Modern Control Engineering

594 Chapter 8 / PID Controllers and Modified PID Controllers

Hence, we have

In this case, ifGydis given, then Gynis fixed, but Gyris not fixed, because Gc1is

independent of Gyd.Thus, two closed-loop transfer functions among three closed-loop

transfer functions Gyr,Gyd,andGynare independent. Hence, this system is a two-degrees-

of-freedom control system.

Similarly, the system shown in Figure 8–30 is also a two-degrees-of-freedom control

system, because for this system

Gyn=

Y(s)

N(s)

=-

Gc1 Gp

1 +Gc1 Gp

Gyd=

Y(s)

D(s)

=

Gp

1 +Gc1 Gp

Gyr=

Y(s)

R(s)

=

Gc1 Gp

1 +Gc1 Gp

+

Gc2 Gp

1 +Gc1 Gp

Gyn=

Gyd-Gp

Gp

Gyr=Gc1 Gyd

Gc 1 (s) Gp(s)

Y(s)

N(s)

R(s)

B(s)

U(s)

D(s)

Gc 2 (s)

B(s) +

+

+

+

+

• 
  

+

• 
  

Figure 8–29

Two-degrees-of-

freedom control

system.

Gc 1 (s) Gp(s)

Gc 2 (s)

Y(s)

N(s)

U(s)

D(s)

R(s)

B(s)

+– ++ ++

++

Figure 8–30

Two-degrees-of-

freedom control

system.

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