9-44. Fig. 9P-44 shows the quarter-car model realization with 2 degrees of freedom.
k_s
C_s
m_s
k_w
C_w
m_w
y
Figure 9P-44
Assuming:
Body mass ($m_c$) = 2500 kg
Suspension mass ($m_w$) = 320 kg
Spring constant of suspension system ($k_s$) = 80,000 N/m
Spring constant of wheel and tire ($k_w$) = 500,000 N/m
Damping constant of suspension system ($c_s$) = 350 Ns/m
Damping constant of wheel and tire ($c_w$) = 15,020 Ns/m
When the vehicle is experiencing any road disturbance, the vehicle body should not have large
oscillations, and the oscillations should be damped quickly. If the deformation tire is negligible, and
the road disturbance (D) is considered a step input,
(a) Design a PID controller that satisfies the following requirements:
(i) Overshoot less than 5%
(ii) Settling time shorter than 5 seconds