A single-pole oil cylinder valve contains a spool that regulates hydraulic pressure,

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, Xp(s) to spool displacement from equilibrium, Xv(s), is given by (Qu, 2010):

where A1 = effective area of a the valve’s chamber, Kq = rate of change of the load flow rate with a change in displacement, and ωh = 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.