In this paper, the problem of designing a full-order unknown input observer(UIO) for a general discrete-time linear system with unknown inputs is proposed. This procedure is based on augmenting a standard system observer with unknown inputs.
The proposed UIO can estimate state and unknown input of systems. The existence conditions of the proposed UIO are provided, and constructive design procedures are discussed. Unknown inputs are considered to be present in the state and output equation, which is more general situation. The main advantage of the proposed UIO is that it can handle the unknown input present in the state and output equation simutaneously, if the modes of unknown inputs have different directions each other. In the previous researches, there needs more restrictive assumption, which is the orthogonal property of fault modes.
The proposed UIO can be used to diagnose a control system, since some faults are can be modeled as addictive unknown input which can be estimated by UIO. The faults of state equation can be considered as actuator faults and the faults of output equation can be considered as sensor faults. Therefore, the proposed UIO can diagnose the dynamical system with simultaneously occurred faults in actuators and sensors.
In practical situations, fault diagnosis can be difficult because of the white noise which includes process noise and measurement noise. In this paper, these problems are considered by introducing time window.
