Page 390 - Automotive Engineering Powertrain Chassis System and Vehicle Body

Vehicle motion control C HAPTER 13.1

subtracting (electronically) the actual speed V a from activated the speed set switch. If the car is traveling on
the desired speed V d : a level road at the desired speed, then the error is zero
and the throttle remains at a fixed position.
e ¼ V V a If the car were then to enter a long hill with a steady
d
positive slope (i.e., a hill going up) while the throttle is
The controller then electronically generates the actuator set at the cruise position for level road, the engine will
signal by combining a term proportional to the error produce less power than required to maintain that speed
ðK P eÞ and a term proportional to the integral of the error: on the hill. The hill represents a disturbance to the cruise
ð control system. The vehicle speed will decrease, thereby
K I edt introducing an error to the control system. This error, in
turn, results in an increase in the signal to the actuator,
causing an increase in engine power. This increased
The actuator signal u is a combination of these two terms:
power results in an increase in speed. However, in
ð
a proportional control system the speed error is not re-
u ¼ K P e þ K I edt
duced to zero since a nonzero error is required so that the
engine will produce enough power to balance the in-
The throttle opening is proportional to the value of this creased load of the disturbance (i.e., the hill).
actuator signal. The speed response to the disturbance is shown in
Operation of the system can be understood by first Fig. 13.1-3a. When the disturbance occurs, the speed
considering the operation of a proportional controller drops off and the control system reacts immediately to
(i.e., imagine that the integral term is not present for the increase power. However, a certain amount of time is
sake of this preliminary discussion). We assume that the required for the car to accelerate toward the desired
driver has reached the desired speed (say, 60 mph) and speed. As time progresses, the speed reaches a steady

Fig. 13.1-3 Cruise control speed performance.

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