Variable structure control of robots with nonlinear friction and backlash at the joints

This paper investigates the control of robots with nonlinear friction and dynamic backlash in the joints. The study is based on the describing function (DF) of nonlinear systems. The controllers studied are the first order model and the second order model variable structure controllers (FOM-VSC and SOM-VSC). The authors start by studying nonlinear plants consisting of a mass subjected to Coulomb plus viscous friction or two masses subjected to dynamic backlash. The worst case for the limit cycle generation is found to be the closed-loop system having two masses with backlash. On the other hand, the closed-loop system of a mass with nonlinear friction is found to be amenable to control without limit cycles. By decoupling the joints of the robot the authors find similar results within a good accuracy range