Task

Consider the DC motor$-$driven wheeled mobile robot shown in Figured below, where $m$ is the mass of the wheeled mobile robot, $r$ is the radius of the driving wheel, and $$ is the torque delivered to the wheeled mobile robot by the DC motor. For simplicity, the motion is restricted to one spatial dimension. Figure b below shows the simplified drive system, including the equivalent electrical circuit of the DC motor, the rotor of the DC motor, the gears, and the driving wheel. The motor parameter values are armature inductance $La=0\mathrm{.}001H,$ resistance $Ra=2\mathrm{.}6,$ back emf constant $Ke=0\mathrm{.}008V\frac{s}{r}ad,$ and torque constant $Kt=0\mathrm{.}008N\frac{m}{A}.$ The mass moment of inertia of the motor can be negligible. The gear ratio is $N=\frac{0}{0}m=t\frac{m}{t}=1/3\mathrm{.}7.$ The wheel and axle mechanism converts the rotational motion to translation, and the wheel radius is $r=0\mathrm{.}00635m.$ The mass of the cart is m $=0\mathrm{.}455kg.$ Build a Simscape model and Simulink on Matlab of the wheeled mobile robot and find the displacement output $x(t)$ when the voltage applied to the DC motor is a pulse function, va $(t)=1$ Vor $1t2s.$