Description

Develop a model of a one degree of freedom joint constituting a planar mechanism as shown below, using the Foundation Library in Simscape. Incorporate a DC motor model (obtain the specifications of the DC motor from the datasheet given below for the model C23-L33 with winding code 10). Use PID controller and simulate the plant for a desired trajectory given. (Use the MATLAB PID auto tuning block)

Physical Parameter Specification
Moment of inertia of the drive shaft, IS1 0.085 kg· m2
Moment of inertia of the driven shaft, IS2 0.37 kg· m2
Gear ratio 2
Mass 4 kg
Length of the link 0.25 m

DESIRED TRAJECTORY:

Obtain the specifications of the DC motor from the datasheet given below for the model C23-L33 with winding code 10
Part Number* C23-L33 C23-L40
Winding Code** 10 20 30 40 50 10 20 30 40 50
L = Length inches 3.33 4
millimeters 84.6 101.6
Peak Torque oz-in 125.0 125.0 125.0 125.0 125.0 250.0 250.0 250.0 250.0 250.0
Nm 0.883 0.883 0.883 0.883 0.883 1.765 1.765 1.765 1.765 1.765
Continuous Stall Torque oz-in 16.5 16.5 16.5 16.5 16.5 27.0 27.0 27.0 27.0 27.0
Nm 0.117 0.117 0.117 0.117 0.117 0.191 0.191 0.191 0.191 0.191
Rated Terminal Voltage volts DC 12 -24 12 – 24 12 -36 12 – 60 12 – 60 12 – 24 12 – 48 12 – 60 12 – 60 12 – 60
Terminal Voltage volts DC 12 12 24 36 48 12 24 36 48 60
Rated Speed RPM 4700 2150 4200 3750 3000 2300 3600 3500 2850 2250
rad/sec 492 225 440 393 314 241 377 367 298 236
Rated Torque oz-in 7.5 12.6 12.7 14.4 15.8 17.3 25.5 25.3 25.6 24.2
Nm 0.05 0.09 0.09 0.10 0.11 0.12 0.18 0.18 0.18 0.17
Rated Current Amps 4.75 4.3 3 2 1.4 4.9 4.3 2.75 1.8 1.1
Rated Power Watts 26.1 20.0 39.5 40.0 35.1 29.4 67.9 65.5 54.0 40.3
Horsepower 0.03 0.03 0.05 0.05 0.05 0.04 0.09 0.09 0.07 0.05
Torque Senstivity oz-in/amp 2.65 4.25 6.2 10.25 15.75 4.84 7.74 12 18.5 28.75
Nm/amp 0.0187 0.0300 0.0438 0.0724 0.1112 0.0342 0.0547 0.0847 0.1306 0.2030
Back EMF volts/KRPM 2 3.15 4.6 7.6 11.5 3.58 5.72 8.82 13.82 21.22
volts/rad/sec 0.0191 0.0301 0.0439 0.0726 0.1098 0.0342 0.0546 0.0842 0.1320 0.2026
Terminal Resistance ohms 0.60 1.00 1.70 4.00 9.00 0.70 0.96 2.30 5.50 12.00
Terminal Inductance mH 0.35 0.94 2.00 5.50 13.00 0.50 1.30 3.10 7.36 18.00
Motor Constant oz-in/watt^1/2 3.4 4.3 4.8 5.1 5.3 5.8 7.9 7.9 7.9 8.3
Nm/watt 0.024 0.030 0.034 0.036 0.037 0.041 0.056 0.056 0.056 0.059
Rotor Inertia oz-in-sec2 0.0022 0.0022 0.0022 0.0022 0.0022 0.004 0.004 0.004 0.004 0.004
g-cm2 155.4 155.4 155.4 155.4 155.4 282.5 282.5 282.5 282.5 282.5
Friction Torque oz-in 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0
Nm 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02
Thermal Resistance °C/watt 6.2 6.2 6.2 6.2 6.2 5.4 5.4 5.4 5.4 5.4
Damping Factor oz-in/KRPM 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
Nm/KRPM 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001
Weight oz 27 27 27 27 27 38 38 38 38 38
g 765 765 765 765 765 1077 1077 1077 1077 1077
Electrical Time Constant millisecond 0.5833 0.9400 1.1765 1.3750 1.4444 0.7143 1.3584 1.3478 1.3382 1.5000
Mech. Time Constant millisecond 26.07623 17.2056 13.72994 11.82747 11.44547 16.91906 9.052773 9.100907 9.00927 8.237676
Speed/Torque Gradient rpm/oz-in -113.2075 -74.69655 -59.60729 -51.34788 -49.68944 -40.39891 -21.61598 -21.73091 -21.51211 -19.66971