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x(t)
f(t)
m Disturbance force : f d(t)
force
(i.e. wind force)
(a)
w (t)
d
u(t) - x(t)
1
s 2
(b)
FIGURE 2.43: Mass-force system model (a) model components, (b) block diagram.
̈ x(t) = u(t) − w (t)
d
2
s x(s) = u(s) − w (s)
d
1 1
x(s) = u(s) − w (s)
d
s 2 s 2
2.12.1 Proportional Control
Let us consider the input and output relationship, and do not consider disturbance for the
purpose of studying proportional control properties only (Figure 2.44),
x(s) 1
=
u(s) s 2
x
x d u f K p
K p m m m=1 K x
- p d
x
2 p
K p
x d (t) x(t)
2. 0
1. 0
1. 0
t t
K p
FIGURE 2.44: Mass–force system with position feedback control and its step response.
