Page 55 - Understanding Automotive Electronics

2735 | CH 2 Page 42 Tuesday, March 10, 1998 10:55 AM

2 THE SYSTEMS APPROACH TO CONTROL AND INSTRUMENTATION

Figure 2.9
Simplified
Suspension System

FPO

occur on a so-called washboard gravel road. The force transmitted by the tire to
the unsprung mass, depicted by the solid curve in Figure 2.10, is represented by
F(t ) = F sinωt
0
where
F = amplitude of the force
0
ω = 2πf
f = frequency or (1/T)
T = period
The displacement of the unsprung mass is represented by x (relative to the rest
position) and is depicted by the dashed curve in Figure 2.10. This displacement
is given mathematically by
x = X sin(ωt – φ)
where φ equals phase, or 2πd/T.
The performance of the example suspension system is given by the
sinusoidal frequency response. For any system, the sinusoidal frequency response
is the ratio of the amplitude of the response to the amplitude of the input. In our
example, the response amplitude is X and the input amplitude is F, yielding
X
H = ---
F
The sinusoidal frequency response of any system is a function of (i.e., depends
on) frequency. In our example, the frequency of the rough road force due to the
washboard road is proportional to the speed at which the car travels over the
road. For the example suspension system, frequency response is depicted in

42 UNDERSTANDING AUTOMOTIVE ELECTRONICS