Yesterday while solving a problem of cramster.com,I successfully modeled a quarter car suspension which can control the vibration actively.Refer below diagram.
m1 = Sprung mass
k1 = spring constant of spring attached between sprung and unsprung mass
d1 = damping co-eff of damper attached between sprung and unsprung mass
q1 = displacement of sprung mass
m2 = Unsprung mass
k2 = spring constant of tire
d2 = damping co-eff of tire
q2 = displacement of unsprung mass
z = displacement of tire
Writing an equation of motion for sprung mass m1, we get
m1 * d^2/dt^2 *q1 + k1 ( q1 - q2) + d1 *d/dt ( q1 - q2) = u
Similarly writing an equation of motion for unsprung mass m2, we get
m2 * d^2/dt^2 *q2+ k1(- q1 + q2) + d1 *d/dt(- q1 + q2)+ k2 ( q2 -z) + d2 *d/dt ( q2 - z ) + u=0
These two equations can easily be solved using MATLAB.
The active control is generated here with non-negligible time lag by using a pneumatic actuator.An active suspension systems offer the possibility to vary the damper characteristics along with the road proļ¬le and thus far better than passive suspension.
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