Active disturbance rejection control for non-minimum phase systems

Active disturbance rejection control (ADRC) has been applied to solve various types of control problems across many engineering disciplines, but largely within the confine of minimum phase systems. This paper, however, explores systematically its applications to non-minimum phase (NMP) systems, particularly those with transfer functions that have right half plane zeros. It is first shown that, a regular ADRC controller, if not tuned carefully, could easily yield an undesirable solution for NMP systems. We then demonstrate the reasons behind the difficulty using transfer function analysis, leading to a solution in how we tune the ADRC for NMP systems. In particular, a systematic design and tuning procedure is obtained based on the relationship between the high frequency gain of the system and the controller bandwidth. Finally, the proposed method allows a user to easily make a tradeoff between the undershoot, which is unique in NMP systems, and the response time, using the frequency response method of gain and phase compensation.