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

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

Decentralised control for complex systems - an invited survey

“…Finally, it should be pointed out that higher order sliding mode control has been well studied (see, e.g., Levant and Fridman, 2010;Bartolini et al, 2003;Dinuzzo and Ferrara, 2009). In addition, many results concerning decentralised schemes for interconnected systems have been obtained as mentioned above (Yan and Dai, 1998;Mahmoud, 2009), even for fully nonlinear interconnected systems (Yan et al, 2010).…”

On oscillatory behavior of two-dimensional time scale systems

“…Two-dimensional systems of first-order equations have several reallife applications in engineering. For example, Bartolini et al [4][5][6] considered a secondorder system in order to control uncertain nonlinear systems by some control techniques, for example, sliding mode and approximate linearization. In addition to nonoscillatory solutions of second-order systems, periodic and subharmonic solutions were also considered in [7][8][9], and important results were obtained.…”

Robust Sliding Mode Control of Permanent Magnet Synchronous Generator-Based Wind Energy Conversion Systems

“…Modifications in the first-order sliding mode control calculation to assume imperfect switching times, such as using hysteresis instead of signum functions, can be utilized in order to compensate for chattering, but such methods complicate calculations for a relatively small reduction in chattering [15][16][17][18]. Thus, the principal method for avoiding chattering is to increase the order of sliding mode control by forcing higher order derivatives of the sliding manifold to zero [19][20][21]. In an ideal case, careful usage of high order sliding mode control removes chattering as a concern [22][23][24].…”