二阶饱和线性系统的线性最优容错吸引域

Linear optimal fault-tolerant attraction domain for second-order saturating linear system

考虑执行器故障影响,研究了二阶饱和线性系统的吸引域估计问题.通过适当定义容错吸引域,并采用椭圆逼近,使得系统的吸引域具有容错能力.为了保证容错吸引域的收敛性能,通过状态反馈将闭环系统极点配置在圆形极点区域内.基于参数空间,给出了圆形极点区域对应的反馈增益向量空间的不等式表示.在反馈增益向量空间和执行器幅值的约束下,基于参考集的缩放构造了一个容错吸引域的优化问题,并提出了一种求解方法.最后给出一个实例进行验证.

The assessment of the attraction domain is studied for the second-order saturating linear system with possible faults of the control actuators. The attraction domain is endowed with the property of fault-tolerance by defining the fault- tolerant attraction domain properly which is approached by the ellipse. To ensure the desired＇convergence speed of the fanlt-tolerant attraction domain, the poles of the closed-loop system are placed in the circle area of the complex plane by state feedback. Based on the parameter space, the feedback gain space described in the form of the inequality is obtained with respect to the circle pole assignment domain. Under the constraints of the feedback gain space and the amplitude limitation of the control actuators, an optimization problem about the fault-tolerant attraction domain is constructed by the scaling of the reference set, and a method is presented to solve it. Finally, an example shows the effectiveness of the method.