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HOSM control under quantization and saturation constraints: Zig-Zag design solutions

In many experimental systems, discrete and bounded actuators implement control laws with sampling, quantization and saturation problems. This paper is dedicated to only the last two in the context of the implementation of a Super-Twisting sliding mode control. A new control design, called “Zig-Zag sliding mode control”, is proposed. Issues of quantization and saturation problems are respectively investigated directly and implicitly by the proposed control. The main contribution of the proposed method consists in having a faster convergence and well performances even when the saturation of the actuators is decreased up to a certain limit in which other methods fail to converge. Simulation results of the proposed method compared to the results of traditional implementations highlight the well founded Zig-Zag design.