Research ArticleDisturbance rejection control for non-minimum phase systems with optimal disturbance observer

- A systematic design strategy of DOB is proposed for stable NMP systems by taken both RHP zeros and time delay into account.
- The optimization function is established by taken robust internal stability, relative order, mixed sensitivity design requirements into account together.
- The solution of Q filter is optimized by introducing the allpass portion into virtually controlled objective of H∞ problem, based on which the unstable poles of inverse of nominal plant can be eliminated for robust internal stability constraints.
- Discussions on how the DOB can compensate the real plant into the nominal one are presented, which are verified in the simulations.

This paper investigates the disturbance rejection control for stable non-minimum phase (NMP) systems with time delay. A robust disturbance observer (DOB) based control structure is proposed. Specifically, the robust DOB is employed to compensate the uncertain plant into a nominal one, based on which a prefilter is adopted to acquire desired performance. Then, a novel DOB configuration strategy for stable NMP systems is proposed. This strategy synthesizes the internal and robust stability, relative order and mixed sensitivity design requirements together to establish the optimization function. The optimal solution is obtained by standard H∞ theory under the condition of guarantying the presented requirements. We also investigate how the DOB can compensate the uncertain plant into a nominal one. The specifical design procedure is presented for an uncertain plant with both unstable zeros and time delay.