Disturbance rejection control based on state-reconstruction and persistence disturbance estimation

In this note, disturbance rejection control (DRC) based on unknown input observation (UIO), and disturbance-observer based control (DOBC) methods are revisited for a class of MIMO systems with mismatch disturbance conditions. In both of these methods, the estimated disturbance is considered to be in the feedback channel. The disturbance term could represent either unknown mismatched signals penetrating the states, or unknown dynamics not captured in the modeling process, or physical parameter variations not accounted for in the mathematical model of the plant. Unlike the high-gain approaches and variable structure methods, a systematic synthesis of the state/disturbance observer-based controller is carried out. For this purpose, first, using a series of singular value decompositions, the linearized plant is transformed into disturbance-free and disturbance-dependent subsystems. Then, functional state reconstruction based on generalized detectability concept is proposed for the disturbance-free part. Then, a DRC based on quadratic stability theorem is employed to guarantee the performance of the closed-loop system. An important contribution offered in this article is the independence of the estimated disturbance from the control input which seems to be missing in the literature for disturbance decoupling problems. In the second method, DOBC is reconsidered with the aim of achieving a high level of robustness against modeling uncertainties and matched/mismatched disturbances, while at the same time retaining performance. Accordingly, unlike the first method, DRC, full information state observation is developed independent of the disturbance estimation. An advantage of such a combination is that disturbance estimation does not involve output derivatives. Finally, the case of systems with matched disturbances is presented as a corollary of the main results.