A survey of applications of second-order sliding mode control to mechanical systems

TLDR

Sliding mode control of mechanical systems suffers from chattering, but higher‑order sliding modes mitigate this by applying switching to higher derivatives, though they require multiple time derivatives of the sliding variable, which can be problematic in noisy environments. The paper aims to identify a class of second‑order sliding‑mode controllers that guarantee finite‑time convergence for relative‑degree‑two systems, thereby reducing differentiator stages and handling unmodelled actuator dynamics. The authors demonstrate that various existing second‑order sliding‑mode controllers belong to this class and apply them to solve challenging mechanical‑system control problems. Simulations and experiments confirm the effectiveness of the proposed controllers.

Abstract

The effective application of sliding mode control to mechanical systems is not straightforward because of the sensitivity of these systems to chattering. Higher-order sliding modes can counteract this phenomenon by confining the switching control to the higher derivatives of the mechanical control variable, so that the latter results are continuous. Generally, this approach requires the availability of a number of time derivatives of the sliding variable, and, in the presence of noise, this requirement could be a practical limitation. A class of second-order sliding mode controllers, guaranteeing finite-time convergence for systems with relative degree two between the sliding variable and the switching control, could be helpful both in reducing the number of differentiator stages in the controller and in dealing with unmodelled actuator dynamics. In this paper different second-order sliding mode controllers, previously presented in the literature, are shown to belong to the above cited class, and some challenging control problems involving mechanical systems are addressed and solved. Simulations and experimental results are provided throughout the paper.