A second-order terminal sliding mode controller for uncertain multivariable systems is proposed in this paper. The controller adopts the hierarchical control structure. The paper derives the state transform matrices which are used to transform a multivariable linear system to the block controllable form consisting of two subsystems, an input-output subsystem and a stable internal dynamic subsystem. The proposed controller utilizes a non-singular terminal sliding mode manifold for the input-output subsystem to realize fast convergence and better tracking precision. Meanwhile, a chattering-free second-order terminal sliding mode control law is presented. The stability of uncertain multivariable systems can be realized using the proposed controller. A derivative estimator is utilized in the paper to estimate the derivatives of the sliding mode functions for the controller. The simulation results are presented to validate the design method.

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This paper proposes a novel discrete-time sliding mode (DTSM) control approach to address the robust stability problem of buck converters with multiple disturbances. The contributions lie in the “unified” modelling and controller design. In modelling, all the possible model uncertainties and external disturbances are considered and further classified into two cases. It can also be extended to the situations with individual/several disturbances. While for the controller design, differing from the traditional DTSM based on the nominal model, the disturbances are directly introduced in the process, giving the robust stability condition and four new regulation subranges. It is suitable for both nominal and perturbed systems. Finally, the influences of the sampling time and disturbances on the control performance are investigated. Simulations and experiments confirm the benefits of the unified approach with greater accuracy and wider applications.

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