Question

For the car suspension system shown below create the state-space representation equations. Plot the position of the car and the wheel after the car hits a “unit bump” (i.e., r is a unit step) using MATLAB. Use MATLAB commands and also use MATLAB Simulink to show state space block. Assume that m1=10kg, m2=250kg, KW=500,000N/m, KS=10,000N/m. Find the value of b that you would prefer if you were a passenger in the car. Show the simulation results.

MATLAB. Use MATLAB commands and also use MATLAB Simulink to show state space block. Assume that mi=10kg, mz=250kg, Kw=500,000N/m, Ks=10,000N/m. Find the value of b that you would prefer if you were a passenger in the car. Show the simulation results. m2 ks Ucar X mi Road surface Inertial reference

Answer 1

kwb ь sol: Y(s) S+ kg b 6 hele ter mm. El R (J) st 6 b kst 33 + + Krib + menys S + m ma m, me kuks this us the hranker function of above love Here, is mimi The mass the cas dellection ks is kw the applied weight. b is the dampmy Considei kw X mi 6 yt ġ the system equahons . ) (x - y) + hinten (y -) + k (Y-2)= ojº Re-arron; equahon equahon o 12 mu and lor M bit b ь t 2+ Yt . kry ks m ä- - The + m mi b ks ks Y m عام m > mi to arile the stole u ☺ and Use equalin vectr O olla d's عام عاد 0 ء کے + m P m m + + HI O ។ อ O o o ks bo la m2 Y el 이로 mm m2 me

Use and equation 5 and write MATLAB code

m1=10;

m2=250;

kw=500000;

ks=10000;

Bd=[1000 2000 3000 4000];

t=0:0.01:2;

for I=1:4;

b=Bd(i);

A=[0 1 0 0;-(ks/m1 + kw/m1) -b/m1 ks/m1 b/m1;0 0 0 1;Ks/m2 b/m2 -ks/m2 -b/m2];

B=[0;kw/m1;0;0];

C=[1 0 0 0;0 0 1 0];

D=0;

y=step(A,B,C,D,1,t);

subplot(2,2,I);

plot(t,y(:,1),':',t,y(:,2),'-');

legend('wheel','car');

title = sprintf(response With b =%4.1f',b);

end

----->Out put wave forms...

24

From the above wave form( that is b=3000) is acceptable coz of lower values of b,the overshoot is too much large and for larger values of b, system gets too fast.thus the system value of b is 3000..

Plz hit the like symbole......