一种新型正弦跟踪微分器的研究与应用

过程信号的微分计算在控制工程领域有广泛的应用,但经典微分运算方法存在显著的噪声干扰放大效应.文中通过分析一种经典微分器的变形结构以及对象阶跃激励响应和斜坡激励响应的正弦滤波信号成分的构成,指出在较高的滤波频率下,可通过信号的正弦滤波或余弦滤波提取这些过程信号的微分信号.提出了一种由正弦滤波器和新型正弦跟踪器所构成的新型微分信号提取方法.该方法有效提高了提取微分信号的质量,与理想微分信号相比的近似度较高.文中提出的微分方法具有良好的抗噪声干扰特性,是线性滤波技术的发展与延伸,并具有良好的理论意义和实际应用前景,可作为经典控制理论的有益补充.数学分析、仿真实验和实际应用结果进一步证实了文中所述方法的正确性和有效性.     

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.     

基于跟踪微分器的四旋翼飞行器控制器

研究小型四旋翼飞行器导航控制优化问题.针对当前许多控制方法需要四旋翼飞行器速度信号,四旋翼无人机无法获取速度信号情况下,传统控制方法便会失效,为解决上述问题,提出采用跟踪微分器的输出反馈控制器.跟踪微分器估算出四旋翼飞行器的速度值,实现无法获取速度信号下的位置和姿态控制,并对基于微分跟踪器的控制器进行了设计和仿真.仿真结果表明上述控制方法和跟踪微分器观测的速度信号的有效性和可行性.     

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.     

基于非线性干扰观测器的高超声速飞行器滑模反演控制

针对高超声速飞行器非线性、强耦合和参数不确定弹性体模型,提出了一种基于非线性干扰观测器的滑模反演控制方法.将飞行器曲线拟合模型分解为速度子系统和高度相关子系统并表示为严格反馈形式,分别采用滑模和反演方法设计实际控制量与虚拟控制量.采用1阶低通滤波器获取虚拟控制量的导数,解决了传统反演控制方法"微分项膨胀"问题.基于改进滑模微分器设计了一种新型非线性干扰观测器,以此对模型不确定项进行估计和补偿.仿真结果表明,该控制器对模型不确定性和气动弹性影响具有鲁棒性,且实现了对速度和高度参考输入的稳定跟踪.     

An approach to improve active disturbance rejection control

ABSTRACT

In order to reduce the error and phase delay of the classical extended state observer (ESO) in estimating the system state and disturbance, in this paper, we combine ESO and tracking differentiator (TD) to construct a tracking differential extended state observer (TDESO). The observation error and observation speed of TDESO are also discussed. Then a nonlinear active disturbance rejection control system improved by TDESO for a linear plant is transformed into a Lurie system. Moreover, the circular criterion is used to analyse the absolute stability of the transformed Lurie system. Finally, TDESO is optimised and an improved linear state error feedback (PLSEF) is proposed to improve the rapidity of the system by using simulation and time domain analysis. And a second-order system is used to illustrate the performance of the proposed scheme. The simulation results show that our algorithm is effective.     

含高阶干扰的非仿射非线性系统自适应跟踪控制

本文考虑了一类带有高阶干扰和未知参数的非仿射非线性系统的自适应跟踪控制问题.为了提高系统的抗干扰性能,首先设计了扩张状态滤波器估计系统受到的高阶干扰,并把干扰估计值引入到控制器中.其次,在每一步递推设计中,为了避免backstepping方法固有的"微分爆炸"问题,引入滑模微分器估计虚拟控制律的微分,进而提出了一种新的自适应控制策略.借助Lyapunov函数理论方法分析了闭环系统的稳定性,即在所提控制策略作用下,可保证闭环系统所有信号是一致最终有界的.最后,利用MATLAB仿真验证了方法的有效性.     

Global second‐order sliding mode control for nonlinear uncertain systems

Second‐order sliding mode (SOSM) control is used to keep exactly a constraint σ of the second relative degree or to avoid chattering phenomenon. Yet, the traditional SOSM controllers are designed based upon the assumption that the uncertainties or their derivatives are bounded by positive constants. In this paper, a global SOSM controller is designed for a general class of single‐input–single‐output nonlinear systems with uncertainties bounded by positive functions. Moreover, a variable‐gain robust exact differentiator is developed such that the SOSM controllers with finite‐time convergence can also be implemented even when the derivative of the constraint σ is unavailable. Simulation results are given to show the effectiveness of the proposed method.     

Sliding Mode Differentiator Based Tracking Control of Uncertain Nonlinear Systems with Application to Hypersonic Flight

This paper presents a performance‐guaranteed adaptive back‐stepping design for a class of nonlinear systems with uncertainties and disturbances. To circumvent the increasing complexity caused by the repeated analytic differentiations in back‐stepping, sliding mode differentiation technique is employed to estimate the derivative of the virtual control. Compared with the well‐known command filtered back‐stepping, no compensating signal is required. Besides, time‐varying parameters, system uncertainties and external disturbances are compensated using nonlinear damping technique, while the output tracking error is regulated in the prescribed range with the adjustable convergence speed and steady‐state error. As a verification example, this method is applied to the longitudinal control of an air‐breathing hypersonic vehicle configured with the variable geometry inlet.     

Fast terminal sliding‐mode finite‐time tracking control with differential evolution optimization algorithm using integral chain differentiator in uncertain nonlinear systems

This paper presents a fast terminal sliding‐mode tracking control for a class of uncertain nonlinear systems with unknown parameters and system states combined with time‐varying disturbances. Fast terminal sliding‐mode finite‐time tracking systems based on differential evolution algorithms incorporate an integral chain differentiator (ICD) to feedback systems for the estimation of the unknown system states. The differential evolution optimization algorithm using ICD is also applied to a tracking controller, which provides unknown parametric estimation in the limitation of unknown system states for trajectory tracking. The ICD in the tracking systems strengthens the tracking controller robustness for the disturbances by filtering noises. As a powerful finite‐time control effort, the fast terminal sliding‐mode tracking control guarantees that all tracking errors rapidly converge to the origin. The effectiveness of the proposed approach is verified via simulations, and the results exhibit high‐precision output tracking performance in uncertain nonlinear systems.