Problem Set-1 c Week 11Challenge : Transient Handling

%THIS IS 11d ASSIIGNMENT , I ACCIDENTALLY UPLOADED 11C ASSIGNMENT IN 11D , THEREFORE IM UPLOADING 11D ASSIGNMENT HERE IN 11C

We have

given that we need to derive del_f / del_r at zero slip condition

therefore dv/dt =0 and dr/dt =0 and v = 0

which gives

substitute in the matrix equation

we get

del_f / del_r = -(Car/Caf)*(a*Caf*l + m*b*u(i)^2)/(b*Car*l - m*a*u(i)^2)

m = 1000; % kg

Izz = 1400; %yaw moment of inertia in kgm^2

l = 2.54; %wheelbase in m

a = 1.14; % m

b = l-a; %m

Caf = 2400*180/pi; % N/rad

Car = 2000*280/pi; % N/rad

r = 0.5; %yaw rate

u = 0:0.1:50;

for i = 1:length(u)

delf_by_delr(i) = -(Car/Caf)*(a*Caf*l + m*b*u(i)^2)/(b*Car*l - m*a*u(i)^2);

end

figure(1)

plot(u,delf_by_delr,'linewidth',2)

xlabel('Longitudinal Speed (m/s)')

ylabel('del_f/del_r')

Results:

At a speed of 23.5 m/s we are experiencing a sudden shift in the ratio, which may lead to jerk.