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Open Loop Control System:
? In this system the output is not feedback 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.
Control Systems 
Page 2


Open Loop Control System:
? In this system the output is not feedback 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.
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
dt
Block Diagram Reduction:
Rule Original Diagram Equivalent Diagram
1. Combining
blocks in cascade
2. . oving 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
G
1
X
1
G
2
X
1
G
1
X
1
G
1
G
2
X
1
G
1
G
2
X
1
G
1
G
2
G
X
1
X
1
X
1
G
G
X
1
X
1
1/G
X
1
G
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FAQs on Control System Formulas for GATE Exam - Control Systems - Electrical Engineering (EE)

1. What are the basic components of a control system?
Ans. The basic components of a control system include the plant or system being controlled, the controller, the feedback sensor, and the actuator. The plant or system being controlled is the physical process or equipment that needs to be controlled. The controller receives the input from the feedback sensor, processes it, and sends signals to the actuator to adjust the system's behavior.
2. What is the transfer function of a control system?
Ans. The transfer function of a control system is a mathematical representation that relates the output of the system to its input. It is usually expressed as the ratio of the Laplace transform of the output to the Laplace transform of the input, assuming all initial conditions are zero. The transfer function provides valuable information about the system's behavior, such as its stability, steady-state response, and frequency response.
3. How do you determine the stability of a control system?
Ans. The stability of a control system can be determined by analyzing the poles of its transfer function. If all the poles lie in the left-half plane of the complex plane, the system is stable. On the other hand, if any pole lies in the right-half plane or on the imaginary axis, the system is unstable. The stability of a control system is crucial to ensure accurate and reliable control.
4. What is the difference between open-loop and closed-loop control systems?
Ans. In an open-loop control system, the output of the system does not affect the control action. The control action is based solely on the input or setpoint. On the other hand, in a closed-loop control system, the output is continuously monitored and compared to the desired setpoint. The control action is then adjusted based on this feedback, allowing for more accurate and precise control.
5. How do you design a feedback control system?
Ans. The design of a feedback control system involves determining the appropriate controller parameters and tuning them to achieve the desired system response. This can be done using various methods such as trial and error, empirical tuning rules, or advanced techniques like PID controller tuning algorithms. It is important to consider factors such as stability, steady-state error, and response time while designing a feedback control system.
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