Switched chattering control vs. backlash/friction phenomena in electrical servo-motors

Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs

“…Sliding mode observers have been shown to be a robust observation scheme in robotics [9,35,45], electrical engineering [15,60] or chemical reactors [46]. Specific applications of asymptotic and finite time observers for systems with unknown inputs can be found in a large number of fields such as fault detection and identification [22,30,58,23], parameter identification [26,55], cryptography [3], or mechanical systems with Coulomb friction [13,27,47].…”

Principles of 2-sliding mode design

“…While finite-time-convergent arbitrary-order slidingmode controllers are mostly still theoretically studied (Levant, 2001(Levant, , 2003Floquet, Barbot and Perruquetti, 2003), 2-sliding controllers with finite-time convergence have already been successfully implemented for solution of real problems (Bartolini, Ferrara & Punta, 2000;Bartolini, Pisano, Punta & Usai, 2003;Levant, Pridor, Gitizadeh, Yaesh & Ben-Asher, 2000;Sira-Ramírez, 2002;Orlov, Aguilar & Cadiou, 2003;Khan, Goh & Spurgeon, 2003;Shkolnikov & Shtessel, 2002;Shkolnikov, Shtessel, Lianos, & Thies, 2000;Shtessel & Shkolnikov, 2003;Shtessel, Shkolnikov & Brown, 2004). There are only few widely used 2-sliding controllers: the sub-optimal controller (Bartolini et al, 1998), the terminal sliding mode controllers (Man, Paplinski & Wu, 1994), and the twisting controller .…”

Homogeneous Approach for Output Feedback Tracking Control of Robot Manipulators

“…Lebastard et al, 2006;Ferrara et al, 2006;Bartolini et al, 2006) because it was demonstrated that homogeneous systems with homogeneity degree 0 < η exhibit robustness and finite-time convergence properties (Bhat & Bernstein, 1997;Hong et al, 2001;Orlov, 2005). Control laws based on the homogeneity approach (Bhat & Bernstein, 1997;Hermes, 1995;Orlov, 2003a;Rosier, 1992) are attractive in robotic applications because they can cope with many mechanical perturbations, including external vibrations, contact forces, and nonlinear internal phenomena such us Coulomb and viscous friction, dead zone and backlash, while it is possible to ensure exact tracking to continuously differentiable desired trajectories. Several homogeneous controllers and studies have been proposed in the literature.…”

“…Levant (2005aLevant ( , 2005b developed robust output-feedback high-order sliding mode controllers that demonstrate finite-time convergence (see also (Fridman & Levant, 1996;Fridman & Levant, 2002)) where the controller design is based on homogeneity reasoning while the accuracy is improved in the presence of switching delay, and the chattering effect is treated by increasing the relative degree. Orlov et al (2003aOrlov et al ( , 2003b proposed applying homogeneous controller to solve the set-point problem dealing with mechanical imperfections such as Coulomb friction, viscous friction, and backlash. Orlov et al, (2005) extended the finite time stability analysis to nonlinear nonautonomous switched systems.…”