Calculate the controller gains for the independent joint controllers for joints 1-3 (using the parameters given in Table
Posted: Mon May 16, 2022 5:59 am
Calculate the controller gains for the independent joint
controllers for joints 1-3 (using the parameters given in Table 1).
Using the calculated gains to design the feedback controllers for
the PUMA and implement the controllers in Simulink model
provided
Shoulder 20 21 2 22 Elbow 03 Yi do + do Y Xo yo X1 12 Waist Figure 1. PUMA robot and its coordinate systems
Table 1. Parameters of the PUMA robot Parameters Values di (m) 0.0 d2 (m) 0.1491 ds () 0.0 den) 0.43307 do(m) 0.05625 ai (7) 0.0 a2 (m) 0.4318 az (M) -0.0203 Mass of the first link Mi (kg) 12.96 Mass of the second link M2 (kg) 22.34 Mass of the third link (including the 4th and 5th link) M (kg) 6.97 Centre of mass for the 1st link along x (x1m) 0.0 Centre of mass for the 1st link along y(ym) 0.3088 Centre of mass for the 1st link along z (zm) 0.0389 Centre of mass for the 2nd link along x (x2 m) -0.3289 Centre of mass for the 2nd link along y (y2 m) 0.005 Centre of mass for the 2nd link along z (22 m) 0.2038 Centre of mass for the 3rd link along x (x3 m) 0.0204 Centre of mass for the 3rd link along y (ym) 0.0137 Centre of mass for the 3rd link along z (zam) 0.1244 Moment of inertia at centre of mass for the 1 link along x (lxx kg m) 2.35 Moment of inertia at centre of mass for the 1' link along y (Isy, kg m) 0.2 Moment of inertia at centre of mass for the 1' link along z (Iz kgar) 2.35 Moment of inertia at centre of mass for the 2nd link along x (1 kg mº) 1.33 Moment of inertia at centre of mass for the 2nd link along y (Isyy kg mº) 3.03 Moment of inertia at centre of mass for the 2nd link along z (le kg ) 3.38 Moment of inertia at centre of mass for the 3'd link along x (I. kg m) 0.3148 Moment of inertia at centre of mass for the 3 link along y (Lay, kg m) 0.3128 Moment of inertia at centre of mass for the 3'd link along z (lar kg mi) 0.01 Gear ratio of the Ist link drive chain (n) 1/[40+(Group No.x51* Gear ratio of the 2nd link drive chain (12) 1/107.82 Gear ratio of the 3rd link drive chain (13) 1/53.71
1/53.71 0.0002 0.0002 0.0002 40 Gear ratio of the 3rd link drive chain (r) Moment of inertia of the motor armature driving the 1st joint (I.) kg/m) Moment of inertia of the motor armature driving the 2nd joint (1.2) kg/mr) Moment of inertia of the motor armature driving the 3rd joint (13) kg/nr) Rated voltage of the motor driving the 1st joint ( VV) Rated voltage of the motor driving the 2nd joint (V.2V) Rated voltage of the motor driving the 3rd joint ( VV) Rated torque of the motor driving the 1st joint (Tim N-m) Rated torque of the motor driving the 2nd joint (T2max N-m) Rated torque of the motor driving the 3rd joint (Tom. N-m) Effective viscous friction coefficient of the Ist joint (vi N-s) Effective viscous friction coefficient of the 2nd joint (v. N-s) Effective viscous friction coefficient of the 3rd joint (V3 N-s) Motor armature resistance (2) (joint 1-3) Motor torque constant K. (N-m/A) Joint (1-3) (same as Kb) Structural resonant frequency of the robot 40 40 1.2 1.2 1.2 0.01 0.005 0.003 1.6 0.2531 10 (H:)
Ko = „(s) V.(s) s(RJFS+R fer +K,K.) , (8) nK V.(s) (R JOS+R fr +K,K.) JIME RJEN m m(s) K V.(s) s(Tms +1) = Rafet +K,KA VK= Rafet +KK 0(s) Ka () K K T 5+1 K KK, m 02 KK, (s) s(TMS+KK+1) + KK, The requirement n T 0, 50.50, $ 21 m 250, KK +1 is: T
Joint1_motor_velocity jym_1 Input Votage for Joint 1 Motor Joint 1 motor position jm_1 Stopper_DTim 日 Stopper_Tim vol_to_motor_1 Jointi_robot_velocity Desired motor 1 position Controller 1 Joir1_robot_position Robot_joint_velocity 04 Joint2_motor_velocity Robot_joint1_position jim_2 Joint2 motor_position Stopper_DT2m Input Votage_for Joint 2 Motor jm_2 vol_to_motor_2 Joint2_robot_velocity Stopper_T2m 0_7 Desired motor 2 position Controller 2 Joint2_robot_position Robot_joint2_velocity Joint3_motor_velocity Robot_joint2_Position jym_3 Joint3 motor position Stopper DT3 jm 3 Input Votage for Joint 3 Motor 10 vol_to_motor_3 Joint3_robot velocity Stopper T3m o 11 Desired motor 3 position Controller 3 Joint3_robot_position Robat_joint3_velocity o 12 Rabot joints Position PUMA SIMULATION MODEL
controllers for joints 1-3 (using the parameters given in Table 1).
Using the calculated gains to design the feedback controllers for
the PUMA and implement the controllers in Simulink model
provided
- Calculate The Controller Gains For The Independent Joint Controllers For Joints 1 3 Using The Parameters Given In Table 1 (21.75 KiB) Viewed 68 times
- Calculate The Controller Gains For The Independent Joint Controllers For Joints 1 3 Using The Parameters Given In Table 2 (107.92 KiB) Viewed 68 times
- Calculate The Controller Gains For The Independent Joint Controllers For Joints 1 3 Using The Parameters Given In Table 3 (57.32 KiB) Viewed 68 times
- Calculate The Controller Gains For The Independent Joint Controllers For Joints 1 3 Using The Parameters Given In Table 4 (39.42 KiB) Viewed 68 times
- Calculate The Controller Gains For The Independent Joint Controllers For Joints 1 3 Using The Parameters Given In Table 5 (45.17 KiB) Viewed 68 times
Table 1. Parameters of the PUMA robot Parameters Values di (m) 0.0 d2 (m) 0.1491 ds () 0.0 den) 0.43307 do(m) 0.05625 ai (7) 0.0 a2 (m) 0.4318 az (M) -0.0203 Mass of the first link Mi (kg) 12.96 Mass of the second link M2 (kg) 22.34 Mass of the third link (including the 4th and 5th link) M (kg) 6.97 Centre of mass for the 1st link along x (x1m) 0.0 Centre of mass for the 1st link along y(ym) 0.3088 Centre of mass for the 1st link along z (zm) 0.0389 Centre of mass for the 2nd link along x (x2 m) -0.3289 Centre of mass for the 2nd link along y (y2 m) 0.005 Centre of mass for the 2nd link along z (22 m) 0.2038 Centre of mass for the 3rd link along x (x3 m) 0.0204 Centre of mass for the 3rd link along y (ym) 0.0137 Centre of mass for the 3rd link along z (zam) 0.1244 Moment of inertia at centre of mass for the 1 link along x (lxx kg m) 2.35 Moment of inertia at centre of mass for the 1' link along y (Isy, kg m) 0.2 Moment of inertia at centre of mass for the 1' link along z (Iz kgar) 2.35 Moment of inertia at centre of mass for the 2nd link along x (1 kg mº) 1.33 Moment of inertia at centre of mass for the 2nd link along y (Isyy kg mº) 3.03 Moment of inertia at centre of mass for the 2nd link along z (le kg ) 3.38 Moment of inertia at centre of mass for the 3'd link along x (I. kg m) 0.3148 Moment of inertia at centre of mass for the 3 link along y (Lay, kg m) 0.3128 Moment of inertia at centre of mass for the 3'd link along z (lar kg mi) 0.01 Gear ratio of the Ist link drive chain (n) 1/[40+(Group No.x51* Gear ratio of the 2nd link drive chain (12) 1/107.82 Gear ratio of the 3rd link drive chain (13) 1/53.71
1/53.71 0.0002 0.0002 0.0002 40 Gear ratio of the 3rd link drive chain (r) Moment of inertia of the motor armature driving the 1st joint (I.) kg/m) Moment of inertia of the motor armature driving the 2nd joint (1.2) kg/mr) Moment of inertia of the motor armature driving the 3rd joint (13) kg/nr) Rated voltage of the motor driving the 1st joint ( VV) Rated voltage of the motor driving the 2nd joint (V.2V) Rated voltage of the motor driving the 3rd joint ( VV) Rated torque of the motor driving the 1st joint (Tim N-m) Rated torque of the motor driving the 2nd joint (T2max N-m) Rated torque of the motor driving the 3rd joint (Tom. N-m) Effective viscous friction coefficient of the Ist joint (vi N-s) Effective viscous friction coefficient of the 2nd joint (v. N-s) Effective viscous friction coefficient of the 3rd joint (V3 N-s) Motor armature resistance (2) (joint 1-3) Motor torque constant K. (N-m/A) Joint (1-3) (same as Kb) Structural resonant frequency of the robot 40 40 1.2 1.2 1.2 0.01 0.005 0.003 1.6 0.2531 10 (H:)
Ko = „(s) V.(s) s(RJFS+R fer +K,K.) , (8) nK V.(s) (R JOS+R fr +K,K.) JIME RJEN m m(s) K V.(s) s(Tms +1) = Rafet +K,KA VK= Rafet +KK 0(s) Ka () K K T 5+1 K KK, m 02 KK, (s) s(TMS+KK+1) + KK, The requirement n T 0, 50.50, $ 21 m 250, KK +1 is: T
Joint1_motor_velocity jym_1 Input Votage for Joint 1 Motor Joint 1 motor position jm_1 Stopper_DTim 日 Stopper_Tim vol_to_motor_1 Jointi_robot_velocity Desired motor 1 position Controller 1 Joir1_robot_position Robot_joint_velocity 04 Joint2_motor_velocity Robot_joint1_position jim_2 Joint2 motor_position Stopper_DT2m Input Votage_for Joint 2 Motor jm_2 vol_to_motor_2 Joint2_robot_velocity Stopper_T2m 0_7 Desired motor 2 position Controller 2 Joint2_robot_position Robot_joint2_velocity Joint3_motor_velocity Robot_joint2_Position jym_3 Joint3 motor position Stopper DT3 jm 3 Input Votage for Joint 3 Motor 10 vol_to_motor_3 Joint3_robot velocity Stopper T3m o 11 Desired motor 3 position Controller 3 Joint3_robot_position Robat_joint3_velocity o 12 Rabot joints Position PUMA SIMULATION MODEL