A Novel Prescribed-Time Second-Order Sliding Mode Controller Using Only Signs of the Variables: Design and Experimental Validation

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Abstract
In practical control systems, limitations such as binary sensing, sensor saturation, and inherent nonlinearities often restrict the available feedback to only the sign of the measured variables. These constraints, however, lead to the adoption of sign-based control strategies, which offer benefits such as reduced sensor cost, lower computational requirements, and improved robustness. In response to such challenges, this article introduces a novel twisting-like second-order sliding mode (SOSM) algorithm using only signs of the state variables. The proposed SOSM controller can achieve exact output regulation for uncertain nonlinear systems within a prescribed convergence time bound, which is independent of the initial conditions and other design parameters. On the one hand, based on a finite time-varying gain function, the proposed SOSM algorithm offers a more straightforward way to adjust the convergence time. Moreover, it has the potential to substantially reduce the demands on both sensing and computational resources. Finally, simulation comparison and experimental validation on permanent magnet synchronous motors (PMSMs) are presented to demonstrate the effectiveness of the proposed controller.

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