Project Guidelines:

System Overview $(10\%)$

You will model a quarter car suspension system consisting of $2$ masses, $2$ springs, and $2$ dampers

representing the car body and the wheel assembly. The system will experience sinusoidal road

inputs, representing disturbances such as bumps.

System Parameters:

Masses:

Car body mass $($sprung mass$)$: m$\_($c$)=400$kg

Wheel mass $($unsprung mass$)$: m$\_($w$)=40$kg

Spring Constants:

Suspension stiffness k$\_($s$)=15,000$N$//$m

$($This models the main suspension stiffness connecting the car body to the wheel assembly.$)$

Tire stiffness k$\_($t$)=200,000$N$//$m

$($This models the tire stiffness, connecting the wheel to the road surface.$)$

Damping Coefficients:

Suspension damping coefficient c$\_($s$)=1,000$Ns$//$m

$($Damping from the car's suspension system, representing the shock absorber$\text{'}$s effect.$)$

Tire damping coefficient c$\_($t$)=100$Ns$//$m

$($Damping effect due to the tire's interaction with the road$)$

Mathematical Modeling $(15\%)$

Objective: Derive the mathematical model of the quarter vehicle system using force analysis and

free$-$body diagrams.

Tasks:

Apply Newton's Second Law or Lagrangian Mechanics to derive the system's equations of

motion.

Model the vehicle's free and forced response.

State$-$Space Representation and Open$-$Loop Analysis $(15\%)$

Objective: Develop a state$-$space representation of the suspension system.

Tasks:

Convert the equations of motion into a state$-$space form.

Perform open$-$loop analysis to assess system stability and performance without a controller.

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