Analysis of discrete-time disturbance observer and a new Q-filter design using delay function

In industrial applications, the disturbance observer (DOB) approach has been widely used due to its robustness and simple structure, and its results in a continuous-time fashion are frequently encountered in many literatures. Although most of DOBs are implemented in a discrete-time form with digital devices, a rigorous analysis on the discrete-time DOB is still insufficient compared to the continuous-time DOB. Therefore, in this paper, we mainly focus on the application of the DOB to discrete-time systems and some phenomena that are not observed in continuous-time systems. In particular, the time constant of the discrete-time Q-filter should have a lower bound, while the continuous-time DOB does not have this constraint. The time constant to sampling time ratio of the discrete-time Q-filter plays a crucial role in the discrete-time DOB, and it is suggested that this ratio be one for stability. Based on the above analysis, a new design method of the discrete-time Q-filter using a delay function is proposed. Furthermore, a robust stability condition for discrete-time systems using the delay function Q-filter is presented. Finally, simulation with an optical disk drive (ODD) model demonstrates the effectiveness of the newly proposed Q-filter.