I$\text{'}$d like to know how would you model a quarter car suspension in matlab$/$simulink given a road profile. The input to the system will be the road profile

I have attached the simulink set up i started. The first road profile must be a square wave. I have also attached the equations of motion, the state space equation and the output equation

State Equation: $dx=Ax+Bu$

$\left[\begin{array}{c}{x}_1^{}\\ *\\ x_2^{}\\ r^{}\\ x_3^{}\\ *\\ x_4\end{array}\right]=\left[\begin{array}{cccc}0& 0& 1& 0\\ 0& 0& 0& 1\\ \frac{-k_s}{m_s}& \frac{k_s}{m_s}& \frac{-b_s}{m_s}& \frac{b_s}{m_s}\\ \frac{k_s}{m_{us}}& \frac{-(k_s-k_{us})}{m_{us}}& \frac{b_s}{m_{us}}& \frac{-(b_s+b_{us})}{m_{us}}\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\\ x_4\end{array}\right]+\left[\begin{array}{cc}0& 0\\ 0& 0\\ 0& 0\\ \frac{k_{us}}{m_{us}}& \frac{b_{us}}{m_{us}}\end{array}\right]\left[\begin{array}{c}{z}_g\\ z_g\end{array}\right]$

Output Equation: $y=Cx+Du$

Outputs we will be using are the sprung mass acceleration$($ddzs$)$ and suspension stroke$($zs$-$zus$)$ and position of

sprung mass

$\left[\begin{array}{c}{y}_1\\ y_2\\ y_3\end{array}\right]=\left[\begin{array}{cccc}\frac{-k_s}{m_s}& \frac{k_s}{m_s}& \frac{-b_s}{m_s}& \frac{-b_s}{m_s}\\ 1& -1& 0& 0\\ 1& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\\ x_4\end{array}\right]+\left[\begin{array}{cc}0& 0\\ 0& 0\\ 0& 0\end{array}\right]\left[\begin{array}{c}{z}_g\\ z_g\end{array}\right]$ Square Wave

Generator

$\sqrt[\phantom{2}]{o}ut.$simout