型控制器的基本理论和基本设计方法,比较了该控制方法与非线性跟踪微分器的控制效果.仿真结果表明:带有跟踪微分器的无模型控制器具有的独特的优点,适合于处理带有强干扰以及大时滞系统的控制问题.     

基于跟踪微分器的广义通用模型控制器研究

广义通用模型控制方法是一般模型控制方法的改进，适用于相对阶大于1的被控对象。为克服广义通用模型控制方法要求被控对象状态完全可观测的不足，基于跟踪微分器可以跟踪输入信号，同时估计输入信号微分的特点，将跟踪微分器与广义通用模型控制器相结合，利用跟踪微分器的信号跟踪和微分估计能力，将输出及其微分进行反馈，克服了广义通用模型控制器要求被控对象状态完全可观的局限性。针对相对阶为2的被控对象，仿真实验验证了该方法的有效性和鲁棒性。     

An adaptive sliding mode differentiator for actuator oscillatory failure case reconstruction

This paper proposes an adaptive sliding mode super-twisting differentiator which allows the gains to adapt based on the ‘quality’ of the sliding motion. A Lyapunov based analysis for the adaptive super-twisting scheme is presented to demonstrate its properties. As an example, the adaptive differentiator proposed in this paper has been used as part of a nonlinear FDI scheme for an Oscillatory Failure Case (OFC) in an actuator. The FDI scheme requires an estimate of the rod speed which is provided by the adaptive super-twisting differentiator. Due to the conditions in which the actuator operates, normally the differentiator gains are initialised at low values to ensure good rod speed estimation in fault free conditions. However for large amplitude/frequency OFCs, the gains must adapt in order to maintain sliding and provide a good estimation. Simulations on a high fidelity nonlinear aircraft benchmark model have been carried out for both liquid and solid OFCs.     

非线性跟踪-微分器的性能分析及其改进

对非线性跟踪-微分器的性质进行分析,用适当的指数函数形式取代开关函数,定性地讨论时间尺度的取值问题,使系统在扰动存在的情况下也能满足跟踪要求,同时对跟踪-微分器的稳定性进行了分析.     

Quadrotor trajectory tracking by using fixed-time differentiator

This paper proposes a fixed-time differentiator running in parallel with a feedback linearisation-based controller, which allows quadrotors to track a given trajectory. The fixed-time differentiator estimates outputs’ derivatives in a predefined convergence time, largely compensating for initial condition problems and solving the delay problem. Combined with a state reconstruction step, a whole observer–estimator–controller scheme can be constructed for quadrotors to solve the trajectory tracking problem. Also, an Linear Matrix Inequality (LMI) optimisation-based algorithm to tune parameters of the differentiator is developed here. The high performance of the proposed model is illustrated by numerical simulations.     

Two-dimensional fractional-order digital differentiator design by using differential evolution algorithm

Designing a fractional-order digital differentiator often requires considerably complex mathematical operations and numerical approximations. Thus this paper will propose a simple method to achieve the fractional-order digital differentiator design, particularly for two-dimensional fractional-order differentiators. A two-dimensional finite impulse response (FIR) digital filter structure is utilized and designed so that its corresponding magnitude response can satisfy that of a desired fractional-order differentiator of two variables. The algorithm used to design such two-dimensional digital differentiator is the differential evolution (DE), which is one of evolutionary computations and has excellent searching capacity. The efficiency of the proposed scheme can be confirmed by some illustrative examples.     

基于滤噪微分器的四旋翼飞行器控制

在飞行器的控制中, 角速率反馈可以提高控制系统的动态特性, 但速率陀螺价格昂贵, 且随运行时间的增加其性能会不断下降. 对此本文提出了一种基于滤噪微分器的四旋翼飞行器滑模变结构控制律. 该控制律使用的反馈信号仅由角度传感器得到, 而无需角速率传感器. 控制律中的角速率信息由王新华等设计的有限时间收敛的微分器得到. 本文通过数学证明, 给出了当测量信号中含有噪声时该微分器的理论跟踪误差上界. 仿真以及对四旋翼飞行器滚转姿态的控制实验验证了微分器的抑制噪声作用和控制算法可行性.     

基于反双曲正弦函数的跟踪微分器

反双曲正弦函数是光滑连续函数,具有快速并消除速度高频震颤的作用.利用反双曲正弦函数构造加速度函数,设计二阶跟踪微分器,证明了跟踪微分器的收敛性,并分析了跟踪微分器频域特性.仿真实验表明,该跟踪微分器能对输入信号进行低通滤波,且跟踪精度高,响应速度快;同时,它较好地抑制了微分信号的噪声放大效应,可以得到输入函数理想的微分信号.     

Model-free fractional order differentiator based on fractional order Jacobi orthonormal functions

The aim of this paper is to design an algebraic and robust fractional order differentiator to estimate both the Riemann–Liouville and the Caputo fractional derivatives with an arbitrary order of an unknown signal in noisy environment, without knowing the model defining the signal. For this purpose, a new class of fractional order Jacobi orthonormal functions is firstly introduced. Secondly, the truncated fractional order Jacobi orthonormal series expansion is applied to filter the noisy signal, whose fractional derivative is used to estimate the desired one. Thus, the obtained differentiator is exactly given by an integral formula which depends on a set of design parameters. Thirdly, by applying the generalized Taylor's formula, some error analysis is provided. In particular, error bounds are given, which permit to study the design parameters' influence. Fourthly, a digital fractional order differentiator is deduced in discrete noisy case. Finally, by comparing with two existing fractional order differentiators, numerical results are given to illustrate the accuracy and the robustness of the proposed fractional order differentiator.     

基于非线性参数的电液伺服系统滑模控制

针对在电液伺服系统跟踪控制中存在非线性不确定参数和外界扰动的问题,提出了一种基于积分微分器的滑模Lyapunov函数的控制方法。首先,在只有位移信号测量输出的情况下,采用高阶积分链式微分器对其速度和加速度信息进行预估。系统存在非线性不确定参数,利用微分器对状态和不确定项的实时估计,设计出积分滑模控制器,实现自适应规律以及对电液伺服系统中不确定扰动的抑制。搭建电液伺服系统AMESim模型并与Matlab构成联合仿真平台,对控制器进行仿真。仿真表明,该控制器具有良好的对非线性不确定参数变化的补偿能力和跟踪性能。     

高阶滑模微分器的分析与改进

首先采用Terminal吸引子函数代替原不连续函数,以避免滑模微分器的抖振;然后针对现有文献中高阶滑模微分器设计参数选取苛刻这一问题,放宽了设计参数选择范围,并分不同情况证明了高阶滑模微分器的稳定性．在此基础上,给出了高阶滑模微分器估计误差的上界与设计参数和滑模微分器阶次的关系式;通过对设计参数的选取和系统整体结构的分析,提出了高阶滑模微分器减小估计误差且更适于工程应用的设计方法,并给出所需条件．仿真结果表明了所得结论的正确性和有效性．     

基于改进跟踪微分器的进气压力控制技术研究

高空台进气压力控制系统是高空模拟的关键部分,直接决定了模拟环境的可靠性。然而,其被控对象存在非线性与时滞特性,易导致反馈信号出现相位延迟和受噪声干扰。针对传统方法不能很好解决相位与滤波之间的矛盾,引入Fal函数滤波器,设计了一种改进的跟踪微分器实现对信号的相位补偿和滤波。数值仿真分析表明,改进跟踪微分器比传统相位补偿器具有更强的滤波和相位补偿能力。通过仿真试验证明了改进跟踪微分器在进气压力控制系统中的有效性。该方法可以提升进气压力控制系统的抗干扰能力。     

Output-feedback finite-time stabilization of disturbed LTI systems

Semi-global finite-time exact stabilization of linear time-invariant systems with matched disturbances is attained using a dynamic output feedback, provided the system is controllable, strongly observable and the disturbance has a bound affine in the state norm. The novel non-homogeneous high-order sliding-mode control strategy is based on the gain adaptation of both the controller and the differentiator included in the feedback. A robust criterion is developed for the detection of differentiator convergence to turn on the controller at a proper time.     

Finite-Time-Convergent Differentiator Based on Singular Perturbation Technique

A finite-time-convergent differentiator is presented that is based on singular perturbation technique. The merits of this differentiator exist in three aspects: rapidly finite-time convergence compared with other typical differentiators; no chattering phenomenon; and besides the derivatives of the derivable signals, the generalized derivatives of some classes of signals can be obtained-for example, the generalized derivative of a triangular wave is square wave, etc. The theoretical results are confirmed by computer simulations.     

柴油发动机气缸压力和燃烧始点的辨识

在柴油发动机气缸压力的识别过程中，针对缸盖振动信噪比较低的问题，提出了对RBF网络训练样本进行时域统计平均降噪的方法，同时在对燃烧始点的辨识中应用了Kaiser差分器。时域统计平均有效提高了信号的信噪比，对柴油发动机气缸压力的恢复获得了很好的结果；Kaiser差分器有效提高了对燃烧始点的辨识。通过实践证明，该计算方法可以有效地从柴油发动机缸盖振动信号恢复气缸压力，并进一步辩识燃烧始点。