How to create a sinusoidal bump for car in road?

This equation for paper: "PID Control of a Nonlinear Half-Car Active Suspension System via Force Feedback ".

In Matlab I code:

a=0.11;%(m)
v=20; %(m/s)
lamda=5;%(m)
lf=1;
lr=1.5;
tf=second(0:20)
td=1+(lf+lr)/v
tr=tf+td
if  1<=tf <=1+(lamda/v)
    td=1+(lf+lr)/v;
    tr=tf+td;
    wf=(a/2)*(1-cos(2*pi*(v/lamda)*tf))
    wr=(a/2)*(1-cos(2*pi*(v/lamda)*tr))
else
    td=0;
    tr=0;
    wf=0;
    wr=0;
end

tf is a time function and I just want it run from 0 to 20 second and continuous ( to put it in my Simulink project). And Matlab show tf is matrix vector. Hope you guy can help me to create that sinusoidal bump. Thank you very much <3

Answer 1

[Sam Chak]

Hi @Nguyen Hieu

Instead of using the If-Else statement, I took the pure math approach of describing the shapes of the road bumps.

By the way, I think there is an error in the profile, where the profile should be defined over the interval .

a      = 0.11;  % (m)
V      = 20;    % (m/s)
lambda = 5;     % (m)
lf     = 1;
lr     = 1.5;

Tspan = 5;      % Can be changed to 20 seconds
Tf    = linspace(0, Tspan, 1000*Tspan+1);
T1    = 1;
T2    = T1 + lambda/V;
wf    = (a/2)*(1 - cos((2*pi*V*Tf)/lambda)).*(heaviside(Tf - T1) - heaviside(Tf - T2));

Td    = T1 + (lf + lr)/V;
Tr    = Tf + Td;
T3    = Td + lambda/V;
wr    = (a/2)*(1 - cos((2*pi*V*Tr)/lambda)).*(heaviside(Tf - Td) - heaviside(Tf - T3));

plot(Tf, wf), hold on
plot(Tf, wr, '--'), grid on
xlabel('Time, (sec)'),
ylabel('Road Disturbance, w (m)')
title('Road Profiles')
annotation('textarrow', [1/5 1.45/5], [0.08/0.12 0.07/0.12], 'String', 'w_{f}')
annotation('textarrow', [2/5 1.65/5], [0.08/0.12 0.07/0.12], 'String', 'w_{r}')

[Nguyen Hieu]

It works, thank you very much. I need to use this time function in my Simulink project, and it must to be a continous signal. Can you develope your code to made wf and wr to be continous signal ? Thank you again.