基于自抗扰控制器的CNC雕刻机控制系统轮廓误差控制

针对CNC雕刻机控制系统因时变时延影响轮廓跟踪精度的问题,设计了基于自抗扰控制的单轴轨迹跟踪控制器和基于非线性PID(NLPID)的轮廓误差补偿控制器.首先,针对单轴轨迹跟踪控制,将时变时延引起的不确定性处理成系统总干扰的一部分,设计扩张状态观测器(ESO),对系统内外总干扰和系统状态进行实时估计,并设计误差补偿控制律,实现系统干扰的估计和补偿,得到良好的单轴轨迹跟踪控制性能.然后,根据轮廓误差估计值,设计基于NLPID的轮廓误差补偿控制器,对系统轮廓误差实时补偿,实现了良好的轮廓跟踪控制性能.最后,通过实验验证了所提方法的有效性.     

冷轧机压下伺服系统的输出反馈有限时间控制研究

针对冷轧机压下电液伺服系统存在非线性、参数不确定性和负载干扰等特点,提出了基于扩张状态观测器的输出反馈有限时间控制方法.利用扩张状态观测器对系统的状态变量进行观测,解决了电液伺服系统的速度和加速度难以实际测量的难题,并对未知函数及扰动具有鲁棒性.依据有限时间控制理论并结合反步构造法设计了有限时间控制器,并证明了系统的全局稳定性.仿真表明:扩张状态观测器能够快速准确的观测系统的状态;基于扩张状态观测器的有限时间控制方法能使系统快速、准确地跟踪指定位置目标,并具有很强的鲁棒性.     

增长依赖于不可测状态非线性系统量化输出反馈控制设计

研究了一类不确定非线性系统的量化输出反馈控制设计问题.不同于现有文献,所研究系统的非线性增长依赖于不可测状态.这使得现有文献中的观测器设计方法不再适用,且闭环系统性能分析更为复杂和困难.文章首先引入了一个新的高增益观测器,进而利用现有文献中的集值映射和迭代设计方法,构造了一个量化输出反馈控制器,最后利用循环小增益定理和动态量化策略,得到了保证闭环系统所有状态有界性且输出最终任意小的充分性条件.     

基于扩张状态观测器的机电伺服系统饱和补偿与自适应滑模控制

针对带有未知摩擦力矩与输入饱和约束的机电伺服系统,提出了一种基于扩张状态观测器的伺服系统自适应滑模控制策略.首先,根据微分中值定理将非光滑饱和函数转化为仿射形式.其次,设计非线性扩张状态观测器并采用极点配置法确定观测器参数,用于补偿未知摩擦、饱和等非线性项以及外部干扰的影响.然后,通过结合参数自适应律和滑模理论,设计自适应滑模控制器,保证系统输出快速稳定地跟踪期望信号且改善抖振问题.仿真对比结果验证了所提方法的优越性.     

Active Disturbance Rejection Control of Quadrotor UAVs Based on Joint Observation and Feedforward Compensation北大核心CSCD

为解决模型参数不确定与外界干扰影响下,四旋翼无人机飞控作业中姿态与轨迹跟踪精度下降,反应迟缓的问题,利用拓展Kalman滤波应对非线性系统问题出色的适应能力和噪声抑制能力,对四旋翼状态信息进行初步估算来抑制高频信号干扰,从而降低了扩张状态观测器的估计负担.同时,与扩张状态观测器联合估计由系统不确定性参数与外界扰动联合组成的“总扰动”,使系统对于精确模型的依赖性降低,并利用扰动估计的微分值进行前馈补偿,以提高对突变扰动的跟踪精度,克服了突变干扰下的相位滞后现象.综合联合观测器、带前馈补偿的LESO及带误差补偿的PD控制律,形成了一种利用拓展Kalman滤波与前馈补偿后的扩张状态观测器联合观测扰动,能较大程度抑制高频噪声和突变扰动的改进型自抗扰控制器.仿真与实验结果表明,联合观测器能有效地减小观测误差幅值且能超前校正观测相位滞后,从而更好地得到更精确的状态信息,改进型自抗扰控制器能更好地满足四旋翼飞行器快速反应、高效稳定的控制要求,精准高效地完成复杂轨迹跟踪.     

一类基于输出非线性量测的变量带误差系统的辨识

研究一类基于输出非线性量测的变量带误差系统的辨识.通过对输出量测的截断,在适当的系统假设下,应用扩张截断随机逼近算法给出了系统参数的递推估计,并证明了估计的强一致.辨识算法适用于多种常见的非线性量测.最后给出了一个仿真例子,仿真结果与理论一致.     

多机电力系统直接自适应输出反馈模糊控制

针对多机电力系统励磁控制模型,考虑电力系统的状态不完全可测及多变量、非线性等特点,以T-S模糊逻辑系统直接逼近控制器,设计出基于状态观测器的直接自适应输出反馈模糊控制器,并通过李亚普诺夫函数进行了稳定性证明.算法具有很好的鲁棒性和动态性能,仿真结果表明所设计的控制器能够快速有效地改善系统在大干扰下的暂态稳定性.     

基于扩张状态观测器的轮式移动机器人抗饱和自适应滑模轨迹跟踪控制

针对带有输入饱和约束的轮式移动机器人鲁棒轨迹跟踪问题,文章提出一种抗饱和自适应滑模控制方法.考虑到系统参数摄动和外部扰动等不确定因素对系统控制性能的影响,首先设计非线性扩张状态观测器来估计系统不确定因素,并基于估计值设计抗饱和自适应滑模控制器,消除系统的参数摄动、外部扰动和输入饱和约束对系统控制性能的影响.仿真对比结果验证了文章所提控制方法的优越性和有效性.     

基于观测器的切换模糊系统的事件触发控制

本文针对一类含有执行器饱和的网络化切换模糊系统,在系统状态不可测的情况下,通过设计状态观测器来估计系统中的不可测状态变量,基于事件触发机制设计了观测器的控制器,用凸组合法来处理执行器饱和对系统性能的影响,并利用多Lyapunov函数理论和平均驻留时间方法证明了闭环系统的稳定性。数值仿真实例验证了提出方法的有效性。     

二阶扩张状态观测器的误差分析

本文利用分片光滑的Ｌｙａｐｕｎｏｖ函数来进行扩张状态观测器的误差分析,指出了非线性扩张状态观测器有更好的估计精度能力,给出了为提高估计精度扩张状态观测器的参数所满足的条件．     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Preservation of equivalence of derivations under reduction of depth of formulas

In this paper we consider derivations in the (&, )-fragment of the intuitionistic propositional calculus. As is known, replacement of any occurrence of a formula [F] in a sequent S by an occurrence of the formula [p], where p is a new propositional variable, with the simultaneous addition to the antecedent of the formula F p or p F depending on the sign of the occurrence of F in S, leaves the derivability unchanged. We give a proof of the fact that the natural extension of this transformation to derivations preserves the relation of equivalence of derivations, i.e., transformed derivations are equivalent if and only if the originals are equivalent. (Derivations are considered equivalent if certain of their normal forms coincide, or, what is the same, if their deductive terms coincide.) It is proved that by the iteration of this transformation, each derivation of an arbitrary sequent S can be transformed into a derivation of a sequent S, depending only on S, whose succedent is a variable, and in the antecedent there occur only formulas of the form a,a & b, a b,,(a b) c, a & b c, a (b & c), wherea, b, c are variables. Here if S is balanced, then S is also balanced. (A sequent is called balanced if each variable occurs in it no more than twice.) The familiar correspondence between certain concepts of the theory of categories and concepts of the theory of proofs allows one to assert that there has been constructed a univalent functor, mapping a free Cartesian closed category into itself.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 197–207, 1979.     

Estimate of growth of Lebesgue functions of linear methods of summation

Sufficient conditions are obtained in terms of matrix elements for the boundedness of Lebesgue functions of linear methods of summation of expansions in orthogonal systems of polynomial type.Translated from Matematicheskie Zametki, Vol. 6, No. 3, pp. 277–286, September, 1969.