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Abstract
A novel scheme for disturbance observer is designed for an extended class of strict-feedback nonlinear systems with possibly unbounded, non-smooth, and state-independent compounded disturbance. To overcome these problems in disturbance observer design, the typical slide mode differentiators are improved by introducing hyperbolic tangent function to make the signals smooth, and then the improved slide mode differentiators are constructively used to estimate the errors of variables in the presence of disturbances. The unbounded, non-smooth or state-independent disturbances are therefore able to be eliminated by using the estimated variable errors. Thus, the bounded or differentiable conditions for disturbance observer design are removed. Furthermore, the convergence of the new disturbance observer is rigorously proved based on Lyapunov stability theorem, and the tracking error can be arbitrarily small. Finally, the simulation results are given to validate the feasibility and superiority of the proposed approach.
Highlights
As is well known, external disturbances, unmodeled dynamics and system uncertainties exist in a wide range of real control processes, which may cause the performance degradation and even the instability of the closed-loop control system
A disturbance observer–based dynamic surface control (DSC) approach was studied for the mobile wheeled inverted pendulum system with bounded lumped disturbance vector in [15]
Remark 4: It can be seen that an auxiliary variable ζ1,0 is designed to estimate e1 by a first order sliding mode differentiator and ζ1,0 can be regarded as the approximator of e1 which can be utilized to design the disturbance observer with the help of (6) and the estimation error can converge to arbitrarily small by appropriately adjusting design parameters
Summary
External disturbances, unmodeled dynamics and system uncertainties exist in a wide range of real control processes, which may cause the performance degradation and even the instability of the closed-loop control system. It has to be mentioned that for all the aforementioned strategies to work, the unknown disturbance is always assumed to be bounded and differentiable [20]–[23], which is very restrictive due to the fact that the compounded disturbances are usually unbounded or differentiable This is because unmodeled dynamics, as same as some non-smooth nonlinearities such as dead zone and backlash, often occur in many physical systems. Combined with fuzzy approximator, a disturbance observer-based adaptive fuzzy control approach was investigated for a class of uncertain MIMO mechanical systems subject to unknown input nonlinearities in [28]. By using the powerful approximation ability of NNs, Chen et al [31] studied an adaptive neural control method based on a disturbance observer for a class of MIMO nonlinear systems with control input saturation.
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