On Positioning and Vibration Control Application to Robotic Manipulators with a Nonideal Load Carrying

Table 1

Parameters of the robot manipulator arm system.

Symbol	Description	Value	Unit
Ra	Motor armature resistance	1.5	Ω
La	Motor inductance	0.0015	H
kt	Motor torque constant	0.0185	Nm/A
kb	Motor electromotive force	0.0185	V/rpm
bv	Equivalent viscous friction	0.018	Nms
κ	Gear ratio	20.68	—
θM	Angular position motor	ηθM (t)	rad
θ	Angular position	—	rad
τf	Total friction force	0.0021	Nm
J	Equivalent inertia load	—	kgm^2
JM	Motor inertia	0.0185
i	Armature electrical current	—	A
	Voltage armature motor	—	Volts
τs	Cubic spring force	0.087	Nm^3
ks	Flexibility of the transmission of the motor	350	Kg/s^2
kc	Flexibility of the arm-load cable	150	Nms
l1	Link 1 length	0.8	m
l2	Link 2 length	0.8	m
m1	Link 1 mass	0.4	kg
m2	Link 2 mass	0.4	kg
m3	Payload mass	0.6	kg
x	State vector	—	—
xd	Setpoint vector	—	—
e	Position error	—	—
A	State matrix	—	—
B	Input matrix	—	—
Q	State weights matrix	—	—
R	Input weights matrix	—	—
	Controllability matrix	—	—