Fast adaptive fault estimation for linear system with actuator effectiveness loss and unmatched unknown inputs

A fast adaptive fault estimation algorithm is proposed to enhance the performance of fault estimation in linear time invariant system with unmatched unknown input. An algebraic method based on the unknown input observer for perfect decoupling of unknown input and estimation, is implementable if matching condition is satisfied. Matching condition limits the practical application of these methods. In this article the method offered for fault estimation doesn't need matching condition. Unlike conventional methods studied in the litreture, this method doesn't require auxiliary output for fault estimation inpresence of unmatched unknown input. In the first step, the unknown input is divided into two parts: matched and unmatched unknown inputs. With an assumption that there exists a dynamic model for unmatched part, the new augmented system is constructed. for state estimation of augmented system, ordinary unknown input observer strategy employed. The observer can estimate all states of the system without being affected by the matched unknown input. Fast adaptive law is employed for fault estimation. Stability condition is derived and explored using LMI criteria. The effectiveness of the proposed method is shown by numerical simulation for a flexible joint example.