Control system block diagram reduction

1. Control System
Block Diagram Reduction
Presented by Dr. Moumita Saha

2. G(S) G(S)
H(S)
R(S) C(S) R(S)
E(S)
C(S)
-
+
Open-Loop Control System Closed-Loop Control System
𝑪(𝑺)
𝑹(𝑺)
= 𝑮(𝒔)
𝑪(𝑺)
𝑹(𝑺)
=
𝑮(𝑺)
𝟏 ± 𝑮 𝑺 𝑯(𝑺)

3. G1(S) G1(S)
G2(S)
R(S) C(S) R(S) C(S)
+
Blocks in Cascade Blocks in Parallel
+
G1(S)
G1(S)G2(s)
R(S) C(S) G1(S)+G2(S)
R(S) C(S)
Take off point Summing point

4. G(S)
R(S)
Moving a take off point
Conversion Rules
H(S)
G(S)
R(S)
𝑯(𝑺)
𝑮(𝑺)
G(S)
R(S)
R(S)G(s)
G(S)
R(S)
G(S) R(S)G(s)
R(S)H(s)
R(S)H(s)
R(S)G(s)
R(S)G(s)
R(S)G(s)
R(S)G(s)
(1) (2)

5. Moving a summing point
Conversion Rules
G(S)
R(S) C(S)
=[R(S)+X(S)]G(S)
+
X(S)
G(S)
R(S)
+
+
G(S)
X(S)
C(S)
=[R(S)+X(S)]G(S)
+ G(S)
R(S)
+
+
X(S)
C(S)
=R(S)G(S) +X(S)
G(S)
R(S)
+
+
𝟏
𝑮(𝑺)
X(S)
C(S)
=R(S)G(S) +X(S)
(3)
(4)

6. Example
G1(S)
R(S)
-
+
+
C(S)
G3(S)
+
G2(S)
𝑪(𝑺)
𝑹(𝑺)
=
[𝑮𝟏 𝑺 + 𝑮𝟐 𝑺 ]𝑮𝟑(𝑺)
𝟏 + 𝑮𝟏 𝒔 𝑮𝟑 𝑺 𝑯 𝑺
H(S)
R(S)
-
+
+
C(S)
G3(S)
+
G2(S)
G1(S)H(S)
G1(S)
R(S)
-
+
+
C(S)
+
G2(S)
G1(S)H(S)
G1(S) G3(S)
C(S)
G1(S)+G2(S)
𝑮𝟑(𝑺)
𝟏 + 𝑮𝟏 𝒔 𝑮𝟑 𝑺 𝑯 𝑺
R(S)