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.

Multiplicity-induced optimal gains of an inverted pendulum system under a delayed proportional-derivative-acceleration feedback

This paper studies the stabilization to an inverted pendulum under a delayed proportional-derivative-acceleration(PDA)feedback,which can be used to understand human balance in quiet standing.The closed-loop system is described by a neutral delay differential equation(NDDE).The optimal feedback gains(OFGs)that make the exponential decaying rate maximized are determined when the characteristic equation of the closed-loop has a repeated real root with multiplicity 4.Such a property is called multiplicity-induced dominancy of time-delay systems,and has been discussed intensively by many authors for retarded delay differential equations(RDDEs).This paper shows that multiplicity-induced dominancy can be achieved in NDDEs.In addition,the OFGs are delay-dependent,and decrease sharply to small numbers correspondingly as the delay increases from zero and varies slowly with respect to moderate delays.Thus,the inverted pendulum can be well-stabilized with moderate delays and relatively small feedback gains.The result might be understandable that the elderly with obvious response delays can be well-stabilized with a delayed PDA feedback controller.

Designing Discrete Predictor-Based Controllers for Networked Control Systems with Time-varying Delays:Application to A Visual Servo Inverted Pendulum System

A discrete predictor-based control method is developed for a class of linear time-invariant networked control systems with a sensor-to-controller time-varying delay and a controller-to-actuator uncertain constant delay,which can be potentially applied to vision-based control systems.The control scheme is composed of a state prediction and a discrete predictor-based controller.The state prediction is used to compensate for the effect of the sensor-to-controller delay,and the system can be stabilized by the discrete predictor-based controller.Moreover,it is shown that the control scheme is also robust with respect to slight message rejections.Finally,the main theoretical results are illustrated by simulation results and experimental results based on a networked visual servo inverted pendulum system.

A SPECTRAL METHOD FOR A WEAKLY SINGULAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATION WITH PANTOGRAPH DELAY

In this paper,a Jacobi-collocation spectral method is developed for a Volterraintegro-differential equation with delay,which contains a weakly singular kernel.We use a function transformation and a variable transformation to change the equation into a new Volterra integral equation defined on the standard interval[-1,1],so that the Jacobi orthogonal polynomial theory can be applied conveniently.In order to obtain high order accuracy for the approximation,the integral term in the resulting equation is approximated by Jacobi spectral quadrature rules.In the end,we provide a rigorous error analysis for the proposed method.The spectral rate of convergence for the proposed method is established in both the L^(∞)-norm and the weighted L^(2)-norm.

Robust Dichotomy Solution-Based Model Predictive Control for the Grid-Connected Inverters with Disturbance Observer

This paper proposes a robust dichotomy-based model predictive control(DS-MPC)with a fixed switching frequency for the grid-connected inverter(GCI).The proposed fast dichotomy algorithm can select and deduce the optimal voltage vector dynamically through the space vector plane.Therefore,the proposed DS-MPC strategy could ensure dynamic performance and steady-state performance as well.Also,the current control robustness can be improved through DS-MPC with disturbance observer(DO)based on the extended Kalman filter(EKF).The novelty of this control is that the current control with fast dynamic response can be realized in the weak grid,even if the grid voltages are greatly distorted.Simulation and hardware experiments on the weak grid validate the effectiveness of the proposed DS-MPC with the EKF observer approach.

Correlations between delayed fluorescence of chlorophyll, metabolism and yield of plants. II. Influence of moisture of leaf and temperature condition on delayed fluorescence of leaves

During various temperatures of incubation the dehydration of leaves up to 3.2-3.8% mainly in-duced increase maximum amplitude of delayed fluorescence of chlorophyll. It was shown that moisture loss with this range could be deter-mined for the most part by the growth of the electrochemical potential of thylakoid mem-branes. The further incubation of detached leaves at 36℃ temperature, with more notable moisture loss, resulted in specific its decline as opposed to cases of 22 and 6℃ of thermal in-cubation. It was confirmed that the increased temperatures and moisture loss damage of the cells of plants occurred together induce a greater influence on plants than in case of oc-curring apart. The results allow to suppose that this can be mostly caused weakly associated polypeptides fallen out from the chloroplast membrane, which may be stipulated by high temperature combined with change ionic and osmotic stresses due moisture loss. Simulta-neously, the results showed that the exposure of the critical lowered air temperature led to considerable typical changes of leaves delayed fluorescence parameters of field plants. There-fore, their use can constitute new approaches to elucidate the molecular basis of plant freezing tolerance in a timely manner, based on concen-tration-related changes and the efficiency of coupling between light and dark processes of plants.

弱电网下基于电网电压前馈的并网逆变器阻抗重塑控制策略

弱电网下,锁相环在基波以上频段引入的负阻特性,会降低系统输出阻抗的相位,严重影响系统稳定性。鉴于此,该文通过系统控制框图等效变换,推导得到可以消除锁相环负阻特性的电网电压前馈函数,进而提出一种基于电网电压前馈控制的并网逆变器阻抗重塑控制策略。同时,为了提高该策略的普适性,该文利用函数近似和多目标约束为电网电压前馈函数的优化提供两种设计方法,并从系统基波电流跟踪性能、并网功率因数等方面进行误差分析,从而证明其函数优化设计方法的可行性。理论分析表明,优化后的电网电压前馈控制策略,可以有效地对系统输出阻抗相位特性进行重塑,很大程度上拓宽了系统对电网阻抗的适应范围。最后,通过仿真与实验验证所提控制策略的有效性。

计及锁相环非线性特性的跟网型逆变器暂态稳定性分析

锁相环作为跟网型逆变器实现相位同步的关键环节,由于其本身所固有的非线性特性,在弱电网情况下,传统小信号模型可能存在不能准确预测锁相环暂态稳定性的问题。为保证受扰后锁相环的稳定运行,提出了一种基于非线性数学模型的稳定性分析方法。首先,根据锁相环工作原理,建立其二阶非线性微分方程,通过相平面法对锁相环输出特性进行定性分析,评估不同参数对锁相环暂态特性的影响;然后,基于等面积法则分析锁相环暂态失稳机理,鉴于传统等面积法则可能导致稳定性的误判,采用非线性动力学多尺度法对锁相环受扰后的暂态时域表达式进行求解,明确锁相环暂态稳定边界;最后,通过Matlab仿真和RT⁃LAB半实物平台验证了所得解析解和锁相环暂态稳定域的准确性,为弱电网条件下锁相环控制参数及电路参数选取提供一定参考。

开环同步型单相并网逆变器小干扰建模与弱电网下稳定性分析

单相并网逆变器中,多采用锁相环(phase-lockedloop,PLL)型闭环同步方法,但PLL引入的低频段负阻特性不利于系统稳定性,在电网阻抗较大时并网逆变器易发生严重失稳。对此,国内外广泛开展了PLL优化或替代技术的研究。其中,开环同步(open-loop synchronization,OLS)方法的无反馈结构使得其自身是完全稳定的,近年来得到了较多关注。然而,OLS结构中非线性特性明显,如何获得准确的小干扰线性化模型仍非常困难,OLS型单相并网逆变器在弱电网下的稳定性仍不清晰。鉴于此,重点研究开环同步型单相并网逆变器小干扰建模与稳定性。借鉴谐波线性化思想,提出OLS的线性化建模方法,建立开环同步型单相并网逆变器的输出阻抗模型。在此基础上,讨论OLS型单相并网逆变器的鲁棒性。较大电网阻抗下,采用OLS的开环同步型单相并网逆变器系统仍有良好的稳定性。通过仿真和对比实验验证上述模型的准确性以及弱电网下OLS的适应性。

弱电网下提升并网逆变器无源性的网侧有源阻尼策略

为抑制“双高”背景下新型电力系统中日趋复杂的电网背景谐波,并网系统通常需要在已有控制方案基础上附加PCC节点电压前馈策略。而现有研究表明,在弱电网下由于并网逆变器与电网阻抗之间的相互作用,该策略会降低并网逆变器等效输出阻抗在中低频段内的无源性,易引发并网系统产生宽频谐振问题。针对这一问题,通过建立弱电网下并网逆变器系统等效输出阻抗模型剖析了传统PCC节点电压前馈策略在抑制电网背景谐波方面的优点及固有缺陷;并在此基础上基于无源性理论提出了一种新型网侧有源阻尼策略,该策略通过在电容支路增加有源补偿装置与主逆变器附加控制相结合,不仅实现了并网逆变器系统等效输出阻抗在宽频段范围内的充分无源,且能有效抑制电网背景谐波,提高并网系统在弱电网下的稳定性与适应性。通过搭建系统仿真模型对所提控制策略在并网逆变器接入弱电网时的有效性进行了验证。

基于双二阶滤波器的LCL型并网逆变器延时补偿方法

为了抑制LCL型滤波器的谐振尖峰,电容电流反馈有源阻尼被广泛应用于LCL型并网逆变器中。由于数字控制延时带来的不利影响,电容电流反馈有源阻尼的阻尼性能被严重削弱。负阻尼区域出现在f_(s)/6到f_(s)/2之间,减弱了并网逆变器的稳定性和对电网阻抗变化下的鲁棒性。在电容电流反馈通道上插入一个双二阶滤波器来补偿数字控制延时带来的相位滞后,正阻尼范围可以扩展到f_(s)/3,从而实现了对电网阻抗变化的高鲁棒性。选择了合适的离散化方法,分析了补偿后的系统稳定性。提出了一个详细的闭环参数设计流程,以获得良好的控制性能。最后,实验结果验证所提方法的有效性和参数设计流程的可行性。

新能源并网逆变器的阻尼互济控制策略

光伏与风电换流站近区并网发电可在一定程度上实现新能源随机波动情况下的电能互补。然而,新能源密集汇入电网易触发宽频振荡风险。目前,常采用逆变器阻抗重塑法抑制电压源逆变器–电网耦合系统宽频振荡现象,但该方法对高频谐振抑制有限。对此,提出一种新能源逆变器的阻尼互济控制策略,利用光伏和风电在时间尺度上的互补特征,将光伏和风电逆变器在间歇阶段重塑为阻抗适配装置,在风光能量互补的同时,实现了阻尼互济,综合抑制新能源并网发电引发的宽频振荡现象。最后,基于RT-Box实验平台验证了所提控制策略的有效性。

计及锁相环动态的单相并网逆变器建模及稳定性研究综述

随着可再生能源渗透率的提高,电网呈现出高电网阻抗的弱电网甚至极弱电网特征,锁相环与电网阻抗交互作用将恶化跟网型逆变器低频稳定性。近年来,诸多文献针对单相跟网型逆变器中的低频振荡问题进行了研究,但缺乏对现有成果系统性地梳理和总结,难以明确进一步的研究重点。为此,该文首先梳理和评述现有计及锁相环影响的逆变器建模及稳定性分析方法,直观地阐述锁相环引起的负阻效应对系统低频稳定性的影响机制,并在此基础上,从改进电流控制环和锁相环角度,系统性地归纳和分析现有各种低频鲁棒性提高方法。最后,总结现有研究在稳定性分析及鲁棒性改进上的不足及研究关键点和难点,指出进一步的研究方向。

弱电网下LCL逆变器的有源阻尼控制策略研究

在弱电网中,由于电网阻抗的存在,会导致新能源并网LCL滤波器固有谐振频率发生偏移,传统有源阻尼控制策略则无法保证系统的稳定性。而且随着新能源发电在电力系统中的占比不断提高,如何降低运营成本成为了研究热点。因此本文提出一种基于并网电流和公共耦合电压反馈的新型控制策略,该控制策略不仅提供了有源阻尼以抑制LCL谐振,而且减少了传感器的使用,还能对大范围变化的电网阻抗有较强的适应能力。通过仿真和实验表明,与传统的控制策略相比,在改进的策略下弱电网的实用范围增加,系统的稳定性得到提高,对谐波的抑制能力提升,并网电流质量有了良好的改善。

适用于弱电网的三电平并网逆变器模型预测控制

弱电网下并网逆变器的鲁棒性较差、谐波较大,而模型预测控制十分依赖系统参数,这限制了其在弱电网中的应用。针对以上问题,提出适用于NPC(二极管中点钳位)型三电平并网逆变器的数据驱动型V-MFPC(基于虚拟电压矢量的无模型预测控制)策略。首先通过不同的开关序列构造大量虚拟电压矢量,然后利用代价函数预选降低控制算法的计算负担,最后选择合适的开关序列寻优抑制中性点电压波动。仿真结果表明,所提策略能有效抑制中性点电压波动和并网电流谐波,并具有较好的参数鲁棒性。

弱电网下并网逆变器恒定带宽及稳定裕度的自适应控制策略

随着可再生能源在电网中的占比不断提高,电网逐渐呈现出弱电网特性,即电网阻抗不可忽略且频繁波动。电网阻抗的存在会改变逆变器控制环路的增益,导致控制环路的稳定裕度减小,因而引发稳定性问题,同时,控制环路的截止频率也因电网阻抗的存在而减小,环路带宽也随之减小,使得逆变器动态性能变差。针对弱电网下电网阻抗变化引发的相关问题,现有的控制策略往往侧重于提升逆变器的并网稳定性,而对其动态性能下降的问题缺乏关注。鉴于此,为同时解决以上问题,该文提出一种基于环路增益测量的自适应控制策略以保障逆变器优越且恒定的控制性能,首先通过环路增益的在线测量实现对逆变器控制性能的实时监测;然后依据实时监测的控制性能指标参数自适应地调整控制器的参数,以提升逆变器对弱电网的适应性;最后以单相并网逆变器为例进行实验验证,实验结果证明了所提方案的有效性。

集成有源阻尼器功能的并网逆变器虚拟电阻补偿控制方法

有源阻尼器通过构造虚拟电阻提高接入弱电网中逆变器的稳定性,但虚拟电阻的准确性受开关频率限制,有源阻尼器的功能难以集成到常规的并网逆变器中,为此,提出一种虚拟电阻补偿控制方法。建立集成有源阻尼器功能的并网逆变器阻抗模型,分析虚拟电阻对提升系统稳定性的作用;阐明控制带宽和数字延时对虚拟电阻准确性的影响,针对并网逆变器易发生谐振稳定性问题的谐振频段,设计一种新的虚拟电阻补偿环节,显著提升了虚拟电阻的补偿精度。系统阻抗稳定性分析表明,所提方法虚拟出的阻抗具有良好的电阻特性。实验结果表明,集成有源阻尼器功能的并网逆变器接入系统后具有较好的阻尼谐振作用,显著提升了系统稳定性。

Weak invertibility of linear finite automata (I)——Classification and enumeration of transfer functions

Let 3V denote the set of all possible transfer function matrices of weakly invertible linear finite automata over a given finite field F. A classification and an enumeration on the infinite set are given.

弱电网下基于导纳合成相量法的单相并网逆变器鲁棒性提升技术研究

为保证并网逆变器的并网电流与电网电压同步,通常采用锁相环获取电网电压相位信息。同时,为提高并网电流质量,常考虑在回路中加入电网电压前馈。然而,当逆变器工作在弱电网下时,它们均有可能对系统的稳定性带来负面影响。该文以单相LCL型并网逆变器为例,旨在研究弱电网下锁相环和电网电压前馈造成系统不稳定的原因并进行优化。针对2 个不稳定因素存在的情况,该文提出一种导纳合成相量法来分析多个导纳共同作用时的影响机理。考虑到带通滤波器可以衰减不稳定因素的影响,文中加入带通环节对系统的鲁棒性进行优化。结合上述导纳合成相量法的分析结果,确定带通环节的设计目标,并进一步给出带通环节参数的具体设计过程。结果表明,并网逆变器加入优化设计的带通环节后,即使在电网阻抗变化范围较大的情况下,系统仍能稳定工作。

弱电网下应对复杂稳定性问题的并网逆变器改进电压前馈通路研究

在并网逆变器中,锁相环和电网电压前馈是提高并网电流质量和输出性能的环节。然而在弱电网下,这两个环节均有可能对并网系统的稳定性产生影响,同时两者的影响范围存在重叠,导致稳定性问题变得更为复杂。该文针对这一复杂稳定性问题展开研究,分析弱电网下两个环节导致系统不稳定的原因,并进一步提出优化方案。首先考虑加入加权系数,讨论其对于电网电压前馈以及锁相环的影响,兼顾这两种因素,需要对加权系数进行权衡取值;然后考虑在更弱电网下,只加入加权系数对于系统稳定性提升效果是有限的,因此需要增加一条用于改善输出导纳相位的电压前馈通路;最后通过实验证明,加入改进方案后的并网逆变器,在阻抗变化较大的弱电网下依然保持良好的鲁棒性。