Hard Deadlines in Real-Time Control Systems

Abstract

In a real-time control system where the control input is computed by a controller computer, the transient computer failures caused by an electromagnetic interference may seriously affect system stability. The faulty controller computer causes either a long delay in the feedback loop thus failing to update the control input for one or more sampling intervals, or control input disturbances by updating the control inputincorrectly until the fault is handled properly. If the period of this abnormal behavior exceeds a certain limit called a hard deadline, either the necessary conditions for system stability will be violated or the system willleave the allowed state space. In such a case a dynamic failure is said to occur in the system. We present a method for deriving hard deadlines for linear time-invariant control systems by examining the stability of the state difference equations resulting from the modification of the original state equations with an assumed maximum delay and several random sequences that represent the effects of stationary occurrences of the disturbances to, as well as the random delays of, the control input. Moreover, a one-shot event model, in which a single long-lasting fault causes a dynamic failure, is presented based on the state trajectory and the allowed state space.