Active disturbance rejection control: Theoretical perspectives

Bao-Zhu Guo, Zhi-Liang Zhao
2015 Communications in Information and Systems  
This paper articulates, from a theoretical perspective, a new emerging control technology, known as active disturbance rejection control to this day. Three cornerstones toward building the foundation of active disturbance rejection control, namely, the tracking differentiator, the extended state observer, and the extended state observer based feedback are expounded separately. The paper tries to present relatively comprehensive overview about origin, idea, principle, development, possible
more » ... ent, possible limitations, as well as some unsolved problems for this viable PID alternative control technology. Mathematics Subject Classification: 93C15, 93B52, 34D20, 93D15, 93B51. The nature of the problem is therefore changed now. System (1.4) is just a linear time invariant system for which we have many ways to deal with it. This is likewise feedforward control yet to use output to "transform" the system first. In a different point of view, this part is called the "rejector" of disturbance ([11]). It seems that a further smarter way would be hardly to find anymore because the control u(t) = −â(t) + u 0 (t) adopts a strategy of estimation/cancellation, much alike our experience in dealing with uncertainty in daily life. One can imagine and it actually is, one of the most energy saving control strategies as confirmed in [57] . This paradigm-shift is revolutionary for which Han wrote in [29] that "to improve accuracy, it is sometimes necessary to estimate a(t) but it is not necessary to know the nonlinear relationship between a(t) and the state variables". The idea breaks down the garden gates from time varying dynamics (e.g., f (x 1 , x 2 , d, t) = g 1 (t)x 1 + g 2 (t)x 2 ), nonlinearity (e.g., f (x 1 , x 2 , d, t) = x 2 1 + x 3 2 ), and "internal and external disturbance" (e.g., f (x 1 , x 2 , d, t) = x 2 1 + x 2 2 + ∆f (x 1 , x 2 ) + d). The problem now becomes: how can we realize y(t) ⇒ a(t) ≈ a(t)? Han told us in [31] that it is not only possible but also realizable systematically. This is made possible by the so called extended state observer (ESO). Firstly, Han considered a(t) to be an extended state variable and changed system (1.3) to (1.5) x 2 (t) = a(t) + u(t), a(t) = a (t), y(t) = x 1 (t).
doi:10.4310/cis.2015.v15.n3.a3 fatcat:nswkimjs5nfztc63t4fr6sly6u