基于θ-D方法的欠驱动TORA系统非线性最优控制

针对TORA (Translational oscillator with rotating actuator)系统的镇定控制问题, 提出一种基于$\theta $-D方法的非线性最优控制方案.应用拉格朗日方程建立TORA系统的数学模型, 为保证状态空间形式的TORA系统数学模型中状态向量系数矩阵$A(\pmb{x})$能够分离出常值矩阵, 且其能与控制位置矩阵构成可控对, 采用不同于传统形式的解耦坐标变换对TORA系统进行了处理, 以此为基础为TORA系统设计基于$\theta $-D方法的非线性最优控制器, 该控制方案可离线得到控制输入的显示表达式.通过数值仿真以及与基于局部线性化的线性最优控制方案进行比较, 验证了所提非线性最优控制方案所具有的良好瞬态性能.     

一类二阶非线性系统的有限时间状态反馈镇定方法

针对一类二阶非线性系统的有限时间状态反馈镇定问题进行了讨论. 给出了三种基于连续状态反馈的全局有限时间状态反馈镇定方法. 首先，利用非线性齐次系统性质，设计出一种状态反馈控制器，使得闭环系统渐近稳定并且具有负的齐次度；其次，基于有限时间Lyapunov函数的反步构造法，给出了一种有限时间控制器；最后，利用非奇异终端滑模控制技术，得到了一种使闭环系统有限时间收敛到平衡点的反馈镇定控制器. 仿真结果表明了这些方法的有效性.     

带两控制器刚体飞行器的姿态镇定

已知带两控制器的刚体飞行器系统不能被连续的纯状态反馈局部渐近镇定.有效的解 决方法包括时变反馈镇定方法和非连续反馈镇定方法.现有的时变反馈镇定方法设计均较为复 杂.已有的光滑时变反馈方法是非指数收敛的.本文通过引入辅助变量以及采用反馈线性化技术 设计出光滑时变的控制器.该方法设计简单且保证闭环系统状态是指数收敛的.仿真结果证明了 本文方法的有效性.     

基于生物启发模型的欠驱动水平TORA系统的有界输入镇定控制

针对欠驱动水平TORA(translational oscillators with rotating actuator)系统,提出一种基于生物启发模型的有界输入控制方法,实现系统在执行器存在饱和约束情况下的镇定控制.首先,根据水平TORA系统的动力学模型分析系统的无源特性,进而给出系统的控制目标;接着,基于无源特性构造一种新颖的Lyapunov函数,在此基础上设计一种结构简单的非线性状态反馈控制器;然后,考虑执行器的饱和约束条件,引入受生物启发建立的神经动力学模型,利用该模型的有界平滑输出特性,设计一种改进的状态反馈控制器;最后,根据LaSalle不变性原理对系统的稳定性进行严格的数学分析和证明.与其他方法相比,所提方法不仅考虑了执行器的饱和约束问题,而且设计的控制算法简单高效,易于工程实现.仿真与对比结果表明,所提方法具有更好的控制性能.     

空空导弹大攻角俯仰自动驾驶仪设计

研究导弹自动驾驶仪优化控制问题,针对空空导弹在大攻角飞行过程中,系统的空气动力学特性存在强非线性耦合和参数不确定性,引起系统稳定性差.为了提高系统性能,在导弹俯仰运动的非线性数学模型的基础上,以导弹攻角为被控信号,舵偏角指令为输入信号,提出采用反馈线性化方法对导弹模型进行线性化,然后运用变结构控制理论进行控制器设计.控制器结构简单,易于实现,能够抑制被控对象中存在的不确定性.并通过数学仿真与全状态反馈控制方法设计的控制器进行了比较.结果表明采用反馈线性化和滑模变结构方法设计的控制系统对气动参数摄动和外部扰动具有较强的鲁棒性.     

磁悬浮球系统的非线性自适应控制方法

针对磁悬浮球系统被控对象变化时控制器自适应问题,提出了一种反馈线性化和在线参数辨识相结合的非线性自适应控制方法。基于状态反馈精确线性化方法建立磁悬浮球系统的数学模型,通过状态反馈设计了一种非线性控制器,并给出了控制器参数的在线辨识方法。MATLAB平台上在线实验结果表明,与反演滑模自适应控制方法相比,提出的方法无须在平衡位置近似线性化,可以在平衡位置实现对不同对象的自适应控制,且具有理想的稳态调节性能。     

一类非线性系统的奇异点克服控制

针对一类非线性系统, 研究存在奇异点时的跟踪控制问题. 在采用反馈线性化方法将对象转换成标准型后, 构造线性补偿器并结合期望轨迹的高阶导数构成伪控制量. 通过引入梯度动力学方法求解控制律, 以克服在控制过程中遇到的奇异点问题. 通过稳定性分析验证了闭环系统的稳定性和跟踪误差的收敛性. 仿真结果表明, 此类控制器具有良好的控制性能, 并且能有效克服奇异点问题.

     

转移概率部分未知的随机Markov 跳跃系统的镇定控制

研究一类随机Markov跳跃系统的稳定性与镇定控制问题.此类系统跳跃过程的转移概率部分未知,包括转移概率完全已知和完全未知两种情形,因而更具一般性.首先,给出保证随机Markov跳跃系统均方渐近稳定的充分性判据,并设计了相应的状态反馈镇定控制器;然后,基于矩阵的奇异值分解给出了系统静态输出反馈镇定控制器的设计方法,并将其归结为求解一组线性矩阵不等式（LMIs）的可行性问题;最后,通过数值仿真验证了所得结论的正确性.     

基于级联标准型的Acrobot反步控制

Acrobot是一种典型的二自由度欠驱动机械系统,针对Acrobot系统镇定控制中需要分别设计起摆控制器和平衡控制器,控制器设计复杂这一问题,提出一种新型的镇定控制策略,该控制策略仅仅需要设计一个控制器,就可以使Acrobot由竖直向下的稳定平衡点起摆,并稳定于竖直向上的不稳定平衡点。首先,采用欧拉-拉格朗日方程为系统建立动力学模型;然后,结合部分反馈线性化,提出一种闭环全局坐标变换方案,将Acrobot系统动力学模型转换为严格反馈级联标准型;最后,采用反步法将系统分为若干个子系统,分别为每个子系统构造Lyapunov函数,并设计虚拟控制输入,最终实现系统的镇定控制。仿真结果表明,所提出的控制策略简单有效,可以应用于与Acrobot系统类似的二自由度欠驱动系统中,具有较高的理论和应用价值。     

具有有界时滞的网络控制系统的镇定

针对具有有界时滞且时滞上界大于一个采样周期的网络控制系统,研究了系统建模和状态反馈镇定问题.在分析有界时滞的所有可能性的基础上,提出一种能够用于处理时变控制律问题的网络控制系统数学模型,进而将该系统的镇定问题转化为镇定一系列模型的鲁棒控制问题.根据 Lyapunov 方法,给出了保证闭环系统稳定的状态反馈控制器.仿真算例验证了所提出方法的有效性.     

基于输出反馈的欠驱动TORA系统的有界输入控制

针对欠驱动TORA(Translational oscillations with a rotational actuator)系统,设计了一种具有执行器饱和约束的输出反馈等[7]特别地,由Rand学者提出的TORA系统,最初控制器.与其他现有方法相比,本文方法不仅考虑了执行器饱和约束和作为双自旋航天器的简化模型用于研究自振现象.后来由于速度信号不可测情形,而且考虑了旋转小球可能存在的循环行为.具体而TORA系统具有强耦合、高度非线性、欠驱动等特性,而被言,首先根据TORA系统模型分析了TORA系统的控制目标;随后,作为一种非线性基准系统主要用于非线性控制器设计、验证构造了一种新颖的能量函数,在此基础上设计了一种考虑执行器饱和约非线性控制算法的控制性能或教学研究.目前国内外已有多束的输出反馈控制器,并通过严格的数学分析证明了闭环系统关于平衡点的稳定性;最后,借助数值仿真测试检验了所提控制器的控制性能,并所高校和研究机构针对TORA系统的控制问题展开研究.对与已有方法进行了对比.仿真测试结果表明本文所提方法具有更好的控法制性能.     

Complementary sliding control of non-linear systems

In this paper, a novel continuous complementary sliding control was proposed to improve the tracking performance given the available control bandwidth and the extent of parameter uncertainty. With this control law, we have shown that the guaranteed ultimate bound of the tracking error was reduced by half, as compared with the conventional continuous sliding control. The error transient response during the reaching phase has also been remarkably improved by the proposed control. To illustrate its superiority, we presented a composite complementary sliding control scheme for a cascade uncertain non-linear system, which includes the benchmark non-linear problem, TORA. Simulation results on TORA showed good responses to any initial conditions and to single-frequency sinusoidal disturbances.     

Nonlinear observers comprising high-gain observers and extended Kalman filters

A full order observer is designed for a class of nonlinear systems that can potentially admit unstable zero dynamics. The structure of the observer is composed of an Extended High Gain Observer (EHGO), for the estimation of the derivatives of the output, augmented with an Extended Kalman Filter (EKF) for the estimation of the states of the internal dynamics. The EHGO is also utilized to estimate a signal that is used as a virtual output to an auxiliary system comprised of the internal dynamics. In the special case of the system being linear in the states of the internal dynamics, we achieve semi-global asymptotic convergence of the estimation error. We demonstrate the efficacy of the observer in two examples; namely, a synchronous generator connected to an infinite bus and a Translating Oscillator with a Rotating Actuator (TORA) system.     

Differential flatness‐based ADRC scheme for underactuated fractional‐order systems

This article mainly studies the fractional‐order active disturbance rejection control (FOADRC) schemes for the underactuated commensurate fractional‐order systems (FOSs). The FOADRC framework for linear FOSs‐based fractional proportion integration differentiation is constructed by using the fractional‐order tracking differentiator and the fractional‐order extended state observer, and the necessary conditions for the system to have stable controllers are provided. The FOADRC scheme for underactuated FOSs based on differential flatness is proposed. For underactuated FOSs, a set of flat output expressions with a fixed format is given under the controllable condition of the system. Moreover, making the flat output as the equivalent of the system output is simple and easy to analyze and calculate. Subsequently, the FOADRC scheme is designed by using the flat output. Finally, the scheme proposed in this article is verified by a simulation example.     

TORA的动力学建模及基于能量的控制设计

针对旋转小球在垂直平面内运动的欠驱动TORA (Translational oscillators with rotating actuator), 采用基于能量的方法, 设计了系统的状态反馈控制器. 基于拉格朗日方程, 建立了TORA的动力学模型, 从能量的角度出发, 说明了系统的无源特性, 在此基础上设计了一个合适李亚普诺夫函数, 从而得到了系统的控制算法; 采用拉萨尔不变性原理分析了控制系统的稳定性. 数值仿真实验证明了控制器的有效性.     

On a switching control scheme for nonlinear systems with ill-defined relative degree

This paper discusses the applicability of a switching control scheme for a nonlinear system with ill-defined relative degree. The control scheme switches between exact and approximate input–output linearisation control laws. Unlike a linear system under a switching control scheme, the equilibria of a nonlinear system may change with the switching. It is pointed out that this is not sufficient to cause instability. When the region of the approximate linearisation control law is attractive to the exact zero dynamics, it is possible that the closed-loop system under the switching control scheme is still stable. The results in this paper shows that the switching control scheme proposed in Tomlin and Sastry (Systems Control Lett. 35(3) (1998) 145) is applicable for a wider class of nonlinear systems.     

Distributed Adaptive Output Consensus of Unknown Heterogeneous Non-Minimum Phase Multi-Agent Systems

This article addresses the leader-following output consensus problem of heterogeneous linear multi-agent systems with unknown agent parameters under directed graphs.The dynamics of followers are allowed to be non-minimum phase with unknown arbitrary individual relative degrees.This is contrary to many existing works on distributed adaptive control schemes where agent dynamics are required to be minimum phase and often of the same relative degree.A distributed adaptive pole placement control sche...     

Robust Model Reference Adaptive Intelligent Control

In this paper a Neural Network based Model Reference Adaptive Control scheme (NNMRAC) is proposed. In this scheme, the controller is designed by using parallel combination of the conventional Model Reference Adaptive Control (MRAC) scheme and Neural Network (NN) controller. In the conventional MRAC scheme, the controller is designed to realize plant output converging to reference model output based on the plant which is linear. This scheme is used to control linear plant effectively with unknown parameters. However, it is difficult for a nonlinear system to control the plant output in real time applications. In order to overcome the above limitations, the NN-MRAC scheme is proposed to improve the system performances. The control input of the plant is given by the sum of the MRAC output and NN controller output. The NN controller is used to compensate the nonlinearities and disturbances of the plant that are not taken into consideration in the conventional MRAC. The simulation results clearly show that the proposed NN-MRAC scheme have better steady state and transient performances than those of the current adaptive control schemes. Thus, the proposed NN-MRAC scheme named as Robust Model Reference Adaptive Intelligent Control (RMRAIC) is found to be extremely effective, efficient and useful in the field of control system.