Non-overshooting continuous in convergence sliding mode control of second-order systems

TL;DR

This paper introduces a nonlinear sliding mode control method for second-order systems that ensures non-overshooting, continuous control action, and finite-time convergence even with disturbances, validated through numerical and experimental results.

Contribution

A novel nonlinear sliding mode controller with a single parameter that guarantees non-overshooting and finite-time convergence for perturbed second-order systems.

Findings

Ensures non-overshooting behavior despite disturbances.

Achieves finite-time convergence with continuous control.

Validated through numerical simulations and experiments.

Abstract

This paper proposes a novel nonlinear sliding mode state feedback controller for perturbed second-order systems. In analogy to a linear proportional-derivative (PD) feedback control, the proposed nonlinear scheme uses the output of interest and its time derivative. The control has only one free design parameter, and the closed-loop system is shown to possess uniform boundedness and finite-time convergence of trajectories in the presence of matched disturbances. We derive a strict Lyapunov function for the closed-loop control system with a bounded exogenous perturbation, and use it for both, the control parameter tuning and analysis of the finite-time convergence. The essential features of the proposed new control law is non-overshooting despite the unknown dynamic disturbances and the continuous control action during the convergence to zero equilibrium. Apart from the numerical results, a revealing experimental example is also shown in favor of the proposed control and in comparison with PD and sub-optimal nonlinear damping regulators.