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Why is chassis acceleration negative for a reduced full-car state space?

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Ramin Farshchi
Ramin Farshchi 2021 年 12 月 16 日
編集済み: Image Analyst 2021 年 12 月 16 日
I have used a reduced full-car model. The reduced full-car is created with the following differential equations:
mc*zcacc = (- F_fl - F_fr - F_rl - F_rr)
Ix*rollacc = br*(F_fr + F_rr) - bl*(F_fl + F_rl)
Iy*pitchacc = lf*(F_fl + F_fr) - lb*(F_rl + F_rr)
F_fl = ks*(zc_fl - zr_fl) + ds*(zc_fldot - zr_fldot) + ufl
F_fr = ks*(zc_fr - zr_fr) + ds*(zc_frdot - zr_frdot) + ufr
F_rl = ks*(zc_rl - zr_rl) + ds*(zc_rldot - zr_rldot) + url
F_rr = ks*(zc_rr - zr_rr) + ds*(zc_rrdot - zr_rrdot) + urr
zc_fl = zc + bl*roll - lf*pitch
zc_fr = zc - br*roll - lf*pitch
zc_rl = zc + bl*roll + lb*pitch
zc_rr = zc - br*roll + lb*pitch
I chose the following states and outputs:
states = zc, roll, pitch, zcdot, rolldot, pitchdot
outputs = zc, zcacc
From the differential equations I get the following state space:
c1 = 2*(br-bl)
c2 = 2*(lf-lb)
c3 = -2*(br^2+bl^2)
c4 = lf*(bl-br) - lb*(bl-br)
c5 = br*(lb-lf) - bl*(lb-lf)
c6 = -2*(lf^2 + lb^2)
%6x6
A = [0 1 0 0 0 0;
-4*ks/mc -4*ds/mc -c1*ks/mc -c1*ds/mc -c2*ks/mc -c2*ds/mc;
0 0 0 1 0 0;
c1*ks/Ix c1*ds/Ix c3*ks/Ix c3*ds/Ix c5*ks/Ix c5*ds/Ix;
0 0 0 0 0 1;
c2*ks/Iy c2*ds/Iy c4*ks/Iy c4*ds/Iy c6*ks/Iy c6*ds/Iy];
%6x12
B = [0 0 0 0 0 0 0 0 0 0 0 0;
1/mc 1/mc 1/mc 1/mc ks/mc ks/mc ks/mc ks/mc ds/mc ds/mc ds/mc ds/mc;
0 0 0 0 0 0 0 0 0 0 0 0;
-bl/Ix br/Ix -bl/Ix br/Ix (bl*ks)/Ix -(br*ks)/Ix (bl*ks)/Ix -(br*ks)/Ix (bl*ds)/Ix -(br*ds)/Ix (bl*ds)/Ix -(br*ds)/Ix;
0 0 0 0 0 0 0 0 0 0 0 0;
lf/Iy lf/Iy -lb/Iy -lb/Iy -(lf*ks)/Iy -(lf*ks)/Iy (lb*ks)/Iy (lb*ks)/Iy -(lf*ds)/Iy -(lf*ds)/Iy (lb*ds)/Iy (lb*ds)/Iy;]
%2x6
C = [0 1 0 0 0 0;
-4*ks -4*ds -c1*ks -c1*ds -c2*ks -c2*ds;]
D = zeros(2,12);
When I simulate the state space with a pulse as the measured disturbance (road bump), the chassi height (zc) is positive (lifted up) but the chassi acceleration get negative. Shouldn't the chassi acceleration be positive when the vehicle reaches the bump (chassi height gets positive)?
I also tried some other models (qvm, half-car and full-car) which have a positive acceleration. The differential equations are similar except that zr is replaced by zw. However, the state space differ a bit as zr will be placed in the B matrix while zw will be placed in the A matrix.

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