High‐gain observers in nonlinear feedback control

Abstract

SUMMARYIn this document, we present the main ideas and results concerning high‐gain observers and some of their applications in control. The introduction gives a brief history of the topic. Then, a motivating second‐order example is used to illustrate the key features of high‐gain observers and their use in feedback control. This is followed by a general presentation of high‐gain‐observer theory in a unified framework that accounts for modeling uncertainty, as well as measurement noise. The paper concludes by discussing the use of high‐gain observers in the robust control of minimum‐phase nonlinear systems. Copyright © 2013 John Wiley & Sons, Ltd.

Robust Task Space Finite-Time Chattering-Free Control of Robotic Manipulators

“…However, its combination with our controller requires further investigations. Application of Luenberger-style observers [60,61], high-gain observers [62,63], model-free observers [64,65] or a class of observers based on the sliding-mode algorithms [66] seems to be an efficient approach compared with both backward difference technique and direct measurement. Although all the aforementioned observers are able to reliably reconstruct manipulator state (both joint velocity and acceleration) based on position measurement, there appears a difficulty to combine our control law and the observer from [60][61][62][63][64][65].…”

“…Application of Luenberger-style observers [60,61], high-gain observers [62,63], model-free observers [64,65] or a class of observers based on the sliding-mode algorithms [66] seems to be an efficient approach compared with both backward difference technique and direct measurement. Although all the aforementioned observers are able to reliably reconstruct manipulator state (both joint velocity and acceleration) based on position measurement, there appears a difficulty to combine our control law and the observer from [60][61][62][63][64][65]. In order to make such combination possible, observers proposed in works [60][61][62][63][64][65] have to satisfy the so-called separation principle [68] which implies both the continuity of the controllers from [60][61][62][63][64][65] with the fully available state and asymptotic stability of the closed-loop system under the continuous state feed-back controllers.…”

“…Although all the aforementioned observers are able to reliably reconstruct manipulator state (both joint velocity and acceleration) based on position measurement, there appears a difficulty to combine our control law and the observer from [60][61][62][63][64][65]. In order to make such combination possible, observers proposed in works [60][61][62][63][64][65] have to satisfy the so-called separation principle [68] which implies both the continuity of the controllers from [60][61][62][63][64][65] with the fully available state and asymptotic stability of the closed-loop system under the continuous state feed-back controllers. Let us observe that our control law (28) is discontinuous what prevents an application of the state observers from [60][61][62][63][64][65].…”

“…In order to make such combination possible, observers proposed in works [60][61][62][63][64][65] have to satisfy the so-called separation principle [68] which implies both the continuity of the controllers from [60][61][62][63][64][65] with the fully available state and asymptotic stability of the closed-loop system under the continuous state feed-back controllers. Let us observe that our control law (28) is discontinuous what prevents an application of the state observers from [60][61][62][63][64][65]. Although the observer offered in [66] fulfils the separation principle, our controller handles unbounded uncertainties (in dynamics and disturbances) and does not require boundedness ofq andq, respectively.…”

Real‐Time Sliding Mode Observer Scheme for Shear Force Estimation in a Transverse Dynamic Force Microscope

“…A robust process is suggested which allows the application of a sliding mode observer, based on a low order linear model, avoiding the requirement of any extra measurements such as the cantilever tip velocity. It is well established that sliding mode observers are a possible robust solution to this problem in comparison to many other options [19][20][21][22][23][24][25]. Sliding mode observers exhibit a high degree of accuracy when estimating state variables in the presence of unknown inputs [26][27][28].…”