inD/A C Servo Amp Servo Valve Load ac o et
 converter I Dynamics I Dynamics |- Load Tach | Converte--1-

Figure 6.1. Open-loop hydraulic servo system.



 D/A
 word liter deg
 t(bits) g-7-"v-"vtq Servo Amp/ [iec Actuator and _sec ----v-olts -bits
 Signal Converter Sero ADnas aValve ad Converter| Signal

Figure 6.2. Reduced block diagram of the open-loop system.


 2
 Au(s) = Kv- -
 2 2
 s +28h(OhS + (Oh (6-1)


where Au(s) = open-loop transfer function ((deg/sec)/(D/A word)),

 s s Laplacian operator (sec-),

 Kv = open-loop gain of the system ((deg/sec)/(D/A word)),

 (h open-loop hydraulic natural frequency (rad/sec), and

 6h = open-loop damping ratio dimensionlesss).

In this system, the open-loop gain includes the gains of the D/A converter, the servo amp/servo

valve combination, and the actuator and load dynamics.

 The hydraulic natural frequency and the damping ratio are functions of parameters of

the fluid and the mechanical components of the controlled system and can generally be

approximated as

 4 eDm
 Wh= V
 VVt t (6-2)


 8h e(6-3)Pe
 Dm V V (6-3)