A single-pole oil cylinder valve contains a spool that regulates hydraulic pressure, which is then applied to a piston that drives a load. The transfer function relating piston displacement, X_p(s) to spool displacement from equilibrium, X_v(s), is given by (Qu, 2010):

where A₁ = effective area of a the valve’s chamber, K_q = rate of change of the load flow rate with a change in displacement, and ω_h = the natural frequency of the hydraulic system. Find the state-space representation of the system, where the state variables are the phase variables associated with the piston.

Transcribed Image Text:

Xp(s) G(s) = X,(s) s(s + 25ons+ w)