Abstract:

An optimal design approach to fault detection filter with H° index and H1 norm for linear time invariant systems is proposed. At first a linear full-order observer is constructed and the dynamics of residual genera-tor which involves unknown inputs represented by disturbances, noise, model uncertainty and faults is acquired. The sensitivity of residual to faults is char-acterized by H° index, and the robustness of residual to unknown inputs is denoted by H1 norm respectively. By using linear matrix inequality (LMI) method, the existence condition of mixed H°/H1 fault detection observer gain and its solving approach is derived, which leads to an iterative algo-rithm for optimal solution. Finally the optimal fault detection filter can be achieved with an optimal trade-off between the sensitivity to faults and the robustness against the unknown inputs. A numerical example is employed to illustrate the effectiveness of the present approach