Robust resonance and displacement tracking in fatigue testing machines via a deadbeat twisting controller

• Model-based control design for resonance-based fatigue testing machines is investigated. • The developed model-based controller is compared with existing model-free ones. • An experimental setup is developed for this study, and the experimental results are presented. This work investigates the design of model-based controllers for resonance-based fatigue testing machines. Unlike conventional fatigue testing machines, resonance-based machines require smaller setups, consume less energy, and significantly reduce test duration by maintaining the specimen at its natural excitation frequency. Achieving this requires a robust control system capable of driving the system to its resonance frequency while rejecting disturbances such as temperature variations and unmodeled dynamics—particularly those caused by crack formation, which alters the specimen’s properties, including its resonance frequency, during testing. A tutorial-style review of state-of-the-art control systems developed for resonance-based fatigue machines is presented in terms of resonance frequency and displacement tracking. Subsequently, a control-oriented model has been developed and validated for the system using system identification, allowing the design of a model-based controller. A robust model-based controller, i.e. , a twisting controller, is then employed for the developed model, and its parameters are designed systematically to address its robustness against uncertainties. Time discretization of the proposed twisting controller, which was initially designed in the continuous-time domain, is then addressed using a deadbeat implementation to mitigate the chattering issue. The developed model-based controller is then compared with conventional controllers such as PID and fuzzy controllers, which are designed based on system behavior rather than a mathematical model. Comparative analyses using both numerical simulations and experimental results demonstrate the advantages of the proposed twisting controller over the existing ones in terms of tracking the resonance frequency and the desired displacement amplitude.