Lars Watermann | Searcharxiv

arXiv2026

Chattering Reduction for a Second-Order Actuator via Dynamic Sliding Manifolds

We analyze actuator chattering in a scalar integrator system subject to second-order actuator dynamics with an unknown time constant and first-order sliding-mode control, using both a conventional static sliding manifold and a dynamic sliding manifold. Using the harmonic balance method, we prove that it is possible to adjust the parameters of the dynamic sliding manifold for the specified system class so as to reduce the amplitude of the chattering in comparison to the static manifold. We illustrate our results with a simulation example. This contribution serves as a proof of concept to motivate further investigations in chattering reduction via dynamic sliding manifolds.

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arXiv2023

Modified Implicit Discretization of the Super-Twisting Controller

In this paper a novel discrete-time realization of the super-twisting controller is proposed. The closed-loop system is proven to converge to an invariant set around the origin in finite time. Furthermore, the steady-state error is shown to be independent of the controller gains. It only depends on the sampling time and the unknown disturbance. The proposed discrete-time controller is evaluated comparative to previously published discrete-time super-twisting controllers by means of the controller structure and in extensive simulation studies. The continuous-time super-twisting controller is capable of rejecting any unknown Lipschitz-continuous perturbation and converges in finite time. Furthermore, the convergence time decreases, if any of the gains is increased. The simulations demonstrate that the closed-loop systems with each of the known controllers lose one of these properties, introduce discretization-chattering, or do not yield the same accuracy level as with the proposed controller. The proposed controller, in contrast, is beneficial in terms of the above described properties.

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