基于MATLAB的磁悬浮系统奇异摄动参数计算

磁悬浮系统的稳定性是磁悬浮列车能否正式投入营运的关键因素。而实际的悬浮系统由于存在小电感奇异摄动参数，使得悬浮系统的动力学模型有相当高的阶数以及病态的数值特性，因此该文采用奇异摄动法处理这类问题。根据奇异摄动理论可知，要使系统稳定，摄动参数必存在一个稳定的上界。该文针对悬浮系统模型复杂和系统变参数的特点，借助MATLAB简化了磁悬浮系统奇异摄动参数稳定上界的计算。结果表明该方法的有效性和可行性，对磁悬浮系统的理论分析和工程研究有一定的参考价值。     

基于收缩理论的一类非线性系统自适应动态面控制

针对一类不确定非线性参数严反馈系统,提出基于收缩理论的自适应动态面控制方法.动态面控制器设计保证了各子系统关于状态误差部分收缩;对不确定参数构造收缩自适应律,并利用收缩下的奇异摄动分析降阶处理子系统,确保降阶前后状态误差间的偏差及滤波误差有界;通过分层子系统的收缩鲁棒性分析,证明了原闭环系统状态半全局收敛到以期望轨迹为中心的球域内,保证了跟踪误差及自适应估计有界.刚性机械臂系统仿真验证了所提出方法的有效性.     

基于积分流形的柔性机械手组合控制

为解决柔性机械手非最小相位的控制问题以及克服运动中的抖振,采用积分流形和奇异摄动理论,将柔性机械手系统分解为快慢两个子系统.对于慢变子系统,设计一种基于一阶鲁棒微分估计器的二阶滑模控制策略,使其轨迹跟踪期望值;对于快变子系统,采用频率成形滤波器设计动态补偿器来抑制弹性振动,并基于线性二次型最优控制方法给出相应的最优控制规律,使系统的输出快速趋于稳定.仿真结果表明了该控制策略的有效性.     

磁悬浮系统的双环自适应控制器设计与仿真

研究了基于机械和电气两种结构的磁悬浮系统的自适应控制方案，实现了双环磁悬浮控制系统的稳定悬浮。根据电磁铁动力学方程和电磁线圈的电压平衡方程，建立了磁悬浮系统基本模型。对系统中的电气部分和机械部分采用不同的控制方法：电气部分采用模型参考自适应控制的方法，加快电流上升的速度，使电流环性能达到设定指标；机械部分简化模型建立在电气自适应控制的基础上，针对系统参数的慢变特点而采用自校正控制方法，给出了能够自动跟踪系统参数，尤其是悬浮质量变化的稳定悬浮自适应控制算法。仿真和实验结果均证明这种控制方法能够使电流环快速跟踪给定信号，保证此悬浮系统能够很好地适应悬浮质量发生突变的情况，具有一定的实用价值。     

阀控电液伺服压力脉冲实验自抗扰控制方法

针对压力脉冲疲劳测试系统在测试过程中工件体积的不确定性以及脉冲疲劳测试系统的机械与液压双动态耦合问题,首先,提出通过奇异值摄动理论将压力脉冲疲劳测试系统的多动态耦合进行解耦降阶;然后,利用自抗扰控制算法实现对系统模型降阶误差以及体积参数不确定性等干扰的补偿,保证测试系统输出的压力对指令信号的准确跟踪;最后,对基于降阶模型的自抗扰算法的稳定性和误差收敛性进行理论和定量分析,并对算法的可行性和有效性进行联合仿真和实验验证.研究结果表明,基于降阶模型的自抗扰控制算法对压力脉冲疲劳测试系统中工件体积参数的变化具有良好的鲁棒性且能够有效估计和补偿系统模型降阶误差等干扰,其跟踪性能相比于传统的PID控制器最大提升35.4%.     

柔性关节机操手的神经网络控制

本文在关节柔性较弱的情况下，对柔性关节机器人操作手的轨迹跟踪问题，提出了一种基于奇异摄动理论的机器人神经网络控制设计方法，在一般框架下证明了系统跟踪误差最终一致有界，并且可以通过选取增益矩阵使该误差界任意地小. 该方法克服了对模型参数线性化条件的要求，无需求解回归矩阵，因而具有很强的鲁棒性和模型推广能力. 数值试验表明，所提出的控制方法是可行且有效的.     

模糊奇异摄动系统动态输出反馈H∞控制

针对一类非线性奇异摄动系统,建立了基于T-S 模糊模型的模糊奇异摄动系统模型．通过李亚普诺夫 方法和Schur 补定理,研究其动态输出反馈H∞控制．将系统动态输出反馈H∞控制器设计归结为求解一组与摄动参 数e 无关的线性矩阵不等式,避免了由e 引起的数值求解的病态问题．所获得的控制器使闭环系统渐近稳定,并达 到了给定的H∞性能指标．该方法适用于标准和非标准非线性奇异摄动系统．仿真实例说明了该方法的有效性     

基于奇异摄动理论的输入有界机器人轨迹跟踪控制

针对机器人轨迹跟踪中驱动扭矩有界的问题.提出一种基于奇异摄动系统稳定性理论的推广算法.通过在控制律中引入含有误差增益的饱和函数,保证扭矩输入绝对值的上界在给定限制范围内.并可通过适当调节误差增益系数改善系统的轨迹跟踪性能.同时,算法中采用仅包含位置跟踪误差信息的线性滤波函数产生用来替代真实速度误差的伪速度误差信号.使得整个系统的闭环控制不需测量转速.根据提出的推广算法,设计了一种全新的输入有界控制律,验证了算法的有效性.仿真试验对比结果表明,该算法能够严格保证扭矩控制输入的有界性,并在相同参数条件下相比于其他算法,具有更优的轨迹跟踪效果.     

小型四旋翼无人机双闭环轨迹跟踪与控制（英文）

近年来,无人飞行器控制繁荣发展对控制精度与品质要求日益增高.为了应对这一挑战,本文基于奇异摄动的思想设计了四旋翼无人机非线性轨迹跟踪控制器.首先,基于牛顿欧拉定律建立了四旋翼无人飞行器非线性奇异摄动形式的数学模型.然后,引入奇异摄动理论,通过时间尺度分解的方法将系统解耦成内环快子系统和外环慢子系统.再者,根据非线性动态逆的思想分别建立快、慢伪线性子系统,并基于此分别设计外环轨迹跟踪、内环稳定子控制器,综合子控制器生成应用于原系统的全阶控制器以兼顾跟踪精度和鲁棒特性.针对内环快系统,采用线性二次调节控制器以实现稳定快速地控制飞行器旋转动态;针对外环慢系统,运用经典的比例–微分–积分控制器以跟踪所给定的轨迹.最后给出了仿真实例说明本文结论的有效性.     

奇异摄动系统的边界层鲁椿控制研究及应用

研究一类非线性奇异摄动系统的边界层鲁棒控制问题。该类系统边界层的不确定项不满足一般匹配条件。鲁棒控制器的设计分为伪名义边界层和整个边界层系统两步进行。在满足某些条件时，设计的控制器可使该类系统的边界层仍保持渐近稳定特性，将此方法用于中程空地导弹的中制导系统，仿真结果验证了该设计方法的有效性。     

Approximate output regulation of a class of nonlinear systems

This work proposes an approximate output regulation of a class of nonlinear systems with time-varying disturbances. Since the implicit manipulated input cannot be solved exactly, a novel input/output linearized framework based on the Lyapunov function is developed. Through the step-by-step systematic design and an applied numerical method, the developed nonlinear controller is found to be a dynamic and state feedback. In terms of a certain invariant manifold, an approximate output regulation design without the need of derivative information of disturbances is proposed. The synthesis of dynamic feedforward/feedback controller includes only one tuning parameter, and is equivalent to a low-and-high gain approach. It is ensured that satisfactory tracking performance can be achieved with only instantaneous values of the exogenous signal available. Moreover the robustness of the system would be enhanced. Finally, an illustrative CSTR example is given to demonstrate the regulation control developed here.     

速度时滞反馈控制下磁浮系统的稳定性与Hopf分岔

The problem of time delay speed feedback in the control loop is considered here.Its effects on the linear stability and dynamic behavior of the maglev system are investigated.It is found that a Hopf bifurcation can take place when the time delay exceeds certain values.The stability condition of the maglev system with the time delay is acquired.The direction and stability of the Hopf bifurcation are determined by constructing a center manifold and by applying the normal form method.Finally,numerical simulations are performed to verify the analytical result.     

速度时滞反馈控制下磁浮系统的稳定性与Hopf分岔

The problem of time delay speed feedback in the control loop is considered here. Its effects on the linear stability and dynamic behavior of the maglev system are investigated. It is found that a Hopf bifurcation can take place when the time delay exceeds certain values. The stability condition of the maglev system with the time delay is acquired. The direction and stability of the Hopf bifurcation are determined by constructing a center manifold and by applying the normal form method. Finally, numerical simulations are performed to verify the analytical result.     

Exact design manifold control of a class of nonlinear singularly perturbed systems

The integral manifold approach captures from a geometric point of view the intrinsic two-time-scale behavior of singularly perturbed systems. An important class of nonlinear singularly perturbed systems considered in this note are fast actuator-type systems. For a class of fast actuator-type systems, which includes many physical systems, an explicit corrected composite control, the sum of a slow control and a fast control, is derived. This corrected control will steer the system exactly to a required design manifold.     

Design of sensitivity-reducing compensators using observers

In this paper the design of compensators for output feedback systems which satisfy a sensitivity, reduction criterion is considered for the case when the dynamic compensator is an observer. Using the conditions for comparison sensitivity design of output feedback systems derived by Naeije and Bosgra [4], it is shown that for arbitrary stable state-observers (full or reduced order) there exist feedback gains multiplying the system output and observer states for which the system is stable and the sensitivity reduction criterion is satisfied. Use of observers enables direct control over some of the feedback system eigenvalues and leads to a useful interpretation of the sensitivity weighting matrix. A design procedure is described and illustrated by an example of an aircraft control. The results are graphically compared with results obtained by a conventional design procedure.     

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.     

奇异摄动磁悬浮系统的串级PID控制稳定性研究

研究采用串级PID控制的奇异摄动磁悬浮系统参数稳定范围.首先给出磁悬浮系统的串级PID控制算法与模型,讨论了系统稳定应该遵循的两个条件:一个是慢变子系统PID控制的渐近稳定条件,另一个是快变子系统电流环稳定条件,从而推导出基于串级PID控制的磁悬浮系统所应遵循的参数稳定范围和摄动参数稳定上界.结论说明由于电流环稳定条件与PID稳定条件存在较强耦合,对系统固有参数要求较为严格,导致实际系统调试难度较大.     

Robustness of dynamic output feedback control for singular perturbation systems

The problem of the robustness of dynamic output feedback control for singular perturbation systems is investigated. The solution to this problem is reduced to the simultaneous design of static output feedback controllers for the fast subsystem and the so-called auxiliary system of the slow subsystem. Some conditions are proposed to ensure the robustness of the actual closed-loop system. The exact upper bound of the parasitic parameter for the controlled system is also determined. Finally, an actual model which failed in dynamic output feedback control in [4] is reexamined successfully here.     

Inversion techniques for trajectory control of flexible robot arms

A general framework is given for computing the torques that are needed for moving a flexible arm exactly along a given trajectory. This torque computation requires a dynamic generator system, as opposed to the rigid case, and can be accomplished both in an open- or in a closed-loop fashion. In the open-loop case, the dynamic generator is the full or reduced order inverse system associated to the arm dynamics and outputs. In order to successfully invert the arm dynamics, the torque generator should be a stable system. The stability properties depend on the chosen system output, that is on the robot variables (e.g., joint or end-effector) to be controlled. The same inversion technique can be applied for closed-loop trajectory control of flexible robots. A simple but meaningful nonlinear dynamic model of a one-link flexible arm is used to illustrate different feasible control strategies. Simulation results are reported that display the effects of the system output choice on the closed-loop stability and on the overall tracking performance.     

Second-order terminal sliding mode control of uncertain multivariable systems

A second-order terminal sliding mode controller for uncertain multivariable systems is proposed in this paper. The controller adopts the hierarchical control structure. The paper derives the state transform matrices which are used to transform a multivariable linear system to the block controllable form consisting of two subsystems, an input–output subsystem and a stable internal dynamic subsystem. The proposed controller utilizes a non-singular terminal sliding mode manifold for the input–output subsystem to realize fast convergence and better tracking precision. Meanwhile, a chattering-free second-order terminal sliding mode control law is presented. The stability of uncertain multivariable systems can be realized using the proposed controller. A derivative estimator is utilized in the paper to estimate the derivatives of the sliding mode functions for the controller. The simulation results are presented to validate the design method.