$H_{\infty}$ Based Disturbance Observer Design for Non-minimum Phase Systems with Application to UAV Attitude Control

This paper presents a disturbance observer (DOB) design methodology, which is applicable to both multi-input-multi-output (MIMO) and non-minimum phase systems. The DOB is designed via minimizing $H_{\infty}$ norm of closed-loop dynamics from disturbance to its estimation error. This proposed design methodology returns the optimal stable plant inverse and $Q$ filter with guaranteed closed loop stability for a given baseline feedback system, which is more efficient than manual design and tunning that involves lots of effort for either MIMO or non-minimum phase systems. Furthermore, it utilizes well-established $H_{\infty}$ synthesis in robust control theory, and can be further transformed to a convex optimization problem with linear matrix inequality (LMI) constraints and solved efficiently using existing software thereafter. This design methodology unifies all cases of single-input-single-output (SISO) and MIMO systems, as well as minimum-phase and non-minimum-phase systems into one design framework, which lays theoretical fundamental for developing potential DOB design toolbox for a general system. This paper also considers measurement noise, which may severely decrease the DOB's performance. To address this issue, besides the original control channel from disturbance to its estimation error, this paper adds an additional channel when formulating the $H_{\infty}$ optimization problem. This design methodology is comprehensively analyzed, and applied to a tail-sitter UAV platform that possesses a non-minimum phase angular rate dynamics. Both simulation and experiment show that the designed DOB successfully estimates and suppresses external disturbances in the presence of measurement noise.