Assignment 3.pdf - UBC Mechanical Engineering

(d)
What is the number of unknown variables, both state and auxiliary, (expressed in
terms of b and s)? Verify that this is equal to the number available equations, and
hence the problem is solvable.
Problem 6 (Problem 4.6 from Textbook)
An approximate model of a motor-compressor combination used in a process control application
is shown n Figure P4.6.
Motor Rotor
T m
Drive Shaft
k
Compressor
T c
J c
J m
ω
m
ω
c
b
m
(viscous)
b
c
(viscous)
Figure P4.6 A model of a motor-compressor unit.
Note that T, J, k, b, and ω denote torque, moment of inertia, torsional stiffness, angular viscous
damping constant, and angular speed, respectively, and the subscripts m and c denote the motor
rotor and compressor impeller, respectively.
(a) Sketch a translatory mechanical model that is analogous to this rotatory mechanical
model.
(b) Draw a linear graph for the given model, orient it, and indicate all necessary variables
and parameters on the graph.
(c) By following a systematic procedure and using the linear graph, obtain a complete
state-space representation of the given model. The outputs of the system are
compressor speed ω c and the torque T transmitted through the drive shaft.
Problem 7 (Problem 4.7 from Textbook)
A model for a single joint of a robotic manipulator is shown in Figure P4.7. The usual notation
is used. The gear inertia is neglected and the gear reduction ratio is taken as 1:r (Note: r < 1).
(a) Draw a linear graph for the model, assuming that no external (load) torque is present
at the robot arm.