Solution Manual for Digital Control System Analysis Design, 4th Edition
Master your textbook problems with Solution Manual for Digital Control System Analysis Design, 4th Edition, providing comprehensive solutions and explanations.
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CHAPTER 1
1.1-1. (a) Show that the transfer function of two systems in parallel, as shown in Fig. P1.1-l(a), is equal to
the sum of the transfer functions.
(b) Show that the transfer function of two systems in series (cascade), as shown in Fig. Pl.1-l(b), is
equal to the product of the transfer functions.
G1 (s)
E(s) C(s)
G1(s)
G2 (s)
(a)
(b)
E(s) M(s) G2(s) C(s)
+
+
Fig. P1.1-1
Solution:
(a) 1 2 1 2( ) ( ) ( ) ( ) ( ) [ ( ) ( )] ( )C s G s E s G s E s G s G s E s= + = +
1 2
( ) ( ) ( )
( )
C s G s G s
E s
∴ = +
(b) 2 1 2( ) ( ) ( ) ( ) ( )C s G s M s G s G s= =
1 2
( ) ( ) ( )
( )
∴ =
C s G s G s
E s
1.1-2. By writing algebraic equations and eliminating variables, calculate the transfer function C s( ) R s( )
for the system of:
(a) Figure P1.1-2(a).
(b) Figure P1.1-2(b).
(c) Figure P1.1-2(c).
1.1-1. (a) Show that the transfer function of two systems in parallel, as shown in Fig. P1.1-l(a), is equal to
the sum of the transfer functions.
(b) Show that the transfer function of two systems in series (cascade), as shown in Fig. Pl.1-l(b), is
equal to the product of the transfer functions.
G1 (s)
E(s) C(s)
G1(s)
G2 (s)
(a)
(b)
E(s) M(s) G2(s) C(s)
+
+
Fig. P1.1-1
Solution:
(a) 1 2 1 2( ) ( ) ( ) ( ) ( ) [ ( ) ( )] ( )C s G s E s G s E s G s G s E s= + = +
1 2
( ) ( ) ( )
( )
C s G s G s
E s
∴ = +
(b) 2 1 2( ) ( ) ( ) ( ) ( )C s G s M s G s G s= =
1 2
( ) ( ) ( )
( )
∴ =
C s G s G s
E s
1.1-2. By writing algebraic equations and eliminating variables, calculate the transfer function C s( ) R s( )
for the system of:
(a) Figure P1.1-2(a).
(b) Figure P1.1-2(b).
(c) Figure P1.1-2(c).
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