Optimization of vibration control using a hybrid scheme with sliding‐mode and positive position feedback

<jats:title>Abstract</jats:title><jats:p>This article presents the design of a nonlinear hybrid controller for an underactuated Duffing oscillator with 2 degrees of freedom. The main control purpose is to reduce the frequency‐response to specific resonant‐frequencies while maintaining its robustness to external disturbances. The resulting hybrid controller uses sliding mode control (SMC) with a positive position feedback (PPF) scheme. This is structured such that the SMC provides system robustness and tracking, while the PPF allows damping specific resonant frequencies. The system was evaluated using frequency sweeps in terms of acceleration in the second degree of freedom. In this case, the control input is applied through the first degree of freedom. Moreover, multi‐objective optimization is implemented to tune of the control parameters. Simulation results show that the system response to external vibrations can be reduced up to 83.88% by using the proposed PPF + SMC scheme.</jats:p>