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### 3.5.  TRANSFER-FUNCTION AND STATE-VARIABLE REPRESENTATION OF TYPICAL HYDRAULIC DEVICES

Hydraulic components are commonly found in control systems that are either all hydraulic or a combination of electromechanical and hydraulic devices [6, 13]. The procedures used for deriving the transfer function representation of some commonly used hydraulic control system devices from their basic differential equations are illustrated in this section. We specifically consider hydraulic motors, pumps, and valves.

#### A.  Hydraulic Motor and Pump

There is no essential difference between a hydraulic pump and motor, just as there is no essential difference between a dc generator and a dc motor. Basically, the hydraulic device is classified as a motor if the input is hydraulic flow or pressure and the output is mechanical position; or a pump if the input is mechanical torque and the output is hydraulic flow or pressure.

Figure 3.21 illustrates a commonly used hydraulic power transmission system. This device, which is capable of controlling large torques, consists of a variable displacement pump that is driven at a constant speed. A control stroke, which determines the quantity of oil pumped, also controls the direction of fluid flow. The angular velocity of the hydraulic motor is proportional to the volumetric flow and is in the same direction as the oil flow from the pump. A functional diagram of the hydraulic transmission is illustrated in Figure 3.22.

The amount of oil displaced per revolution of ...

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