Non-linear sliding surface: towards high performance robust control

The study proposes a method to design a non-linear sliding surface to achieve better transient response for a class of single-input and single-output (SISO) non-linear uncertain system represented in a Brunowsky canonical form. The proposed surface can also be used for linear uncertain systems with matched perturbations. The proposed surface increases the damping ratio of the closed-loop system from its initial low value; as the output approaches the setpoint from its initial value. Initially, the system is lightly damped resulting in a quick response and as the output approaches the setpoint, the system is overdamped to avoid overshoot. The existence of sliding mode is proved and a new control law is proposed to enforce sliding motion. The scheme is able to achieve low overshoot and short settling time simultaneously which is not possible with a linear sliding surface. To ease the synthesis of the non-linear surface, linear matrix inequalities-based algorithm is proposed. Effectiveness of the proposed scheme is illustrated by the simulation results.