Design and Application of Energy-saving Sub-Optimal Sliding Mode Control

The recently introduced energy-saving extension of the sub-optimal sliding mode control (SOSMC), which is known in the literature for the last two and half decades, incorporates a control-off mode that allows for saving energy during the finite-time convergence process. This novel energy-saving algorithm (denoted by ES-SOSMC) assumes the systems with relative degree two between the sliding variable and the switching control with a bounded magnitude, while the matched upper-bounded perturbations are not necessarily continuous. The design and practical application of the ES-SOSMC are the subject of this chapter. A method for parameterizing the ES-SOSMC through a constrained minimization of the energy cost function is recalled which guarantees the total energy consumption is lower than that of the conventional SOSMC. Also the residual steady-state oscillations (chattering), occurring when additional (actuator) dynamics are taken into account, are addressed. An application example for scanning and machining a rough surface, both of which require a stiff position control in contact with a moving surface, demonstrates practical suitability of the control. Here, ES-SOSMC is compared with SOSMC by showing an equivalent tracking and stabilization performance and evaluating the energy-saving operation with respect to a fuel consumption norm.