The use of Python and

StateMint are encouraged, but alternative computing tools are allowed. Use

your own paper, work neatly, and clearly mark your answers. Partial credit

may be given.

Consider the linear graph model $($with normal tree$)$ of Fig. $1.$ This is a model

of a motor with constant Ka connected to a pair of meshing gears with

transformer ratio N$,$ the output over input gear ratio. An ideal voltage

source drives the motor$$modeled as an ideal transducer with armature

resistance R and inductance L$.$ The motor$$s rotational mechanical side $(2)$ is

connected to a moment of inertia J$2$ modeling the rotor and drive gear

combined inertia. The damping element B$2$ models the internal motor

damping and the drive gear bearing damping. The output side of the gear

transducer $(4)$ is connected to a moment of inertia J$4$ modeling the output

gear and load combined inertia. The damping element B$4$ models the

internal motor damping and the drive gear bearing damping. Use the

parameter values given in Table $1.$

a$.$ Derive a state$-$space model for the system with outputs $$J$2$

and $$J$4$

$.$

b$.$ Create a Matlab ss model for the system and simulate its response from

rest to an input voltage VS $=20$ V$.$

c$.$ Plot the outputs through time until they reach steady state.Table $1$: System parameter values.

Figure $1$: A linear graph model with normal tree in green of an electromechanical

system with a gear reduction. Please show all numbers and use the required variables from the question in the solution.