Research Initiation Award: Stability of Feedback Systems with Sensor or Actuator Failures

该项目将研究线性、时不变、多输入、多输出反馈系统的完整性问题。考虑了在三种传感器或执行器故障情况下，单位反馈系统的闭环稳定性问题。在第一类中，任意数量的循环，包括所有循环，都可能失败；在第二类中，除了所有循环之外，任何数量的循环都可能失败；在第三类中，除了一个循环外，任何循环都可能失败。我们分析了在三种情况下均存在故障的单位反馈系统的稳定性。对于第一类故障，设备和补偿器必须从一开始就稳定，因为所有回路的故障将使配置减少为级联连接。对于给定的无不稳定隐模的多输入多输出对象，可以对稳定闭环系统的所有补偿器的类别进行参数化。我们的目标是参数化补偿器的类别，使其对这三类故障中的每一类都能达到完整性。正如预期的那样，这种参数化只对某些类型的植物是可能的。我们的目标是找出那些能使每次故障都能同时稳定的装置，找到一种系统的方法来合成补偿器来实现这种同时稳定，并找出所有可实现的闭环传递函数。这将表明哪些性能目标可以与完整性一起实现。在所有补偿器参数化的基础上，该结果也将用于在反馈回路中引入恒定增益因子的部分回路失效系统的补偿器的综合，并扩展为针对这种情况的代数综合方法结构动力学被引入到回路中。

The project will study the problem of integrity in linear, time-invariant, multi- input, multi-output feedback systems. We consider the closed-loop stability of the unity-feedback system under three classes of sensor or actuator failures. In the first class any arbitrary number of loops, including all, may fail; in the second class any number of loops, except all, may fail; in the third class, any loop but only one loop may fail. We analyze the stability of the unity-feedback system with failures in each of the three classes. For the first class of failures, the plant and the compensator have to be stable from the start since the failure of all loops will reduce the configuration to a cascade connection. For a given multi-input multi-output plant which has no unstable hidden modes it is possible to parametrize the class of all compensators that stabilize the closed-loop system. Our goal is to parametrize the class of compensators that achieve integrity for each of the three classes of failures. As expected, such parametrization is possible only for certain classes of plants. The objectives are to identify those plants for which simultaneous stabilization of the nominal plant with each failure can be achieved, to find a systematic method to synthesize compensators that achieve this simultaneous stabilization, and to find the class of all achievable closed-loop transfer functions. This will indicate which performance objectives can be achieved together with integrity. Based on the parametrization of all compensators that the results will also be used in synthesis of compensators for systems with partial loop failures where constant gain factors are introduced in the feedback-loops and extended to an algebraic synthesis method for the case of structured dynamics being introduced in the loops.