奇异线性系统在执行器饱和受限下不变集条件的改进(英文)

本文考虑饱和线性反馈下奇异线性系统扩大吸引域估计的问题.根据每个输入是否饱和,将输入空间分成若干子区域.在每个子区域内部,系统模型中没有显示的部分状态的时间导数可被显式表达.利用含有全部系统状态的二次Lyapunov函数,建立一组双线性矩阵不等式形式的改进的不变集条件.该组条件下,二次Lyapunov函数的水平集可诱导出一个吸引域估计.为得到最大的吸引域估计,构建了以这些双线性矩阵不等式为约束条件的优化问题,并为其求解给出了迭代算法.仿真结果表明本文得到的吸引域估计明显大于现有结果.     

Low-and-high gain design technique for linear systems subject to input saturation —a direct method

The low-and-high gain design technique, which was initiated for a chain of integrators and completed for general linear asymptotically null controllable with bounded controls systems, was conceived for semi-global control problems beyond stabilization and was related to the performance issues such as semi-global stabilization with enhanced utilization of the available control capacity and semi-global disturbance rejection. Although the low-and-high gain design technique, as initiated for a chain of integrators, is based on an explicit eigenstructure assignment algorithm, its full development is based on the solution of an algebraic Riccati equation (ARE) which is paramterized in an arbitrarily small scalar, called low gain, parameter. In this paper, we develop a new complete low-and-high gain design procedure which is based on an explicit eigenstructure assignment algorithm. The new design approach avoids the solution of the numerically stiff parametrized ARE. © 1997 by John Wiley & Sons, Ltd.     

分区四元数姿态控制

提出了一种基于分区控制策略的四元数姿态控制律. 其基本思想是基于姿态四元数误差分区设计目标角速度, 由此将问题降阶为一个角速度跟踪问题; 基于不同的角速度跟踪误差, 设计了切换类型的抗干扰姿态控制律. 该控制策略可以使得姿态快速收敛, 并且在合适的参数选择条件之下还能同时满足控制力矩的饱和约束. 通过综合相平面和Lyapunov函数的分析方法严格证明了闭环系统全局收敛的性质. 最后, 通过数值仿真验证了本文提出的控制方案的有效性.     

Analysis and design for discrete-time linear systems subject to actuator saturation

We present a method to estimate the domain of attraction for a discrete-time linear system under a saturated linear feedback. A simple condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant. Moreover, the condition can be expressed as linear matrix inequalities (LMIs) in terms of all the varying parameters and hence can easily be used for controller synthesis. The following surprising result is revealed for systems with single input: suppose that an ellipsoid is made invariant with a linear feedback, then it is invariant under the saturated linear feedback if and only if there exists a saturated (nonlinear) feedback which makes the ellipsoid invariant. Finally, the set invariance condition is extended to determine invariant sets for systems with persistent disturbances. LMI based methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements.     

Analysis and design of delta operator systems with nested actuator saturation

In this paper, the problem of estimating the domain of attraction is considered for delta operator systems subject to nested actuator saturation. A set invariance condition is established for the delta operator system with nested actuator saturation in terms of auxiliary feedback matrices. Based on the set invariance condition, an optimisation approach is proposed to estimate the domain of attraction for the delta operator system. Thereby, the partial results of nested actuator saturation for both continuous-time systems and discrete-time systems are extended to delta operator system framework. A numerical example is provided to illustrate the effectiveness of the proposed design techniques.     

受限的非仿射非线性系统的自适应控制

针对受限的非仿射非线性系统,结合自抗扰思想提出了非仿射系统的扩张状态观测器(ESO)设计,从而将辅助系统设计技巧拓展到了非仿射系统,然后利用反演和指令滤波器设计了自适应控制器,为受限的不确定非仿射系统提供了新的设计思路.为了补偿受限带来的影响,引入了辅助系统,它的状态被用来补偿跟踪误差.指令滤波器用来处理虚拟控制受限问题,同时获得虚拟控制导数的估计,避免了backstepping中对它的繁琐计算,扩张状态观测器被用来估计系统的未知非仿射非线性项和外部干扰.利用输入状态稳定性(ISS)分析了闭环系统的全局一致有界稳定性.最后仿真结果验证了该设计方案的有效性.     

A unified framework for passive–active fault-tolerant control systems considering actuator saturation and L∞ disturbances

This paper presents a unified passive–active fault-tolerant control strategy to compensate the loss of actuators’ effectiveness. The proposed approach is capable of handling the system in pre- and post-fault diagnosis intervals by passive and active approaches, respectively. The stability of the designed system is independent of the accuracy of information provided by the fault detection and diagnosis unit, however, a precise estimation could improve the conservation. Actuator saturation and L_∞ disturbances effects are considered in the design stage. The trade-off between maximising the domain of attraction and minimising the effects of L_∞ disturbances is tackled by developing a non-constant state feedback strategy. The feedback gains are determined by solving an optimisation problem. The proposed method is implemented on a model of Boeing 747 and results are discussed.