“…Some researchers (Thomson, 1999; Chatterjee et al, 2004; Sahoo and Chatterjee, 2020) have used high-frequency external excitations, while others (Chatterjee, 2007; Das and Mallik, 2006; Chatterjee and Mahata, 2009a, 2009b; Saha and Wahi, 2014) have utilized time-delay active feedback controllers to reduce friction-induced vibration. A nonlinear saturated relay proportional–derivative (PD) control (Zheng et al, 2019a, 2019b) is proposed for faster positioning of 1-DOF mechanical systems with friction and actuator saturation. The proposed control includes a relay position error for friction compensation and a saturated nonlinear function for faster transient with bounded input.…”