A Nonlinear Exact Disturbance Observer Inspired by Sliding Mode Techniques

Abstract

Inspired by sliding mode techniques, a nonlinear exact disturbance observer is proposed. The disturbance and its derivatives up to the second order are assumed to be bounded. However, the bounds of the disturbance and its derivatives are unknown, and they are adaptively estimated online during the observation of the disturbances. The exact convergence of the disturbance observer to the genuine disturbance is assured theoretically. The convergence speed of the disturbance estimation error is controlled by design parameters. The proposed method is robust to the type of disturbance and is easy to be implemented. Computer simulation results show the superiority and effectiveness of the proposed formulation.

Super-twisting disturbance observer-based finite- time attitude stabilization of flexible spacecraft subject to complex disturbances

“…One is the output embedding method (Chen, 2015) in which the state ω in J0 -1ω×J0ω is replaced with the output y directly in the design of SMDO. Although the nonlinear item J0 -1ω×J0ω can be removed from the error dynamics of SMDO without considering the measurement noise, this method will make the effects of the measurement noise heavier since the difference between J0 -1ω×J0ω and J0 -1y×J0y includes more complicated noise properties if the measurement noise is considered in the output y .…”

“…Compared with the output embedding method in Chen (2015), the proposed STDO can avoid the problem caused by the nonlinear item J0 -1ω×J0ω by turning the nonlinear system equation (8) into a linear equation (11). Hence, STDO will not bring more complicated noise by replacing ω with y directly, which avoids the shortcoming of the output embedding method.…”

“…In DOBC, a disturbance observer is applied to estimate the lumped disturbance and the estimated result is used as a feedforward compensator. Then, a feedback controller is applied to attenuate the uncompensated disturbance and achieve the desired control objective (Guo and Cao, 2014; Chen et al., 2015). Thus, the ability of disturbance rejection for DOBC depends on the accuracy of the disturbance observer to a great extent.…”

“…Disturbance observer was designed first in the frequency domain for linear plant (Nakao et al., 1987; Chen et al., 2015). Then, it was designed in the time domain for linear plants as well as nonlinear ones (Chen et al., 2000; Guo and Chen, 2005; Yang et al., 2012, 2013a, 2013b; Sun and Guo, 2014).…”

“…To avoid the problem caused by high-order disturbance observers, a sliding mode technique was introduced into the design of the disturbance observer, and this was called a sliding mode disturbance observer (SMDO) (Davila et al., 2005; Hall and Shtessel, 2006 ; Lu et al., 2012; Moreno and Osorio, 2012; Xiao et al., 2013; Hu et al., 2014; Chen, 2015; Duraffourg et al., 2016). In the design of the SMDO for spacecraft attitude control systems, the angular velocity is often considered as measurement output to estimate system states including angular velocity and augmented disturbance.…”