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。我们考虑了三类传感器或执行器故障下单位反馈系统的闭环稳定性。在第一类中，任意数目的循环，包括所有循环，都可能失败；在第二类中，除全部之外，任何数目的循环都可能失败；在第三类中，除了一个循环之外，任何循环都可能失败。分析了三类故障下的单位反馈系统的稳定性。对于第一类故障，对象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。对于给定的没有不稳定隐模的多输入多输出对象，可以将使闭环系统稳定的所有补偿器的类别参数化。我们的目标是将实现三类故障中每一类故障的完整性的补偿器类参数化。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。目标是确定哪些工厂可以在每次故障时同时实现标称工厂的稳定，找到一种系统的方法来综合实现这种同时镇定的补偿器，并找出所有可实现的闭环系统传递函数的类。这将表明哪些绩效目标可以与诚信一起实现。基于所有补偿器的参数化，其结果也将用于具有部分环路故障的系统的补偿器的综合，其中恒定增益因子是在反馈回路中引入，并推广到回路中引入结构动力学时的代数综合方法。

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.