We also need to have a mathematical model for

mechanical brake system between the hydraulic brake

pressure $P$ and corresponding brake torque TBRK$,$ now

because these parameters have mechanical and

geometrical dependencies so we introduce a proportional

factor $f.$ Treating response of the brake pressure as step

response$[3],$ our derived transfer function for brake

pressure controller will be:

$G_{BRK}(s)=\frac{L(T_{BRK})}{L(P)}=f*\frac{1}{(s)*T_p+1}$

Fig $12$: Brake pressure step response and motor torque step

response. $[17].$

Do modeling on Matlab for the transfer function highlighted in yellow. Provide screenshots for step response plots, root locus plots. Provide block diagrams on Simulink of the transfer function. Also, use different controllers $($P$,$ PI$,$ PID$)$ to improve system response. Also, show system responses when adding step input, ramp input, and parabolic input.