分数阶PI^λD^μ控制器控制性能的研究

现实控制系统研究中存在很多分数阶系统,因此对系统提出了分数阶PI~λD~μ控制器,控制器将传统整数阶PID控制器的微分与积分阶数扩展到分数,增加了两个参数微分阶数μ和积分阶数λ.为了对比研究分数阶系统分别在分数阶PI~λD~μ控制器控制下和在整数阶PID控制器控制下的系统性能,针对一个典型的分数阶系统,分别设计两类控制器,再进行性能比较.实验仿真结果表明,与整数阶PID控制器相比,该系统在分数阶PI~λD~μ控制器控制下整个闭环系统具备较好的动、静态性能,并且鲁棒性较强,说明分数阶PI~λD~μ控制器控制性能的优越性以及当被控系统为分数阶系统时应该设计分数阶PI~λD~μ控制器.     

阈值阵列模型下的超阈值随机共振信噪比增益

研究了阈值阵列模型和超阈值随机共振现象.对该模型进行剖析,认为阈值阵列系统可以分解为单个阈值系统与集总平均器的级联.为了研究周期输入下的超阈值随机共振现象,理论分析了周期输入下的阈值阵列模型输出随机过程的统计特性,以输出信噪比增益作为随机共振的测度,固定输入信噪比,观测输出信噪比增益相对于阈值噪声方差的变化规律.证实当输入噪声为高斯噪声时,在阈值阵列系统中加入统计独立的高斯白噪声可使输出信噪比增益大于1,当输入噪声为非高斯噪声时,可获得更高的输出信噪比增益.     

对称二值噪声下线性系统的随机共振

对于受到外部周期力、乘性和加性的二值噪声共同作用下的线性系统,通过运用Shapiro-Loginov公式,计算出系统一阶矩和信噪比的表达式。信噪比作为加性噪声强度D2的函数,数值结果表明在负相关区域-1≤λ〈0条件下有随机共振现象出现,而在非负相关区域0λ1却未出现;作为乘性噪声强度D1的函数时,仍在负相关区域-1≤λ〈0有共振现象发生,峰值高度随D2的增大而增大,位置右移;输入信号频率ω和外部力振幅α作为信噪比的变量时,随机共振现象也被发现,峰值的位置却不随着λ、α的变化而变化。     

可能性线性模型中的参数选优与输入噪声间关系的研究

基于可能性理论的可能性线性模型(PLM)在模糊建模等应用中有重要的作用.本文首先借鉴统计学习理论将此模型扩展为正则化(regularized)的可能性线性模型(RPLM),以提高其泛化能力.然后利用将其优化问题转换为最大后验估计问题的新方法,研究当数据含有噪声时,模型中的拟合门限值λ和输入噪声均方差σ之间的关系.理论推导和仿真实验均证明,当输入噪声为高斯模型时,λ和σ成近似的线性反比关系.该结论对PLM和RPLM均有借鉴意义,为已知输入噪声均方差时,合理选择λ提供理论依据.     

基于BF-PSO的船舶电站柴油机分数阶控制器

针对船舶电力系统的频率稳定性问题,对船舶电站柴油机调速系统设计了分数阶PIλDμ控制器。采用细菌觅食-粒子群混合优化(BF-PSO)算法对分数阶PIλDμ控制器参数进行优化整定,解决了分数阶PIλDμ控制器整定参数多、设计复杂的问题。对分别采用分数阶PIλDμ控制器和传统整数阶PID控制器的柴油机调速系统进行了仿真和对比。结果表明,在同等条件下优化得到的分数阶PIλDμ控制器能够有效抑制模型参数摄动,鲁棒性更强,具有更好的控制效果。     

采用多拍脉冲的快速脉冲系统

在通常的脉冲控制系统中,当输入信号是阶跃函数时,系统的过渡过程至少在n个采样周期内才能完全结束(n 是控制对象的阶数).文中考虑了采用宽度不等的多拍脉冲代替通常的单拍脉冲以加快系统的过渡过程.在采用多拍脉冲以后,系统的过渡过程可以在少于n个采样周期内,甚至在一个采样周期内完全结束.文中叙述了这种脉冲系统的综合方法,也讨论了系统中有关组成部分——脉冲组成器和校正装置——的构成方案及其参数的计算方法.最后并考虑了由于时滞引起的对系统动态特性有害影响的补偿问题.文中举有例题,对文中各节内容作必要的说明.     

采用多拍脉冲的快速脉冲系统

在通常的脉冲控制系统中,当输入信号是阶跃函数时,系统的过渡过程至少在n个采样周期内才能完全结束(n是控制对象的阶数).文中考虑了采用宽度不等的多拍脉冲代替通常的单拍脉冲以加快系统的过渡过程.在采用多拍脉冲以后,系统的过渡过程可以在少于n个采样周期内,甚至在一个采样周期内完全结束.文中叙述了这种脉冲系统的综合方法,也讨论了系统中有关组成部分——脉冲组成器和校正装置——的构成方案及其参数的计算方法.最后并考虑了由于时滞引起的对系统动态特性有害影响的补偿问题.文中举有例题,对文中各节内容作必要的说明.     

带形状参数的双曲Bézier曲线

提出了一类带形状参数λ,μ的双曲Bézier曲线(简称H-Bézier曲线),这类曲线与二次Bézier曲线类似,每一段曲线由相继的3个顶点生成,它们不仅具有二次Bézier曲线许多常见的性质,而且利用λ,μ的不同取值能够局部或整体调控曲线的形状.当λ,μ增大时,曲线能连续逼近控制多边形.此外,它还能精确表示直线和双曲线.     

三次Bezier曲线的一种双参数扩展及应用

对三次Bernstein基函数进行扩展,给出了含有双参数λ,μ的一组四次多项式基函数,基于该组基定义了带双参数的多项式曲线。该曲线不仅具有三次Bezier曲线的诸多特性,而且具有更加灵活的形状可调性。参数λ,μ的几何意义非常明显：在控制顶点不变的情况下,λ,μ分别起到了对曲线相对于控制多边形两内顶点的推拉作用,当λ=μ时,曲线退化为三次Bezier曲线的单参数扩展情形。重点讨论了在不改变控制点位置的情况下如何实现两曲线间的C¹拼接。     

一类磁性刚体航天器的混沌控制研究

采用基于误差线性系统稳定性准则的混沌控制方法,控制具有结构内阻尼的磁性刚体航天器在重力场与磁场共同作用下在圆形轨道的混沌姿态运动.讨论了航天器姿态运动方程中部分参数的取值对于运动姿态的影响,给出了这些参数通过倍周期分岔或逆倍周期分岔通往混沌的途径.当参数使系统做混沌姿态运动时,采用上述方法将混沌运动控制至周期-4轨道,并实现周期-1、2、4轨道之间转换的灵活控制.此外,分析了控制参数的变化对于控制效果的影响,并分别给出了控制至不同轨道时的输入扰动范围及控制参数范围.仿真结果表明,该方法能够实现混沌姿态运动在预定周期轨道间的灵活控制,且输入扰动量小、控制速度快、具有高精度,从而验证了该方法在航天器混沌姿态运动控制方面的有效性.     

输入向量控制细胞神经网络全局指数稳定

利用输入向量来控制细胞神经网络的稳定性.所得结果表明,当输入向量的绝对值大于某个仅仅只与细胞神经网络的物理参数有关的值时,不附加其它任何条件,细胞神经网络是全局指数稳定的.也讨论了输入向量的部分分量的绝对值大于某个仅仅只与细胞神经网络的物理参数有关的值时,细胞神经网络的全局指数稳定性,所得结论推广和改进了某些已有文献的相应结果.     

网络控制系统鲁棒性能μ综合控制

针对网络控制系统的延时问题,分析了具有乘性输入不确定性的被控对象中嵌入加权函数的μ鲁棒性能,并利用鲁棒控制中μ分析的D-K迭代法设计出网络控制器。仿真结果表明μ控制器能够保证系统在一定延时范围内的稳定性和鲁棒性。     

Feedback decoupling-controller design of 3-D systems in state space

This paper solves the input-output decoupling problem of three-dimensional (3-D) systems formulated in state-space representation. The control policy adopted is of the static state feedback type u=Kx+Nw where K, N are appropriate matrices to be determined, x is the system state vector, and w is the new input vector assumed equidimensional to the actual input vector u. The procedure derived determines K and N such that the resulting closed-loop system has a diagonal and nonsingular transfer-function matrix. The case, where only partial input-output decoupling is possible, is also considered, and the corresponding state-feedback matrices K and N are determined. The results are illustrated by simple numerical examples. The required 3-D generalization of the well known Cayley-Hamilton theorem is provided.     

Fault coverage modeling in nonlinear dynamical systems

In this paper, we propose an approach for modeling fault coverage in nonlinear dynamical systems. Fault coverage gives a measure of the likelihood that a system will be able to recover after a fault occurrence. In our setup, the system dynamics are described by a standard state-space model. The system input (disturbance) is considered to be unknown but bounded at all times. Before any fault occurrence, the vector field governing the system dynamics is such that, for any possible input signal, the corresponding system reach set is contained in some region of the state space defined by the system performance requirements. When a fault occurs, the vector field that governs the system dynamics might be altered. Fault coverage is defined as the probability that, given a fault has occurred, the system trajectories remain, at all times, within the region of the state-space defined by the performance requirements. Input-to-state stability (ISS) concepts are used to compute estimates of the proposed coverage model. Several examples are discussed in order to illustrate the proposed modeling approach.     

Matrix generalized inverses in the handling of control problems containing input derivatives

A solution method using generalized matrix inverses is proposed for the following problem. Given a linear control system consisting of a plant equation and an output. equation, the latter or both containing the first derivative of the input vector. If the output vector is a given function of the time variable t, find input vectors which yield the desired output.     

Robust redesign of a neural network controller in the presence of unmodeled dynamics

This work presents a neural network control redesign, which achieves robust stabilization in the presence of unmodeled dynamics restricted to be input to output practically stable (IOpS), without requiring any prior knowledge on any bounding function. Moreover, the state of the unmodeled dynamics is permitted to go unbounded provided that the nominal system state and/or the control input also go unbounded. The neural network controller is equipped with a resetting strategy to deal with the problem of possible division by zero, which may appear since we consider unknown input vector fields with unknown signs. The uniform ultimate boundedness of the system output to an arbitrarily small set, plus the boundedness of all other signals in the closed-loop is guaranteed.     

Recursive state estimation: Unknown but bounded errors and system inputs

A method is discussed for estimating the state of a linear dynamic system using noisy observations, when the input to the dynamic system and the observation errors are completely unknown except for bounds on their magnitude or energy. The state estimate is actually a set in state space rather than a single vector. The optimum estimate is the smallest calculable set which contains the unknown system state, but it is usually impractical to calculate this set. A recursive algorithm is developed which calculates a time-varying ellipsoid in state space that always contains the system's true state. Unfortunately the algorithm is still unproven in the sense that its performance has not yet been evaluated. The algorithm is closely related in structure but not in performance to the algorithm obtained when the system inputs and observation errors are white Gaussian processes. The algorithm development is motivated by the problem of tracking an evasive target, but the results have wider applications.     

Identification and control of a nonlinear discrete-time system based on its linearization: a unified framework

This paper presents a unified theoretical framework for the identification and control of a nonlinear discrete-time dynamical system, in which the nonlinear system is represented explicitly as a sum of its linearized component and the residual nonlinear component referred to as a "higher order function." This representation substantially simplifies the procedure of applying the implicit function theorem to derive local properties of the nonlinear system, and reveals the role played by the linearized system in a more transparent form. Under the assumption that the linearized system is controllable and observable, it is shown that: 1) the nonlinear system is also controllable and observable in a local domain; 2) a feedback law exists to stabilize the nonlinear system locally; and 3) the nonlinear system can exactly track a constant or a periodic sequence locally, if its linearized system can do so. With some additional assumptions, the nonlinear system is shown to have a well-defined relative degree (delay) and zero-dynamics. If the zero-dynamics of the linearized system is asymptotically stable, so is that of the nonlinear one, and in such a case, a control law exists for the nonlinear system to asymptotically track an arbitrary reference signal exactly, in a neighborhood of the equilibrium state. The tracking can be achieved by using the state vector for feedback, or by using only the input and the output, in which case the nonlinear autoregressive moving-average (NARMA) model is established and utilized. These results are important for understanding the use of neural networks as identifiers and controllers for general nonlinear discrete-time dynamical systems.     

A dynamic observer for a synchronous machine†

The closed-loop optimal control law obtained for a linear time-invariant system always requires the entire state vector to be available for direct measurement. It is seldom that all the state variables of a physical system are available for measurement. A compatible dynamic observer of the Luenberger type is designed to reconstruct the entire state vector for a synchronous machine-infinite bus system. The performance of the system with the observer cascaded to the optimal controller is compared with the performance of the system when all the state variables are available for feedback. The transfer matrix relating the output and input is derived.