0195136047.pdf

5.6 PRACTICAL APPLICATION: A CASE STUDY 257

y = −∫

t

0 ydτ^ +^ y(0)

−y y

.

y.

.

y = −a .....

1 y −^ a 2 y +^ f

...

..

y

−f

y 0

y = −∫

t

f(t)^0 ydτ^ −^ y(0)

a 1

a 2 y a 1 y

a 2

1

Integrator Integrator

Multiplicative constants

Summer

−y 1

1

1

1

− 1

Figure 5.4.19Connection diagram for analog computer simulation for solving the second-order differential
equationy ̈=−a 1 y ̇−a 2 y+fsubject to initial conditionsy( 0 )=y 0 andy ̇( 0 )=y 1.

• Amplifier block as a two-port device and its circuit model.


• Ideal operational amplifier and its characteristics.


• Analysis and design of simple amplifier circuits including feedback.


• Properties of practical op-amps.


• Op-amp applications, including active filters.


• Understanding the operation of analog computers.

5.6 PRACTICAL APPLICATION: A CASE STUDY

Automotive Power-Assisted Steering System

In terms of negative feedback, there exists an analogy between the operational amplifier and
the power-steering mechanism of an automobile. The hydraulic pump is analogous to the power
supply in an op-amp circuit. The position of the booster-cylinder piston that is linked to the steering
is analogous to the op-amp output signal; the mechanical linkage between the control valve and
the booster-cylinder piston is analogous to the feedback circuit; the control-valve response to the
difference between the input from the steering wheel and the position of the steering linkage is
analogous to the op-amp response to its differential input signal. Thus the automotive power-
assisted steering system is but an example of negative feedback in a mechanical sense.
Figure 5.6.1 illustrates in a simplified manner how a hydraulic pump driven by the engine
continuously supplies pressure to a control valve which in turn supplies the fluid to the two sides
of the booster cylinder. A negative feedback path is established from the booster cylinder through
the mechanical linkage back to the control valve.
For straight steering, the pressure applied is equal on both sides of the cylinder and, as such,
no turning force results. When the steering wheel is moved by the driver to turn the wheels in the
desired direction, more pressure is applied to one side of the cylinder or the other.
A mechanical feedback arm from the steering linkage causes the valve to return to its neutral
position as the wheels turn, thereby allowing the driver to make a gradual turn. As and when the
steering wheel is turned, the wheels move a proportional amount rather than moving all the way
to the extreme position.
Feedback control systems are discussed in Section 16.2 in more detail.