Abstract
The research work presented within this paper deals with an innovative second-order sliding mode control (SOSMC) allocated to adaptive gain and associated with nonlinear systems subject to unknown but bounded uncertainties. The derived controller guarantees the control gain dynamical adaptation for the sake of counteracting the system’s uncertainties and to mitigate the chattering phenomenon. The Lyapunov method is also used to analyses the stability of any closed loop system (CLS) within a finite-time under bounded uncertainties assumptions. To assess how effective is the approach considered within this paper, the adaptive controller has been carefully studied on a benchmark of nonlinear systems on a damped overturned pendulum.
Highlights
A damped overturned pendulum cart is an interesting non-linear system, which is an under-actuated mechanical system including several less number of inputs compared to the degrees of freedom [1]
The system was extensively used as a benchmark for testing various control algorithms due to its highly unstable nonlinear dynamics. controlling a nonlinear system happens when the cart is moved along the horizontal direction in between two positions while the pendulum is kept at the upright position known to have the lowest level of mechanical oscillations. from
We focus on designing an adaptive second-order sliding mode control (SOSMC) for expression (3) such that the closed loop system (CLS) is considered robust against the uncertainty satisfying the condition (5)
Summary
A damped overturned pendulum cart is an interesting non-linear system, which is an under-actuated mechanical system including several less number of inputs compared to the degrees of freedom [1]. The proposed approach does not require the knowledge of the control gain bounds and it allows the reduction of the chattering phenomenon as well as the convergence of the sliding variables to the origin in infinitetime. It allows in adjusting the tuning parameters of the controller whilst guaranteeing a sliding motion. The system, operating under closed-loop considerations, becomes stable system and converges in finite-time to the anticipated system states It contributes a controller handling the control.
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