Trajectory Following Quasi-Sliding Mode Control for Arbitrary Relative Degree Systems

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1196)


This study presents a new approach to discrete-time sliding mode control, based on a new trajectory following reaching law for arbitrary relative degree output systems. We divide the control design to two stages. First, we generate a desired profile of the sliding variable with a conventional switching type reaching law of Gao et al. Next, utilizing arbitrary relative degree sliding variable, we introduce a trajectory following reaching law for the real disturbed system. Our strategy ensures that the representative point of the system approaches the sliding plane monotonically and crosses it in finite time. After the sign of the sliding variable has changed for the first time, it changes again in each consecutive time step and its absolute value does not exceed an a priori known constant. Moreover, the strategy guarantees a reduction of the quasi-sliding mode band width, which results in improved robustness of the system. The paper is concluded with a simulation example.


Discrete-Time systems Arbitrary relative degree Reaching law Sliding mode control Trajectory generator 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute of Automatic ControlŁódź University of TechnologyŁódźPoland

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