Question Solved1 Answer mo b V m т u = mt The system is described by duo(t) ть - fo(t) +bs ((u(t) - vo(t)) dt df.(t) = ks ((u(t) - vy(t)) dt dvy(t) = -f(t) - bs (v:(t) – vo(t)) + f(t) dt df:(t) = kt (u(t) - vi(t)) dt where vy and vare the vertical velocities of the body and of the unsprung mass, respectively, Ss and ft are the forces stored in the spring and the tire, respectively, and u is the (vertical velocity) excitation from the road. MATLAB exercise: Parameter values are given as follows, my = 240 kg, m+ = 36 kg, bs = 1000 Ns/m, ks = 16,000 N/m and kt = 160,000 N/m. Enter the system in the state space form, convert to the transfer function form, and find poles and zeros of the system. Obtain the frequency response plot (Bode plot is fine) from u to vs. Repeat the problem for bs = 0. (1) By hand: Obtain the state space form. The output of the system is 05. (2) In MATLAB Enter the state space form and convert it to the transfer function from u to vb. • Find poles and zeros of the system. Obtain the bode plot from u to vb. (3) Repeat (2) with bg=0. .

4DQ2U1 The Asker · Mechanical Engineering

Transcribed Image Text: mo b V m т u = mt The system is described by duo(t) ть - fo(t) +bs ((u(t) - vo(t)) dt df.(t) = ks ((u(t) - vy(t)) dt dvy(t) = -f(t) - bs (v:(t) – vo(t)) + f(t) dt df:(t) = kt (u(t) - vi(t)) dt where vy and vare the vertical velocities of the body and of the unsprung mass, respectively, Ss and ft are the forces stored in the spring and the tire, respectively, and u is the (vertical velocity) excitation from the road. MATLAB exercise: Parameter values are given as follows, my = 240 kg, m+ = 36 kg, bs = 1000 Ns/m, ks = 16,000 N/m and kt = 160,000 N/m. Enter the system in the state space form, convert to the transfer function form, and find poles and zeros of the system. Obtain the frequency response plot (Bode plot is fine) from u to vs. Repeat the problem for bs = 0. (1) By hand: Obtain the state space form. The output of the system is 05. (2) In MATLAB Enter the state space form and convert it to the transfer function from u to vb. • Find poles and zeros of the system. Obtain the bode plot from u to vb. (3) Repeat (2) with bg=0. .
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Transcribed Image Text: mo b V m т u = mt The system is described by duo(t) ть - fo(t) +bs ((u(t) - vo(t)) dt df.(t) = ks ((u(t) - vy(t)) dt dvy(t) = -f(t) - bs (v:(t) – vo(t)) + f(t) dt df:(t) = kt (u(t) - vi(t)) dt where vy and vare the vertical velocities of the body and of the unsprung mass, respectively, Ss and ft are the forces stored in the spring and the tire, respectively, and u is the (vertical velocity) excitation from the road. MATLAB exercise: Parameter values are given as follows, my = 240 kg, m+ = 36 kg, bs = 1000 Ns/m, ks = 16,000 N/m and kt = 160,000 N/m. Enter the system in the state space form, convert to the transfer function form, and find poles and zeros of the system. Obtain the frequency response plot (Bode plot is fine) from u to vs. Repeat the problem for bs = 0. (1) By hand: Obtain the state space form. The output of the system is 05. (2) In MATLAB Enter the state space form and convert it to the transfer function from u to vb. • Find poles and zeros of the system. Obtain the bode plot from u to vb. (3) Repeat (2) with bg=0. .
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(1) Here states ary alpha=(:v_(b)" fo "v_(t)f_(t)}^(TT) input r=l and iutput y=v_(b) Sor state space form is %Matlab Code: clc;clear close all mb=240;mt=36;bs=1000; ks=16000;kt=160000; A=[-bs/mb 1/mb bs/mb 0;     -ks 0 ks 0;     bs/mt -1/mt -bs/mt 1/mt     0 0 -kt 0]; B=[0;0;0;kt];C=[1 0 0 0];D=0; Sys=ss(A,B,C,D) [num,den] = tfdata(Sys); [z,p,k]=tf2zp(num{1},den{1}); fprintf('zerosn') display(z) fprintf('polesn') display(p) bode(Sys)   Output:   Sys =     a =               x1        x2        x3        x4    x1    -4.167  0.004167     4.167         0    x2  -1.6e+04         0   1.6e+04         0    x3     27.78  -0.02778    -27.78   0.02778    x4         0         0  -1.6e+05         0     b =              u1    x1        0    x2        0    x3        0    x4  1.6e+05     c =         x1  x2  x3  x4    y1   1   0   0   0     d =         u1    y1   0   Continuous-time state-space model. zeros z =   -16.0000 poles p =  -14.2243 +67.7641i  -14.2243 -67.7641i   -1.7479 + 7.6646i   -1.7479 - 7.6646i Figure 1File Edit View Insert Tools Deskt ... See the full answer