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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motor supplies 200 kW at 6 Hz to flange A of the shaft shown in Figure. Gear B transfers 125 W of power to operating machinery in the factory, and the remaining power in the shaft is mansferred by gear D. Shafts (1) and (2) are solid aluminum (G = 28 GPa) shafts that have the same diameter and an allowable shear stress of t= 40 MPa. Shaft (3) is a solid steel (G = 80 GPa) shaft with an allowable shear stress of t = 55 MPa. Determine: a) the minimum permissible diameter for aluminum shafts (1) and (2) b) the minimum permissible diameter for steel shaft (3). c) the rotation angle of gear D with respect to flange A if the shafts have the minimum permissible diameters as determined in (a) and (b).

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