A Sub-Optimal Control of a Non-linear Vibrating System Excited by a Non-ideal Energy Source

Abstract Purpose Non-Ideal Systems (NIS) are distinguished by their unique dynamic properties, which present considerable challenges to the application of conventional control techniques. The present study examines non-ideal excitation sources with limited power. Nonlinear phenomena were observed in a range of applications, providing insights for future NIS engineering. Methods The governing equations of Non-Ideal Systems (NIS) with multiple degrees of freedom are derived, accounting for nonlinear damping, stiffness, and time-varying excitations. The implementation of a state-dependent Riccati equation (SDRE) control strategy is proposed as a means to optimise system stability and dynamic performance. Results For the ideal system (case 1, $$a_0 = 0$$ ), the proposed control strategy effectively regulates the system’s response, reducing amplitude and stabilizing the orbits, as confirmed by time-domain and frequency-domain analyses. For the non-ideal system (case 2, $$a_0 > 0$$ ), despite the increased excitation complexity, the controller successfully suppresses vibrations and mitigates nonlinear effects, demonstrating robust performance in both time- and frequency-domain measures. Conclusions The present study focuses on excitation sources that deviate from ideal conditions. The inherent limitations of these sources are characterised by their constant parameters of power and inertia. The article demonstrates that the chosen control strategy yields satisfactory results for controlling both ideal and non-ideal excitation systems.