Adaptive Fuzzy Dynamic Surface Sliding Mode Position Control for a Robot Manipulator with Friction and Deadzone

Table 1

Manipulator parameters.

Symbol	Parameter	Quantity
𝑚1,𝑚2	Mass of links 1 and 2	12.1 kg, 3.59 kg
𝐿1,𝐿2	Mass of links 1 and 2	0.3 m, 0.41 m
𝐹𝑠1,𝐹𝑠2	Stiction level of joints 1 and 2	0.063 Nm, 0.0648 Nm
𝐹𝑐1,𝐹𝑐2	Coulomb friction of joints 1 and 2	0.061 Nmsec/rad, 0.06 Nmsec/rad
𝑣𝑠1,𝑣𝑠2	Stibeck velocity of joints 1 and 2	0.00075 rad/sec, 0.00063 rad/sec
𝜎01,𝜎02	Bristle stiffness of joints 1 and 2	5400 Nm/rad, 8700 Nm/rad
𝜎11,𝜎12	Presliding damping of joints 1 and 2	5.4 Nmsec/rad, 6.2 Nmsec/rad
𝜎21,𝜎22	Sliding damping of joints 1 and 2	10.2 Nmsec/rad, 10.8 Nmsec/rad
𝜃1,𝜃2	Transient friction parameter of joints 1 and 2	0.87, 0.9
𝑚𝑟1,𝑚𝑙1	Slope of deadzone of joint 1	1, 1
𝑚𝑟2,𝑚𝑙2	Slope of deadzone of joint 2	1, 1
𝐵𝑟1,𝐵𝑙1	Deadzone width of joint 1	0.28, −0.28
𝐵𝑟2,𝐵𝑙2	Deadzone width of joint 1	0.25, −0.25
𝑛𝑖	Gear ratio of reduction gear	65.5
𝐿𝑚𝑖	Inductance of motor	0.6292 mH
𝑅𝑚𝑖	Resistance of motor	0.8294 Ω
𝑘𝑡𝑖	Torque constant	0.0182 Nm/A
𝑘𝑏𝑖	Back emf constant	0.0182 V/rad/sec