Sliding Mode Control Based Whale Optimization Algorithm for Duffing Oscillator

The Duffing oscillator is particularly useful in numerous applications, owing to its unique dynamic features. It integrates a periodically excited system with a nonlinear elastic restoring force. This paper proposes a sliding mode control (SMC) for trajectory tracking of the Duffing oscillator. To guarantee best dynamic performance of the SMC, two reaching laws are examined. The first reaching law of the SMC is based on the hyperbolic tangent function (SMC_tah) whereas the second one is based on the saturation function (SMC_sat). The design parameters of the proposed controllers are optimized through tuning with the whale optimization algorithm (WOA) to achieve enhanced performance. Extensive MATLAB-based simulations were carried out to confirm the effectiveness of the proposed approaches. The simulation outcomes reveal that the tracking error based on the integral of absolute error (IAE) of the system controlled by the SMC_tah is reduced by 8.6% compared to that of the system controlled by the SMC_sat. Furthermore, under uncertainty scenario, SMC_sat shows more robustness than SMC_tah.