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The car dynamics associated with the vehicle’s speed can be expressed by the following LTI equation:

$mdy/dt(t)=u(t)-45by(t)-45bw(t)-mg\theta(t) $

How do I write that on MATLAB in a Laplace representation?

$y(t)$ is the car’s speed in m/s,

$u(t)$ is the engine’s propelling force,

$w(t)$ represents the wind speed along the car’s travelling trajectory (if $ws(t) > 0$ then the wind direction is opposing the car’s travelling trajectory and vice versa),

$m = 1000 kg$ is the car’s nominal mass,

$g = 9.81m/s^2$ is the gravitational acceleration constant,

$b = 0.377$ is the aerodynamic coefficient associated with drag,

$\theta(t)$ is the road’s inclination angle in rad

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  • $\begingroup$ How to write the equation in Matlab is going to depend somewhat on what you want to do with it afterwards...also, are $w$ and $\theta$ given or do you want to get the solution in terms of them? $\endgroup$ – Ian Dec 2 at 22:02
  • $\begingroup$ They’re not given, I have to get the solution in terms of them. $\endgroup$ – user731133 Dec 2 at 22:19
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You cannot physically transform this LTI into a Laplace transform on Matlab. It’ll have to be done by mathematically.

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