How to differentiate a noise signal.

I am doing a project of analyzing influence of tire damping using a full car state-space model with random road input. To analyze the acceleration of body, I want the data regarding acceleration of random input. Random road profile is generated as follows for my project:

Here, Zr is road excitation displacement with respect to time.

But derivative block is not giving the expected answer. Please help me to solve the problem.

[Mathieu NOE]

hello

maybe you should give more details about what is the expected result and how it differs to the actual result ?

[Divya Pawar]

Thanks for reply Mathieu NOE

What I have shown above is a small part of my project. Here I have attached complete problem in pdf file. Please help me to find the way out of it.

Values of different constant used in model is given as:

m1= 40;

C1= 600;

k1= 200000;

m2=332;

C2=100:50:3500;

k2= 25000;

Velocity of vehicle:

V=20;

[Mathieu NOE]

hello

in your pdf you writte that the only issue would be to use SS representation instead of the multiple blocks you have implemented

is this really your issue because this is not what I understood from the first post (generation of tire excitation)

[Divya Pawar]

Thanks for reply, Mathieu NOE.

Actually, I am using SS representation to solve the problem. For which, I need differentiation of random excitation (y_dot). If I use multiple blocks approach, then there is no such need of differentiation of random excitation. That is why, I am getting correct answer using multiple blocks. But i have to use SS represenation only so how can I differentiate y_dot to get right graph. (What can I use in place of derivative block ? - this is what, I wanted to ask from my first post)

Kindly give some suggestions, if u understood the problem.

[Mathieu NOE]

hello

do you have a script and simulink file to share ?

[Divya Pawar]

Hii Mathieu NOE,

Here is my Matlab script and simulink file:

m1= 40; % unsprung mass
c1= 600; % unsprung damping coefficient
k1= 200000; % Tire stiffness

m2=332; % sprung mass
C2=100:50:3500; % suspension damping 
k2= 25000; % suspension stiffness

%velocity of vehicle in m/s
V=20; 

stepsize= 0.001;
T_s= 10;

% Sampling frequency
Fs= 1000;
Ts= 0.001; % sampling period Ts=1/Fs
seed= 23341;

Gq= 256*10^-6; % road roughness in m^3

M= [m1 0; 0 m2]; % mass matrix
K= [k1+k2  -k2; -k2 k2]; %stiffness matrix

n=size(C2,2);
Acc_rms= zeros(n,1); % rms of acceleration vetor

for i=1:n
    c2= C2(i);
    C= [c1+c2 -c2; -c2  c2];
    A= [ zeros(2) eye(2);
         -M\K   -M\C];
    B= [ zeros(2);
        1/m1 0;
        0   0];
    C= eye(4);
    D= zeros(4,2);
    
    sim('QuarterCarStateSpacePreviousVersion.slx');
    x1= Output.data;
    Acceleration= x1(:,4);
    Acc_rms(i)= rms(Acceleration);
end
plot(C2, Acc_rms ,'r', 'LineWidth', 1);
xlabel('Damping Coefficients, Ns/m');
ylabel('Acceleration, m/s^2');
grid on

[Mathieu NOE]

sorry I have R2020b

can you export the slx file in that version please ?

[Divya Pawar]

Done.

Answer 1

[Mathieu NOE]

hello again

I think your model was correct only the solver parameters could be more adapted - now I forced the solver to use fixed steps (and equal to Ts = 1/Fs); your original settings was "variable step size" which for me seemed incorrect to me

also you can avoid filling your workspace with all the default data that simulink generates (section "Save to Workspace" below) so I unticked all of them (you have a dedicted block for the output in your model so that suffices)

at the end the curve looks better as you had expected

this is you script with minor modification (Ts and stepsize are defined from Fs and not independently)

m1= 40; % unsprung mass
c1= 600; % unsprung damping coefficient
k1= 200000; % Tire stiffness
m2=332; % sprung mass
C2=100:50:3500; % suspension damping 
k2= 25000; % suspension stiffness
%velocity of vehicle in m/s
V=20; 
T_s= 10;
% Sampling frequency
Fs= 1000;
stepsize= 1/Fs; % could be replaced by Ts below...
Ts= 1/Fs; % sampling period Ts=1/Fs

seed= 23341;
Gq= 256*10^-6; % road roughness in m^3
M= [m1 0; 0 m2]; % mass matrix
K= [k1+k2  -k2; -k2 k2]; %stiffness matrix
n=size(C2,2);
Acc_rms= zeros(n,1); % rms of acceleration vetor
for ci=1:n
    c2= C2(ci);
    C= [c1+c2 -c2; -c2  c2];
    A= [ zeros(2) eye(2);
         -M\K   -M\C];
    B= [ zeros(2);
        1/m1 0;
        0   0];
    C= eye(4);
    D= zeros(4,2);
    
    sim('QuarterCarStateSpacePreviousVersion.slx');
    x1= Output.data;
    Acceleration= x1(:,4);
    Acc_rms(ci)= rms(Acceleration);
end
plot(C2, Acc_rms ,'r', 'LineWidth', 2);
xlabel('Damping Coefficients, Ns/m');
ylabel('Acceleration, m/s^2');
grid on

attached is your model with the new solver parameters

all the best

[Divya Pawar]

Thanks a lot Mathieu NOE for your great help.

[Mathieu NOE]

My pleasure !