An approximate model of a motor-compressor combination used in a process control application is shown n Figure P3.23.
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 ωc and the torque T transmitted through the drive shaft.
Figure P3.23
