Page 79 - Understanding Automotive Electronics

2735 | CH 2 Page 66 Tuesday, March 10, 1998 10:55 AM

2 THE SYSTEMS APPROACH TO CONTROL AND INSTRUMENTATION

In mathematical terms, the control signal at sample time t , which we
k
denote v , is given by
k
M
k ∑
v = – Ge – K e km
k
–
m = 1
where
e is the most recent sample
k
e k – m is the mth oldest sample (m = 1, 2, . . . , M)
G is proportional gain
K is integral gain
The dynamic properties of a PI controller with the above control law are
determined by the sizes of the proportional (G ) and integral (K ) gains as well
as the number (M ) of error samples included in the sum (Σ).
PROPORTIONAL INTEGRAL DIFFERENTIAL CONTROLLER

Still another control type that finds wide application in practice is the
proportional integral differential (PID) controller. In a PID controller, the
control signal is given by
M
k ∑
–
[
v = – Ge K e – De – e )/T]
(
k km k k 1
–
–
m = 1
The final term in this expression for the control signal involves the difference
between the two most recent samples of the error. This term represents the rate
of change of the error, and its inclusion in the control law often improves
dynamic response greatly. For the corresponding analog (continuous-time)
controller, the control signal is given by
de
d
v = Ge + k e t + D-----
c ∫ dt
CLOSED-LOOP LIMIT-CYCLE CONTROL
In a proportional control The control electronics in the previous example provided what is called
system the control signal proportional control because the control signal is proportional to the error
is proportional to the signal. Other combinations of control electronics are possible, and it is a
error between desired and challenge to the system designer to develop imaginative types of control
actual output. electronics to improve the performance of a given plant.
Another type of control that is used in automotive applications is limit-
cycle control. Limit-cycle control is a type of feedback control that monitors
the system’s output and responds only when the output goes beyond preset

66 UNDERSTANDING AUTOMOTIVE ELECTRONICS