Presence Of Nonparametric Uncertainties Research Articles

Design of an integral super twisting sliding mode controller for position control and extending the traveling range of initially curved micro-beams

Based on the super twisting concept, this article develops an integral sliding mode controller with nonlinear disturbance observer for position control and extending the traveling range of an initially curved micro-beam. The nonlinear damped model of the curved micro-beam is modeled based on the non-classical continuum theory. The single-mode assumption is used to transform the nonlinear governing PDE of the system into a nonlinear state-space form. The robust controller is designed to overcome the position control problem in the presence of non-parametric uncertainties and unknown non-symmetric input saturation due to the existing constraints in the electrostatic actuation. The effects of the uncertainties are considered as a compound disturbance term which can be estimated in finite time. Furthermore, due to the estimation properties of the observer, knowledge about the bounds of the uncertainties is not required. Extensive simulation results clearly verified the effectiveness of the controller in position tracking and extending the traveling range of the initially curved micro-beam to the unstable zones under smooth control effort.

Immersion and Invariance Based Composite Adaptive Control for Nonlinear Systems with Both Parametric and Non-Parametric Uncertainties

The design of an immersion and invariance (I&I) based composite adaptive control for a class of uncertain nonlinear systems is presented in this paper. The key feature of this control scheme lies in the construction of the novel adaptive laws, aiming to address both parametric and non-parametric uncertainties simultaneously. Composite adaptive laws, which are driven by both the information of tracking error and prediction error, are first proposed using I&I theory for the estimations of parametric uncertainties. Then the technique of σ-modification is used to guarantee the stability in the presence of non-parametric uncertainties. Stability analysis is presented using the Lyapunov theory. Improved performance of the proposed control scheme is observed via numerical simulations.