This paper constructs a new type of observer structure called dynamic observer for the problem of sensor fault detection under finite frequency disturbance and noise in networked control systems. A joint optimization of zero and pole for fault detection is proposed, which features a dynamic observer whose zero can be freely assigned. The dynamic observer is based on the traditional proportional integral observer and can be expanded to more general types. It has the property that its zero can be assigned to anywhere. The dynamic observer overcomes the problem of invariant zero associated with traditional observers. Zero of the dynamic observer is assigned to the characteristic spectrum of the finite frequency disturbance signal and the network transmission delay, so the effect of disturbance on the residual can be better attenuated. A comprehensive performance of the observer for fault detection is proposed. The pole of the dynamic observer is designed by the $H_2/H_\infty $ method to optimize the comprehensive performance of the observer. Finally, taking the model of a networked two-wheel self-balancing robot as an example, the fault detection performance of the dynamic observer, the proportional integral observer and the proportional observer are compared. The comparison results show the advantages and effectiveness of the dynamic observer fault detection method.