Control Systems Engineering
Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 3, Problem 29P

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):

G s = X p s X v s = K q ω h 2 / A 1 s s 2 + 2 ς ω h s + ω h 2

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 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.

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