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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.

IAE Minimization in Sliding Mode Control With Input and Velocity Constraints