The applications of control theory to hydraulic systems were presented by Merritt

(1967) and supported by Gibson and Tuteur (1958), Johnson (1977), and McCloy and Martin

(1980). Merritt presented the background necessary for determining the dynamic characteristics

of many hydraulic systems. He demonstrated the methods for deriving the characteristic

equations for each of the system components. Then, he pointed out that the closed-loop response

of a system is limited by the response of the slowest element. Thus, the selection of the

components should take into consideration the hydraulic natural frequency by choosing

actuators that are capable of the desired system response. By choosing system components with

fast response rates (i.e., large natural frequencies), the response rate of the actuator and load

combination is left as the performance-limiting factor of the system. Merritt noted that after

choosing fast control components a normal position control hydraulic servo can be reduced to a

second-order system with an integration. Thus, the position servo system is represented by

 2
 Gp(s) = Koh 2
 s + 28h(hS + (Oh (3-8)

where s = Laplace operator (secr')

 Kp = position system gain (appropriate units),

 Oh = system natural frequency (rad/sec), and

 Sh = system damping ratio (unitless).

A normal velocity control servo can be reduced to a second-order system as in the following

transfer function:

 2
 G, (s) Kv(Oh
 s +28h(hS + (Oh (3-9)

where s = Laplace operator (sec-1)

 K, = velocity system gain (appropriate units),

 (Oh system natural frequency (rad/sec), and

 Sh = system damping ratio (unitless).