Abstract
In this work an optimal sliding mode controller for second order, nonlinear systems is proposed. First, the sliding surface is selected to obtain finite time convergence to the desired state. Moreover, to ensure robustness with respect to unknown external disturbances and model uncertainties, the surface is time-varying and at the start of the control process it intersects the point, whose coordinates are defined by the initial state. Thus, the existence of the sliding mode is ensured for the whole control process. Next, admissible values of the hyperplane parameters, that ensure satisfaction of velocity and/or control signal constraints are determined. Lastly, optimal values of these parameters, in terms of integral absolute error (IAE) are calculated. The main motivation of this paper was to obtain the good dynamical performance of the system and robustness by eliminating the reaching phase, overcoming the external, unknown disturbances and obtaining a finite-time convergence of the representative point to the desired state. The other main issue was to include some key limitations such as control signal and velocity constraints in order to facilitate the practical application of this strategy.
Highlights
Sliding mode control is one of the well-known variable structure control methods
A sliding mode controller is enhanced by a neural network, that compensates for the impact of disturbances
As in the previous subsection we get that in the case when the sliding line stops during the control process, the optimal parameters ρ and τ0 lie on the intersection of lines, which are the boundaries of the admissible set
Summary
Its main favorable properties are robustness with respect to external disturbances [10] and minimal requirements of computational power Due to these advantages sliding mode control is frequently used in electric drives, mechanical systems, and many diverse practical systems [1]–[8], [11], [12]. That the proposed approach ensures formation control robust to the wind disturbances acting on the UAVs. The problem of formation control was solved using a nonsingular terminal sliding mode controller in [6]. In [11] a sliding mode observer for stator current and rotor flux linkage is developed for a bearingless induction machine This type of motors has some significant advantages due to replacing the mechanical bearings by additional windings in the stator. The approach enables the designer to enforce a priori known bounds on the system velocity and/or the control signal value
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