Modern Control Engineering

Problems 97

referred to the motor shaft. When J 0 and are multiplied by 1/n^2 ,the inertia and

viscous-friction coefficient are expressed in terms of the output shaft. Introducing new parameters

defined by

moment of inertia referred to the output shaft

viscous-friction coefficient referred to the output shaft

the transfer function G(s)given by Equation (3–51) can be simplified, yielding

or

where

The block diagram of the system shown in Figure 3–29(b) can thus be simplified as shown in

Figure 3–29(c).

Km=

K

B

, Tm=

J

B

=

Ra J 0

Ra b 0 +K 2 K 3

G(s)=

Km

sATm s+ 1 B

G(s)=

K

Js^2 +Bs

K=K 0 K 1 K 2 nRa

B =Cb 0 +AK 2 K 3 RaBDn^2 =

J =J 0 n^2 =

b 0 +AK 2 K 3 RaB

Problems

B–3–1.Obtain the equivalent viscous-friction coefficient
beqof the system shown in Figure 3–30.

B–3–2.Obtain mathematical models of the mechanical sys-

tems shown in Figures 3–31(a) and (b).

x

b 3

y

b 2

b 1 k m

(a)

No friction

x (Output)

u(t)

(Input force)

m

(b)

No friction

x (Output)

u(t)

(Input force)

k 1 k 2

Figure 3–31

Mechanical systems.

Figure 3–30

Damper system.