Page 112 - Mechatronics with Experiments

98 MECHATRONICS
Proportional control (P)

r + e K u u(t) = K p e(t )
- p D(s) = u(s) = K
e(s) p
y

Integral control (I)

t
r + e u u(t) = K e( )dττ
K I 0
- I u(s)
D(s) = = K I
e(s) s
y
Derivative control (D)

r + e K d( ) u u(t) = K D d e(t)
- D dt dt
u(s)
D(s) = = K D s
e(s)
y
FIGURE 2.40: Basic feedback control actions: proportional control, integral control, derivative
control.

r + e u
D(s)
-
y

u(t) “Present error”
e(t)
K e
e p0
0
K p
t t

“Past error”
K A
A I
K I
s
t t t t t t
1 2 3 1 2 3

“Future error”
K D a
a b K D s
1 1 - Kb
t t t D
1 2 3 t
FIGURE 2.41: Illustration of the input–output behavior of basic feedback control actions:
proportional, integral, derivative control.