基于神经网络的跟踪-微分器设计

针对自抗扰控制的跟踪-微分器模块中存在着待定参数的问题,借助人工神经网络便于建立非线性映射的思想,提出了基于神经网络的跟踪-微分器的设计方法.运用该方法可以对任意阶的跟踪-微分器进行参数设计,设计出的跟踪-微分器具有良好的鲁棒性.仿真实验表明,由该设计方法设计出的跟踪-微分器能够提供精确的微分信号,有一定的工程应用参考价值.     

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.     

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.     

改进的非线性跟踪微分器设计

在对典型跟踪微分器深入研究的基础上,提出一种改进的非线性跟踪微分器.该跟踪微分器综合了线性跟踪微分器和非线性跟踪微分器的优点,不但无颤振现象,而且具有良好的动态响应和较强的滤波能力,兼顾了快速性和准确性的要求,可实现任意信号的跟踪和微分.该跟踪微分器形式简单、易于实现.仿真结果表明,改进型非线性跟踪微分器具有优良的性能.     

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。     

高精度快速非线性离散跟踪微分器

对二阶连续系统最速控制设计中采用的综合函数作了分析, 得到了一种新的高精度、快速离散非线性跟踪微分器, 并对其滤波特性、微分提取特性进行了初步分析. 分析表明, 这种跟踪微分器对输入信号具有很好的跟踪能力, 能够滤除噪声和提取微分信号. 相位延迟小, 幅值衰减小, 因而具有跟踪的快速性、准确性. 最后, 给出了数值仿真例子来验证该算法; 并给出了一个实验结果, 证实了算法的可行性.     

反正切形式跟踪微分器设计及相平面分析

跟踪微分器可以从不连续或含有噪声的测量信号中提取连续滤波信号和微分信号. 本文从二阶跟踪微分器的加速度函数式入手, 提出一种反正切形式的跟踪微分器结构, 利用李雅普诺夫第二方法证明其具有全局一致渐进稳定性, 利用相平面分析方法研究, 说明原点是稳定结点或稳定焦点, 并给出跟踪微分器参数调节的定性规律和约束条件. 最后在含有噪声的方波输入下进行仿真, 结果表明反正切形式跟踪微分器可以兼顾跟踪快速性与过渡过 程平稳性, 并且具有很好的滤波效果, 可以给出连续平滑的跟踪信号和微分信号, 而且待调节的参数较少, 具有工程实用价值.     

基于微分器与神经网络的PID控制算法研究

在工控系统微分器设计优化问题的研究中,由于在工业生产实践中,传统PID参数整定方法难以得到合理优化的PID参数,传统增量式PID控制存在抗干扰性较差、控制精度不高的问题.针对上述问题,提出了基于跟踪微分器与神经网络的PID控制算法.对跟踪微分器的原理进行了阐述,通过跟踪微分器实现位置信号滤波与速度信号求解;对增量式自适应PID控制算法进行了改进.在上述基础上,构建了基于微分跟踪器与神经网络的PID控制器.对控制算法进行了仿真,仿真结果表明,提出的控制算法具有抗扰动能力强、控制精度高等优点.     

某型航空涡轴发动机起动过程控制研究

针对涡轴发动机起动过程复杂的特点,提出了"跟踪-微分器"的二阶动态结构来对其加速过程进行控制;首先,在对涡轴发动机起动过程分析的基础上,给出了其起动控制逻辑;其次,通过对起动过程主燃油供油系统规律分析,给出了起动过程的供油计划,并采用"跟踪-微分器"的二阶动态结构来求取转速加速度;最后,对所研究的涡轴发动机起动过程控制规律进行了仿真验证;仿真结果表明,所设计的过程控制方法满足起动时限的要求,且不超温超转,达到了系统设计要求。     

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.     

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.     

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.     

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.     

A robust controller for trajectory tracking of a DC motor pendulum system

This work presents a solution to the output feedback trajectory tracking problem for an uncertain DC motor pendulum system under the effect of an unknown bounded disturbance. The proposed algorithm uses a Proportional Derivative (PD) controller plus a novel on-line estimator of the unknown disturbance. The disturbance estimator is obtained by coupling a standard second-order Luenberger observer with a third-order sliding modes differentiator. The Luenberger observer provides estimates of the motor angular position and velocity. Moreover, an ideal disturbance estimator in terms of the Luenberger observer error and its first and second time derivatives is obtained from the observer error formulae; these time derivatives are not available from measurements. Subsequently, the sliding modes third-order differentiator allows obtaining estimates of these time derivatives in finite time. The estimates replace the real values of the first and second time derivatives in the ideal disturbance estimator thus producing a practical disturbance estimator, and also permit obtaining an estimate of the motor angular velocity. A depart from previous approaches is the fact that the disturbance is not directly estimated by the Luenberger observer or the third-order differentiator. Numerical simulations and real-time experiments validate the effectiveness of the proposed approach.     

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.     

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。     

一种基于边界特征的简易非线性二阶离散跟踪微分器的设计

用等时区方法确定最速离散二阶系统的线性区域的边界,以开关曲线和边界线来界定控制量的线性变化,区分可达区和线性区,得到最速系统综合函数,并依此构造线性函数形式的跟踪微分器.仿真结果表明,所提出的跟踪微分器具有快速跟踪输入信号、无颤振、无超调的特点,能得到较好的微分信号,算法简洁实用.     

Active disturbance rejection control for nonlinear fractional‐order systems

This paper investigates active disturbance rejection control involving the fractional‐order tracking differentiator, the fractional‐order PID controller with compensation and the fractional‐order extended state observer for nonlinear fractional‐order systems. Firstly, the fractional‐order optimal‐time control scheme is studied to propose the fractional‐order tracking differentiator by the Hamilton function and fractional‐order optimal conditions. Secondly, the linear fractional‐order extend state observer is offered to acquire the estimated value of the sum of nonlinear functions and disturbances existing in the investigated nonlinear fractional‐order plant. For the disturbance existing in the feedback output, the effect of the disturbance is discussed to choose a reasonable parameter in fractional‐order extended state observer. Thirdly, by this observed value, the nonlinear fractional‐order plant is converted into a linear fractional‐order plant by adding the compensation in the controller. With the aid of real root boundary, complex root boundary, and imaginary boot boundary, the approximate stabilizing boundary with respect to the integral and differential coefficients is determined for the given proportional coefficient, integral order and differential order. By choosing the suitable parameters, the fractional‐order active disturbance rejection control scheme can deal with the unknown nonlinear functions and disturbances. Finally, the illustrative examples are given to verify the effectiveness of fractional‐order active disturbance rejection control scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

时滞对象的自抗扰控制

时滞系统的控制在自动化领域具有重要意义。在剖析时滞系统控制的Smith预估法的本质的基础上,提出利用具有强大噪声抑制能力的"跟踪微分器"来实现"相位超前"、"相位滞后"等功能,从而解决时滞系统控制问题的新办法,其中包括把时滞算子近似成单位1的无视时滞法;把时滞算子近似成一阶惯性环节的提高阶次法;模仿Simith预估法把相位超前的虚拟输出当作被控量来进行无时滞对象控制的输出超前法;及引入虚似控制量的输入超前法等。相应的仿真研究表明,这些新方法都能控制好大时滞系统的控制问题,时滞大小已不再成为"难控"和"易控"的标准。