Optimal feedback gains of a delayed proportional-derivative(PD) control for balancing an inverted pendulum

In the dynamics analysis and synthesis of a controlled system, it is important to know for what feedback gains can the controlled system decay to the demanded steady state as fast as possible. This article presents a systematic method for finding the optimal feedback gains by taking the stability of an inverted pendulum system with a delayed proportional-derivative controller as an example. First, the condition for the existence and uniqueness of the stable region in the gain plane is obtained by using the D-subdivision method and the method of stability switch. Then the same procedure is used repeatedly to shrink the stable region by decreasing the real part of the rightmost characteristic root. Finally, the optimal feedback gains within the stable region that minimizes the real part of the rightmost root are expressed by an explicit formula. With the optimal feedback gains, the controlled inverted pendulum decays to its trivial equilibrium at the fastest speed when the initial values around the origin are fixed. The main results are checked by numerical simulation.

Fixed-Time Stabilization of a Class of Strict-Feedback Nonlinear Systems via Dynamic Gain Feedback Control

This paper presents a novel fixed-time stabilization control(FSC)method for a class of strict-feedback nonlinear systems involving unmodelled system dynamics.The key feature of the proposed method is the design of two dynamic parameters.Specifically,a set of auxiliary variables is first introduced through state transformation.These variables combine the original system states and the two introduced dynamic parameters,facilitating the closed-loop system stability analyses.Then,the two dynamic parameters are delicately designed by utilizing the Lyapunov method,ensuring that all the closed-loop system states are globally fixed-time stable.Compared with existing results,the“explosion of complexity”problem of backstepping control is avoided.Moreover,the two designed dynamic parameters are dependent on system states rather than a time-varying function,thus the proposed controller is still valid beyond the given fixedtime convergence instant.The effectiveness of the proposed method is demonstrated through two practical systems.

High-Speed Trains Automatic Operation with Protection Constraints: A Resilient Nonlinear Gain-based Feedback Control Approach

This paper addresses the control design for automatic train operation of high-speed trains with protection constraints.A new resilient nonlinear gain-based feedback control approach is proposed,which is capable of guaranteeing,under some proper non-restrictive initial conditions,the protection constraints control raised by the distance-to-go(moving authority)curve and automatic train protection in practice.A new hyperbolic tangent function-based model is presented to mimic the whole operation process of high-speed trains.The proposed feedback control methods are easily implementable and computationally inexpensive because the presence of only two feedback gains guarantee satisfactory tracking performance and closed-loop stability,no adaptations of unknown parameters,function approximation of unknown nonlinearities,and attenuation of external disturbances in the proposed control strategies.Finally,rigorous proofs and comparative simulation results are given to demonstrate the effectiveness of the proposed approaches.

Analysis of gain distribution in cladding-pumped thulium-doped fiber laser and optical feedback inhibition problem in fiber-bulk laser system

The steady-state gain distribution in cladding pumped thulium-doped fiber laser（TDFL） is analytically and numerically solved based on the rate equations including loss coefficients and cross relaxation effect. With the gain curve, a problem, which is named optical feedback inhibition（OFI） and always occurs in tandem TDFL-Ho：YAG laser system, is analyzed quantitatively. The actual characteristics of output spectra and power basically prove the conclusion of theoretical analysis. Then a simple mirror-deflected L-shaped cavity is employed to restrain the external feedback and simplify the structure of fiber-bulk Ho：YAG laser. Finally, 25 W of 2097-nm laser power and 51.2% of optical-to-optical conversion efficiency are obtained, and the beam quality factor is less than 1.43 obtained by knife-edge method.

高超声速飞行器指定时间时变高增益反馈跟踪控制

研究了高超声速飞行器控制通道存在未知环境干扰时的指定时间跟踪控制问题.基于高超声速飞行器的输入输出线性化模型,借助参量Lyapunov方程的一些性质,设计一种光滑、有界的时变高增益控制律.相比于现有的高超声速飞行器有限/固定时间控制方法,该算法不会出现抖振现象,同时收敛时间不依赖于初始状态且可以事先设定.当高超声速飞行器存在未知的有界环境匹配干扰时,该控制器能使高度和速度在指定时间跟踪上参考信号.仿真结果验证了方法的有效性.

Optimal feedback based control for Mars entry trajectory tracking

The various uncertainties of Mars environment have great impact on the process of vehicles entering the atmosphere.To improve the robustness of control system against the model errors and to reduce the computational burden, an optimal feedback based tracking control law is developed. The control scheme presented in this paper determines the amplitude and the reversals of bank angle respectively in the longitudinal and lateral flight plane. At each control cycle, the amplitude of the bank angle is obtained by an optimal feedback controller to minimize tracking errors. The control gains are tuned according to the closed-loop error dynamics by using optimization methods. The bank reversals are executed if the crossrange exceeds a predetermined corridor which is designed by setting a boundary function. The accuracy and robustness of the proposed closed-loop optimal feedback based control law in tracking the reference trajectory is verified via500 deviation simulations, in which modeling errors and external disturbances are considered.

感应电机全阶磁链观测器反馈矩阵增益研究

基于自适应全阶磁链观测器的感应电机无编码器矢量控制技术在工业电气传动领域获得广泛应用,其反馈矩阵增益对于提高感应电机控制性能至关重要。根据速度估算系统的稳定性条件推导出反馈增益设计要求,获得特定的反馈增益以保证系统的完全稳定性。在DSP控制平台上通过欧拉法对全阶磁链观测器进行离散化,利用7.5 kW的感应电机对拖机组对推导的反馈增益有效性进行了实验验证。结果表明,该速度估算系统能保证电机在全调速范围内稳定运行。

基于AD9361的快速增益控制研究

研究了AD9361的自动增益控制(AGC)模式和手动增益控制(MGC)模式,分析了两种模式的优、缺点,对AGC模式的闭环反馈时间进行了实际测试验证;针对AGC模式闭环反馈时间长的缺点,提出了一种基于MGC模式的快速增益控制策略,并进行了工程测试验证,可有效提高增益控制的闭环反馈时间,广泛应用于无线电导航和无线通信信号的抗干扰接收。

基于未知多智能体系统的新型增益控制策略

针对一类具有未知状态与磁滞输入的多智能体系统稳定性问题,提出了一种基于新型时变增益的自适应控制方案。该方案包括构建新型高增益观测器、整合所有未知项并在微分控制环节中进行统一处理,以及调整时变增益信号中的补偿参数实现输入信号的波形降噪与上、下限约束。通过应用这一控制方案,可以实现系统的一致稳定性,还可有效降低微分控制环节中的计算量。除此之外,在系统频率响应的允许范围内调整补偿参数,可以实现输入降噪与上、下限约束。仿真实验结果表明,该方案成功实现了系统输入波形的上、下限约束和降噪优化,同时能够降低微分控制环节的计算量,提高系统的鲁棒性和适应性。

Robust Output Feedback Control for a Class of Nonlinear Systems with Input Unmodeled Dynamics

The robust global stabilization problem of a class of uncertain nonlinear systems with input unmodeled dynamics is considered using output feedback, where the uncertain nonlinear terms satisfy a far more relaxed condition than the existing triangulartype condition. Under the assumption that the input unmodeled dynamics is minimum-phase and of relative degree zero, a dynamic output compensator is explicitly constructed based on the nonseparation principle. An example illustrates the usefulness of the proposed method.

Spatially Inhomogeneous Gain Modification in Photonic Crystals

The electric and magnetic energy distributions in photonic crystals （PC） are calculated by using the plane wave expansion （PWE） method. Even though the total electric and magnetic energy in each unit cell of photonic crystals are equal to each other, the ratio of electric and magnetic energy densities varies depending on the local position. Based on Fermi＇s golden rule, the optical gain is analysed in the full quantum framework that takes the nonuniform energy density ratio into account. This nonuniform energy density ratio in photonic crystals, defined in an equal form as gain modification factor, leads to spatially inhomogeneous modification of optical gain. Results reported in the paper provide a new perspective for analysing gain characteristics, as well as the lasing properties, in photonic crystals.

Output Feedback Nonlinear General Integral Control

This paper proposes an output feedback nonlinear general integral controller for a class of uncertain nonlinear system. By solving Lyapunov equation, we demonstrate a new proposition on Equal ratio gain technique. By using Equal ratio gain technique, Singular perturbation technique and Lyapunov method, theorem to ensure regionally as well as semi-globally exponential stability is established in terms of some bounded information. Moreover, a real time method to evaluate the ratio coefficients of controller and observer are proposed such that their values can be chosen moderately. Theoretical analysis and simulation results show that not only output feedback nonlinear general integral control has the striking robustness but also the organic combination of Equal ratio gain technique and Singular perturbation technique constitutes a powerful tool to solve the output feedback control design problem of dynamics with the nonlinear and uncertain actions.

一种高增益、高带宽全差分运算放大器的设计

采用增益提升(Gain-boosting)技术,使用2个三输入管的折叠式共源共栅运算放大器(运放)作为辅助运放,设计了一种宽输入共模范围的高增益、高带宽的全差分运算放大器。主运放输入部分由一对NMOS管和一对PMOS管共同构成,其输入跨导提高至由单MOS管构成的运放输入跨导的2倍。主运放输入跨导的提高间接提升了主运放的增益和带宽。而辅助运放在不改变主运放带宽的同时,通过降低主运放的主极点增大输出阻抗,再次提升主运放的增益,达到了高增益、高带宽的目的。该运算放大器采用商用55 nm CMOS工艺设计,经仿真可得,当负载电容为5 pF时,运放低频增益为115 dB,增益带宽积为209 MHz,总功耗为2.8 mW。

走向卓越的教学:学生视角下优质讲授的生成机制研究

优质讲授是影响本科教学质量的重要因素,可以显著提升学生的课堂感知与教育获得感,但它常被忽视而处于被边缘化的境地。通过采用回忆性叙事和非结构访谈的质性研究方法收集16位大学生的调查资料,从学生视角考察优质讲授的特征及生成机制,结果发现,优质讲授彰显出教师人格魅力渗透形塑、课堂讲授主动建构和学生课堂反馈调试三个特征,它以“教师人格魅力”为基石,以“课堂讲授”为保障,以“课堂反馈”为检验,探索教学过程全域互动、双向交流反馈新机制,打破了传统低质课堂的束缚和藩篱,给有效教学找到一个切入点和突破口。教师通过倾注个体特征的情感教学、注重自主创设的情境教学和“以学生为中心”的理念教学搭建新型教学模式,生成优质讲授,实现“教”“学”有效互动,由此耦合成高质量的课堂教学图景。为打造优质讲授,切实提升高校课程育人成效,教师需要引领课堂教学,塑造并突显人格魅力,做好教学设计,推行系列教学整体实施方案,聚焦学生中心观的教学理念,采用灵活多样的教学策略,把握好教学节奏,以切实提升学生的教育获得感。

基于极值搜索的四旋翼无人机姿态跟踪控制

针对具有不确定性四旋翼无人机姿态跟踪问题,提出了基于极值搜索的鲁棒控制方法。首先,建立四旋翼无人机非线性姿态模型,并考虑模型参数的不确定性,设计鲁棒控制器来确保跟踪误差动态的有界性。然后,将鲁棒控制器与无模型学习算法结合,设计基于学习的控制器,从而自动迭代地调整鲁棒控制器的反馈增益,并在线优化期望性能成本函数。最后,通过MATLAB进行数值仿真,所述控制方法的系统稳态跟踪误差相较于经典鲁棒控制方法降低了0.246,证明了所述方法鲁棒性和优越性。

基于动态转矩反馈的机械臂柔性系统振动抑制

针对机械臂关节伺服系统由于谐波减速器、齿皮带等柔性环节的存在使系统发生机械振动现象,建立了考虑刚度系数变化和大减速比的数学模型,分析机械谐振产生机理,提出了一种动态转矩反馈的控制策略,由扰动观测器实时观测动态转矩构成动转矩闭环。为进一步抑制振动现象,增强系统鲁棒性和抗扰能力,研究了随动态转矩实时调整的转速变增益PI控制方法。仿真表明,采用动态转矩反馈的转速变增益PI控制策略能够很好地抑制机械振动且有较强的抗扰能力和动态响应性能。

基于混合狼群算法的永磁同步电机状态反馈控制

为提高永磁同步电机的控制精确,减少超调带来的影响,提出了一种基于混合狼群算法的状态反馈控制。以通过电压前馈补偿的线性化的永磁同步电机模型为基础,构建含有转子转速误差和d轴电流误差的离散增广状态空间模型,并构建状态反馈控制器;利用混合狼群算法,通过优化寻求状态反馈控制增益矩阵的全部参数,添加超调惩罚项减少超调带来的影响;算法继承灰狼算法与郊狼算法的优点,同时保证算法的快速收敛性与全局性。基于Matlab/Simulink进行仿真验证,并与其它控制器进行比较,结果表明带有惩罚项的状态反馈控制器具有快响应,零超调的优越性。

鸭式导弹自动驾驶仪开环截止频率的设计约束

极点配置方法在三回路驾驶仪设计中应用较广,针对开环截止频率这一关键参数的设计约束较为模糊。通过建立控制增益、闭环极点与系统开环截止频率的解析关系,将控制系统设计问题转化为开环截止频率的合理选择。结合鸭式布局导弹工程设计经验,分别讨论了舵机带宽、舵偏角速率、闭环零点和控制增益极性对开环截止频率选取的约束准则和工程应用修正,通过典型条件验证了该准则的适用性。