一类自适应控制系统的稳定性分析

对一类模型参考自适应控制映射进行了稳定性分析,通过使用中心流形简化和范式方法以及计算机辅助计算讨论了该类系统在参数空间内的所有1-余维和2-余维分岔行为及其性质,全面了解了系统在不同参数区域内的动态.从而为如何选取此类控制系统的参数以避免导致控制失效的多吸引子共存或长期存在的瞬态等动力学行为提供了方法和理论依据,并为在线调整参数以避免控制失效指明了方向.     

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.     

一种双寡头垄断Cournot-Puu模型的混沌控制研究

基于非线性动力学的基本原理,研究了经济系统中的双寡头垄断Cournot-Puu模型及其混沌控制方法.Cournot-Puu模型具有双曲线形需求函数和彼此不同的不变边际成本,离散化的差分系统显示出其复杂的非线性、分岔和混沌行为.在此基础上,结合Cournot-Puu模型的基本特征,应用延迟反馈控制方法以及自适应控制方法对该系统的混沌行为进行了研究.在结合实际经济意义的条件下,对该模型的输出进行调整并实现混沌控制.     

高阶控制增稳系统等效拟配参数时域在线辨识方法

现代控制增稳飞机是高达几十阶的复杂系统,将其降阶为特定形式的低阶等效系统才能与已有飞行品质规范进行比较,进而预测和评价飞机飞行品质.从时域角度出发,提出了一种高阶控制增稳系统等效拟配参数在线辨识方法.分析了时域等效系统拟配的基本方法,提出了等效系统实时在线拟配的系统框架思路,基于Tustin变换法推导了由高阶系统时域响应获取四阶等效系统参数的数学公式,应用最小二乘法在MATLAB中实现了算法编程,并用试飞数据验证了所提方法的可行性.计算结果表明,所提方法可以快速准确地实现高阶控制增稳系统的等效系统参数辨识.     

基于复合干扰观测器的CMG框架系统高精度转速控制北大核心CSCD

为使控制力矩陀螺(CMG)输出高精度力矩,框架转速必须具有足够高的控制精度.然而,在CMG框架伺服系统中,存在转子动不平衡力矩,齿槽力矩,电流脉动,非线性摩擦等多种干扰,严重影响了框架控制性能.为抑制各种干扰对框架控制性能的影响,文章设计了一种基于复合干扰观测器的非线性鲁棒控制器.首先,将系统中存在的干扰模化为频率已知的周期性干扰和变化率有界的慢变干扰,建立了三阶干扰动态模型,设计了复合干扰观测器,从而实现了对复杂干扰的准确估计.在此基础上,采用backstepping方法设计了框架转速非线性鲁棒控制器,实现系统的反馈控制.针对某CMG框架系统的转速控制仿真表明,该方法是可行的.     

替代产品的动态库存决策与控制

考虑了替代产品的动态库存决策与控制问题,建立了替代产品的多周期动态库存决策与控制模型.得到了目标函数的一些重要性质,给出了系统最优参数的求解算法,利用动态规划方法对系统的库存参数进行了优化求解.     

参激白噪声作用下蔡电路的脉冲控制

考察了参激白噪声和脉冲信号联合作用下蔡电路的渐近P阶矩稳定性问题,得到该随机脉冲系统的比较系统,从而可由该确定性比较系统的稳定性得到原随机脉冲系统的渐近P阶矩稳定性.并从理论上得到能使该随机脉冲系统渐近P阶矩稳定的参数取值范围,即在稳定区域内取值的参数组合能够用脉冲方法对该随机蔡电路实现混沌控制.最后用数值仿真验证了理论结果的正确性.     

基于经验似然比检验的高维非参EWMA控制图

随着传感技术和数据采集系统的逐渐完善,大量复杂高维数据可以被收集,对多变量和高维数据流进行监控往往是现代制造业和质量管理部门的一个基本要求.然而,在高维数据监控领域中,由于“维数的诅咒”以及变量的分布通常是复杂未知的,大多数传统的多元控制图不再适用.针对这种情况,一些研究者讨论了对分布未知且复杂高维数据的均值向量的各种检验,但这些检验很少适用于Phase II阶段的过程监控.文章提出了一种基于高维经验似然比检验的EWMA型非参数监控方案,该方案可用于多元过程和高维过程均值向量的监控,并且适用于子组数据流.所提出的控制图不仅易于实现和解释,而且蒙特卡罗数值模拟结果显示该控制图在对称、偏态、厚尾分布中都能有效地监测均值漂移.最后,将所提出的控制图应用于半导体制造过程,结果显示文章的方法对未通过测试的半导体具有良好的监控效果.     

一类系统构造问题的多输入-多输出基本方程与多目标优化

Renato Pennachi 讨论了以 S(M,N,C,λ_0)表示的参数系统抽象化定义,给出了参数系统的矩阵表示.Franz R.Pichler 总结 Salovara,Blomberg,Messarovic,Ma-cko,Windeknecht,Klir,Kalman,Zadeh 等人的工作,介绍了一般系统理论中若干以集合论与代数体系为基础的较有成效的动态系统建造与实现理论.G.M.Ostrovsky 等人在大规模复杂系统的优化问题中,运用了带有0—1变量的系数,研究了具有复杂平行序列的结构问题.     

托卡马克中低模态到高模态转迁模型的混沌运动

利用Melnikov方法详细研究了在托卡马克(Tokamaks)中,等离子区边缘附近低模态到高模态转迁方程的混沌动力学.该转迁方程是一个含外激励和参数激励的系统.对含周期外激励和线性参数激励、三次参数激励的系统分别绘出了用来划分混沌区和非混沌区的临界曲线.得到的结果表明,含有线性或三次参数激励的系统存在不可控区域,在该区域中异宿轨分岔总是导致混沌发生.特别地,三次参数激励系统存在一个"可控频率",施以该频率的激励,不论激励的振幅多大,同宿轨分岔总是不会导致混沌发生.得到了这类系统的一些复杂的动力学行为.     

System identification and control using adaptive particle swarm optimization

This paper presents a methodology for finding optimal system parameters and optimal control parameters using a novel adaptive particle swarm optimization (APSO) algorithm. In the proposed APSO, every particle dynamically adjusts inertia weight according to feedback taken from particles’ best memories. The main advantages of the proposed APSO are to achieve faster convergence speed and better solution accuracy with minimum incremental computational burden. In the beginning we attempt to utilize the proposed algorithm to identify the unknown system parameters the structure of which is assumed to be known previously. Next, according to the identified system, PID gains are optimally found by also using the proposed algorithm. Two simulated examples are finally given to demonstrate the effectiveness of the proposed algorithm. The comparison to PSO with linearly decreasing inertia weight (LDW-PSO) and genetic algorithm (GA) exhibits the APSO-based system’s superiority.     

基于遗传算法的LuGre轮胎模型参数辨识研究

LuGre轮胎模型是一种动态轮胎摩擦力模型,该模型能够精确描述轮胎摩擦环节的动态特性,但由其高度非线性使得参数辨识非常困难.针对LuGre轮胎模型,提出一种基于遗传算法的模型参数两步辨识方法.首先由PD控制辨识出静态参数;然后由PID控制辨识出动态参数.在每一步辨识中,均采用遗传算法作为优化工具,从而避免了采用拟和辨识方法中误差较大,试验条件难以控制的缺点.该算法仅仅使用轮胎转速数据,而转速传感器是汽车防滑刹车控制系统(ABS)的基本组成部分,因此该算法可以与ABS结合工作,低成本的实现LuGre轮胎模型参数辨识.     

Realization of PID controls by fuzzy control methods

This paper shows that PID controllers can be realized by fuzzy control methods of “product-sum-gravity method” and “simplified fuzzy reasoning method”. PID controllers, however, cannot be constructed by min-max-gravity method known as Mamdani's fuzzy reasoning method. Furthermore, extrapolative reasoning can be executed by the product-sum-gravity method and simplified fuzzy reasoning method by extending membership functions of antecedent parts of fuzzy rules.     

时变滞后系统的一种自校正混合模糊PID控制

普通模糊控制不能对时变滞后系统进行有效控制 ,甚至使系统失去稳定 .在 W.L.Bialkowski 1 983年提出的混合模糊 PID控制器的基础上 ,提出了一种自补偿混合模糊 PID控制器 ,并在此基础上提出了一种对积分系数 KI进行自校正的算法 .经 MATLAB仿真验证 ,该算法具有良好的控制品质 ,适应对象参数大范围变化的时滞系统 ,且易于工程实现 .     

An improved generalized predictive control algorithm based on the difference equation CARIMA model for the SISO system with known strong interference

ABSTRACT

The single input single output (SISO) system with known strong interference is widely used in various occasions. Due to its strong interference, the control accuracy is hard to guarantee. To solve this problem, an improved generalized predictive control (IGPC) algorithm is developed. The IGPC firstly builds the difference equation CARIMA (Controlled Auto-Regressive Integrated Moving-Average) model of the SISO system and then treats the system as a two input single output (TISO) system and calculates its predictive vector, then transforms it into a SISO system and uses the TISO system predictive vector to calculate the SISO system control increment. A new parameter called phase coefficient is added to inhibit the control lag. Simulations are performed to make the comparison among the traditional GPC, PID control, velocity synchronization control (VSC), fuzzy adaptive PID control (FAPID), model-based robust PID control (BPID) and the IGPC. Results show that IGPC has best performance compared to the others. Finally, experiments are developed which proved that the IGPC algorithm has a higher accuracy in the SISO system with known strong interference than that of VSC.     

Robust suboptimal control of nonlinear systems

In this paper, we consider a nonlinear dynamic system with uncertain parameters. Our goal is to choose a control function for this system that balances two competing objectives: (i) the system should operate efficiently; and (ii) the system’s performance should be robust with respect to changes in the uncertain parameters. With this in mind, we introduce an optimal control problem with a cost function penalizing both the system cost (a function of the final state reached by the system) and the system sensitivity (the derivative of the system cost with respect to the uncertain parameters). We then show that the system sensitivity can be computed by solving an auxiliary initial value problem. This result allows one to convert the optimal control problem into a standard Mayer problem, which can be solved directly using conventional techniques. We illustrate this approach by solving two example problems using the software MISER3.     

城市水供需系统投资的鲁棒控制

针对城市水需求具有增长性和周期性的情形,建立城市水供需系统投资的离散时间控制模型.由于城市水管理系统参数估计值可能具有不确定性和时变性,为使此情形下仍能有效满足城市水需求,利用内模原理设计了系统补偿器,并证明了其可行性,然后利用补偿器对系统实施鲁棒控制.在预测城市水需求的基础上,通过合理控制城市水供给的投资,使城市的剩余供水能力逐渐准确逼近给定目标值,且系统具有鲁棒性.     

基于复合控制的电液负载模拟器多余力抑制研究

针对电液负载模拟系统存在多余力且该多余力严重影响系统加载精度与控制性能的问题,建立了系统各部分以及整个系统的数学模型.通过对数学模型的研究,分析了系统多余力的产生机理,并建立了系统多余力的传递函数.提出了前馈PID复合控制的方法,并对该方法进行了仿真分析和实验研究.在仿真分析中,通过对多余力消扰前、引入前馈控制消扰后及引入复合控制消扰后3种情况的比较,说明前馈PID复合控制能够有效抑制系统多余力.实验结果进一步验证了前馈PID复合控制的有效性,同时实验结果显示在运动换向时系统多余力将出现突变,为下一步的研究指明了方向.     

Steady-state,self-oscillating and chaotic behavior of a PID controlled nonlinear servomechanism by using Bogdanov–Takens and Andronov–Poincaré–Hopf bifurcations

This paper analyzes a controlled servomechanism with feedback and a cubic nonlinearity by means of the Bogdanov–Takens and Andronov–Poincaré–Hopf bifurcations, from which steady-state, self-oscillating and chaotic behaviors will be investigated using the center manifold theorem. The system controller is formed by a Proportional plus Integral plus Derivative action (PID) that allows to stabilize and drive to a prescribed set point a body connected to the shaft of a DC motor. The Bogdanov–Takens bifurcation is analyzed through the second Lyapunov stability method and the harmonic-balance method, whereas the first Lyapunov value is used for the Andronov–Poincaré–Hopf bifurcation. On the basis of the results deduced from the bifurcation analysis, we show a procedure to select the parameters of the PID controller so that an arbitrary steady-state position of the servomechanism can be reached even in presence of noise. We also show how chaotic behavior can be obtained by applying a harmonical external torque to the device in self-oscillating regime. The advantage of achieving chaotic behavior is that it can be used so that the system reaches a set point inside a strange attractor with a small control effort. The analytical calculations have been verified through detailed numerical simulations.     

A computational approach for understanding immune response to multiple epitopes based on optimal control formulation

The immune system does not response in equal probability to every epitope of an invader. We investigate the immune system’s decision making process using optimal control principles. Mathematically, this formulation requires the solution of a two-point boundary-value problem, which is a challenging task especially when the control variables are bounded. In this work, we develop a computational approach based on the shooting technique for bounded optimal control problems. We then utilize the computational approach to carry out extensive numerical studies on a simple immune response model of two competing controls. Numerical solutions demonstrate that the results of optimal control depend on the objective function, the limitations on control inputs, as well as the amounts of peptides. Moreover, the state space of peptides can be divided into different regions according the properties of the solutions. The developed algorithm not only provides a useful tool for understanding decision making strategies of the immune system but can also be utilized to solve other complex optimal control problems.