Control Systems Formulas for GATE EE Exam | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE) PDF Download

 Page 1


ECE FORMULA BOOK CONTROL SYSTEMS
1. BLOCK DIAGRAM
Open Loop Control System:
? In this system the output is not fedback for comparison with the input.
? Open loop system faithfulness depends upon the accuracy of input calibration.
When a designer designs, he simply design open loop system.
Closed Loop Control System: It is also termed as feedback control system. Here
the output has an effect on control action through a feedback. Ex. Human being
Transfer Function:
C(s) G(s)
Transfer function =
R(s) 1 + G(s)H(s)
? Comparison of Open Loop and Closed Loop control systems:
Open Loop:
1. Accuracy of an open loop system is defined by the calibration of input.
2. Open loop system is simple to construct and cheap.
3. Open loop systems are generally stable.
4. Operation of this system is affected due to presence of non-linearity in its
elements.
Closed Loop:
1. As the error between the reference input and the output is continuously
measured through feedback. The closed system works more accurately.
2. Closed loop systems is complicated to construct and it is costly.
3. It becomes unstable under certain conditions.
4. In terms of performance the closed loop system adjusts to the effects of non-
linearity present.
Transfer Function: The transfer function of an LTI system may be defined as the
ratio of Laplace transform of output to Laplace transform of input under the
assumption
Y(s)
G(s)=
X(s)
? The transfer function is completely specified in terms of its poles and zeros and
the gain factor.
Page 2


ECE FORMULA BOOK CONTROL SYSTEMS
1. BLOCK DIAGRAM
Open Loop Control System:
? In this system the output is not fedback for comparison with the input.
? Open loop system faithfulness depends upon the accuracy of input calibration.
When a designer designs, he simply design open loop system.
Closed Loop Control System: It is also termed as feedback control system. Here
the output has an effect on control action through a feedback. Ex. Human being
Transfer Function:
C(s) G(s)
Transfer function =
R(s) 1 + G(s)H(s)
? Comparison of Open Loop and Closed Loop control systems:
Open Loop:
1. Accuracy of an open loop system is defined by the calibration of input.
2. Open loop system is simple to construct and cheap.
3. Open loop systems are generally stable.
4. Operation of this system is affected due to presence of non-linearity in its
elements.
Closed Loop:
1. As the error between the reference input and the output is continuously
measured through feedback. The closed system works more accurately.
2. Closed loop systems is complicated to construct and it is costly.
3. It becomes unstable under certain conditions.
4. In terms of performance the closed loop system adjusts to the effects of non-
linearity present.
Transfer Function: The transfer function of an LTI system may be defined as the
ratio of Laplace transform of output to Laplace transform of input under the
assumption
Y(s)
G(s)=
X(s)
? The transfer function is completely specified in terms of its poles and zeros and
the gain factor.
ECE FORMULA BOOK CONTROL SYSTEMS
? The T.F. function of a system depends on its elements, assuming initial
conditions as zero and is independent of the input function.
? To find a gain of system through transfer function put s = 0
Example: G(s) = Gain =
If a step, ramp or parabolic response of T.F. is given, then we can find Impulse
Response directly through differentiation of that T.F.
(Parabolic Response) = Ramp Response
(Ramp Response) = Step Response
(Step Response) = Impulse Response
Block Diagram Reduction:
Rule Original Diagram Equivalent Diagram
1. Combining
blocks in cascade
2. Moving a
summing point
after a block
3. Moving a
summing point
ahead of block
4. Moving a take
off point after a
block
2
4
6 9
s
s s
? ? ? 4
9
d
dt
d
dt
d
dt
G
1
X
1
G
2
X G
1 1
X G G
2 1 1
X
1
G G
2 1
X G G
2 1 1
G
X
1
X
1
X G
1
G
X
1
X
1
1/G
X G
1