Constrained Control of Impact Oscillator with Delay

Often, the system nonlinearities adversely impact system behaviour/performance. A deeper understanding of these nonlinearities and the parametric dependencies thereof has the potential to enable the formulation of robust, energy-efficient control strategies. Moreover, input constraints and/or delays significantly impact the controlled system performance and overall system stability. In this work, we present a systematic investigation to test the performance of control methodology in the presence of delay and control input constraints. Impact oscillators have been proved to be suitable testbeds to implement nonlinear control methods considering the system’s dynamic rather than using high, control-effort-consuming gains. Therefore, a mass-excited impact oscillator is chosen as a candidate system to demonstrate the proposed control scheme’s effectiveness. As a case study, the coexistence of impacting and non-impacting behaviour of the system is considered. A time-delayed feedback (TDF) scheme is employed in closed loop with the impact oscillator to achieve a non-impacting solution. Subsequently, the closed-loop performance of the overall system with and without constraints and delay are simulated and contrasted. It has been observed that the controller successfully exchanges the chosen attractors. However, the controller fails to stabilise the system with higher delays and constraints, even with higher gains. Therefore a new approach would be required to deal with delays and constraints in such scenarios.