# Hydraulics System and Models of Control Systems

## HYDRAULICS SYATEM

The Hydraulics system of interest to control engineers may be classified into,

1. Liquid Level system and
2. Hydraulics devices

The liquid level system consists of storage tanks and connecting pipes. The variables to be controlled are liquid height in tanks and flow rate in pipes. The driving force is the relative difference of the liquid heights in the tanks.

The Hydraulic devices are devices using incompressible oil as their working medium. These devices are used for controlling the forces and motions. The driving force is the high pressure oil supplied by the Hydraulics pumps.

Liquids are slightly compressible at high pressures. In hydraulics system, the compressibility effects may be neglected and conservation of volume is used as the basic physical law. The variables of hydraulic system are volumetric flow rate, q and pressure, P. The volumetric flow rate, q is through variable and it is analogous to current. The pressure, P is across variable and it is analogous to voltage.

Three basic elements of hydraulic systems are the Resistance, Capacitance and Inertance. The liquid flowing out of a tank can meet the resistance in several ways. Liquid while flowing through a pipe meet with resistance due to the friction between pipe walls and liquid. Presence of valves, bends, coupling of pipe of different diameter also offer resistance to liquid flow.

The capacitance is an energy storage element and it represents storage in gravity field. The inertance represents fluid inertia and is derived from the inertia forces required to accelerate the fluid in a pipe. It is also an energy storage element. But the energy storage due to inertance element is negligible compared to that of capacitance element.

Consider the flow through a short pipe connecting two tanks. The Resistance, R for liquid flow in such a pipe or restriction, is defined as the change in the level difference, necessary to cause a unit change in the flow rate.

R = Change in level difference, m
R = Change in flow rate, m³ / sec

The Capacitance, C of a tank is defined to be the change in quantity of stored liquid, necessary to cause a unit change in the potential (head)

C = Change inquid stored, m³
C = Change in head, m

### HYDRAULICS DEVICES

The hydraulic devices are used in hydraulic feedback systems and in combined electro mechanical hydraulic systems. In hydraulic devices, power is transmitted through the action of fluid flow under pressure and the fluid is incompressible. The fluid used are petroleum based oils or non-inflammable synthetic oils.

The hydraulic devices used in control systems are generally classified as hydraulic motors and hydraulic linear actuators.

The output of hydraulic motor is rotary motion and that of linear actuator is translational. The hydraulic motor is physically smaller in size than an electric motor for the same power output. Also, the hydraulic components are more rugged than the corresponding electrical components. The applications of hydraulic devices are power steering and brakes in automobiles, the steering mechanism of large ships, the control of large machine tools.

1. Hydraulic fluid acts as a lubricant and coolant.
2. Comparatively small sized hydraulic actuators can develop large forces or torques.
3. Hydraulic actuators can be operated under continuous, intermittent, reversing and stalled conditions without damage.
4. Hydraulic actuators have a higher speed of response. They offer fast starts, stops and speed reversals.
5. With availability of both linear and rotary actuators, the design has become more flexible.
6. Because of low leakages in hydraulics actuators, when loads are applied the drop in speed will be small.
7. For the same power output, hydraulics motor is much smaller in physical size than an electric motor.
8. Hydraulic components are rapidly acting and more rugged compared to the corresponding electrical component.

1. Hydraulic power is not readily available compared to electric power.
2. They have the inherent problems of leaks and of sealing them against foreign particles.
3. Operating noise.
4. Costs more when compared to electrical system.
5. Tendency to become sluggish at low temperature because of increasing viscosity of fluid.
6. Fire and explosion hazards exist.
7. Hydraulics lines are not flexible as electric cables.
8. Because of the non-linear and other complex characteristics involved, it is difficult to design sophisticated hydraulic systems.

### EXAMPLE OF HYDRAULIC DEVICE

The most frequently consists of a variable used hydraulic device in control system is hydraulic motor-pump set. It stroke hydraulic pump and a fixed stroke hydraulic motor as shown in image. The device accepts a linear displacement (stroke length) as input and delivers a large output torque.

The hydraulics motor is controlled by the amount of oil delivered by the pump. By mechanically changing the pump stroke, the oil delivered by the pump is controlled. Like in a DC generator and motor, there is no essential difference between hydraulic pump and motor. In a pump the input is mechanical power and output is hydraulics power and in a motor, it is viceversa.