Nonlinear Friction Effect Compensation

We overview different friction models and classical compensation techniques, in addition to highlighting the substantially nonlinear and set-valued phenomena associated with friction characteristics. We then focus on nonlinear compensation techniques with special emphasis towards a few recent reset-based solutions capable of addressing well-known stability and convergence issues experienced when adopting proportional-integral-derivative (PID) feedback. For each one of these two cases, we provide an easy-to-grasp formulation of the corresponding reset laws, which are independent of the friction parameters and ensure performance improvement with Coulomb friction and stability recovery with Stribeck friction. We illustrate the theory on a one-degree-of-freedom motion system, but the simulations on a two-degree-of-freedom robotic arm show that the proposed reset-based compensation laws are effective when implemented in a decentralized fashion on a more complex nonlinearly coupled dynamics.