Sliding mode control of continuous time systems with reaching law based on exponential function

12th European Workshop on Advanced Control and Diagnosis

Gamorski, Piotr^1

Institute of Automatic Control, Technical University of Lód, Lód, Poland^1

关键词: Arbitrary trajectories;    Asymptotic convergence;    Exponential rates;    External disturbances;    Reaching law;    Sliding manifolds;    Sliding variables;    State vector;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/659/1/012048/pdf
DOI  :  10.1088/1742-6596/659/1/012048

来源: IOP

【 摘 要 】

In this paper a pseudo-sliding mode control is proposed by introducing a continuous and smooth input signal in order to guarantee both chattering elimination and boundedness of sliding variable derivative in the presence of non-zero external disturbance. For this purpose, having fixed a suitable sliding manifold, a homogeneous differential equation describing the sliding variable evolution is considered. It is discussed later in this paper that the input signal formed on the basis of this equation provides asymptotic convergence of the sliding variable and its derivative to zero as well as the asymptotic stability of the non-linear system in the absence of external disturbance. The dynamics of the system affected by non-zero external disturbance make the state vector converge to domains in a vicinity of the origin at the exponential rate, as the norm of arbitrary trajectory is limited to decreasing exponential function. In order to expand the variety of controllers based on a reaching law and providing the above-mentioned properties, a certain class of functions is presented.