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# Basics of Control System Study Notes for GATE Electrical (EE) and ECE Exams

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Control systems are a fundamental concept in engineering that involve the regulation and management of dynamic processes or systems. They are designed to maintain desired conditions or behaviors by automatically adjusting inputs or parameters based on feedback.

In this article, we are providing you with the basics of Control Systems, an important topic which carries good weight in the electrical and electronics & communication engineering exams. The Control Systems cover the topics such as Open Loop System, Closed Loop System, Temperature Control System, Mason’s Gain Formula & Block Diagram Reduction Method. The Basics of Control Systems topic is commonly asked in various competitive exams such as GATE, ISRO, ESE, and other electrical & ECE exams.

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**Control Engineering**

Basically, Control engineering is applicable to aeronautical, chemical, mechanical, environmental, civil, and electrical engineering which is based on the foundations of feedback theory and linear system analysis, and it generates the concepts of network theory and communication system theory.

Hence according to the theory of control engineering, it is not limited to any engineering discipline but applicable to the different areas which require the control process for their functioning & Stable Operations.

**Open Loop Control System**

- An open-loop control system consists of a control actuator or controller to receive the desired response.
- It uses an switching device to control the process directly without using any device.
- An illustration of an open-loop control system is an electric toaster.
- In Open Loop Controlling action, there is no feedback system present to sense the error in the desired output.

### Closed Loop Control System

- In a closed-loop control system, it consists of an additional measure of the actual output to compare the actual output with the desired output response.
- This additional measure of the output is called the feedback signal.
- A feedback control system that set out to maintain the relationship of one system variable to another by comparing the functions of these variables and using the difference as a means of control.
- Since as the system becomes more complex, the interrelationship of many controlled variables may be considered in the control scheme.
- An example of a closed-loop control system is a person steering (or driving) an automobile by looking at the auto’s location on the road and making the appropriate adjustments.

**TEMPERATURE CONTROL SYSTEMS**

- In the electric furnace, the temperature is measured by a thermometer, which is an analog device.
- The analog temperature converted to digital temperature using an A/D converter. The digital temperature is then fed to a controller through an interface.
- The digital temperature is then compared with the programmed input temperature, and if there is any error, the controller then sends out a signal to the heater, through an amplifier, interface, and relay to bring the furnace temperature to the desired value.

**Download Formulas for GATE Electrical Engineering – Signals and Systems PDF**

**Comparison between Open Loop & Closed Loop Control System**

Feature |
Open Loop Control System |
Closed Loop Control System |

Effect of Output on Input |
No effect on input. | The output signal affects the controller output into the system. |

Stability |
Very Stable | The response changes with the change inn input signal. |

Response to external disturbances |
No reaction to disturbances. The open Loop control works on fixed output. | The output of controller adjust itself in response to the input signal. |

Ease of Construction |
The controller is easy to construct. | Controller is difficult to construct as it is complex. |

Cost |
Cheap | Expensive |

Bandwidth |
Small Bandwidth | Large Bandwidth |

Maintenance |
Low Maintenance | More Maintenance is required. |

Feedback |
There is no Feedback | Feedback is always present. |

**Block Diagram Reduction technique **

**Need for Block Diagram Reduction:- **Some of the block diagrams are complex, such that the evaluation of their performance required simplification (or reduction) of the block diagrams which is done by the block diagram rearrangements.

**Advantages of Block Diagram reduction**

- Its very simple to construct the block diagram for complicated systems.
- Single, as well as the overall performance of the system, can be studied by using transfer functions shown in the block diagram.
- Overall closed loop transfer function can be calculated easily using block diagram laws.
- The function of the individual element can be visualized with the help of block diagram.

**Rules of Block Diagram :**

**Signal Flow Graphs:**

The objectives for this technical note are:

- Define the key terms describing signal-flow graphs.
- Draw signal flow graphs for a block diagram.
- Draw a block diagram from a signal-flow graph.
- List down the steps in the process to solve a system using Mason’s gain formula.
- Apply Mason’s gain formula to systems in block-diagram or signal-flow-graph form.

**Basic Definition Related to Meson’s Gain Formula**

**Forward paths:**Forward paths are continuous paths through the graph from the input to the output. No node is passed more than once.**Feedback loops:**Feedback loops are continuous paths through the graph that starts and end at the same node.**Path gain:**Path gain is the product of the signal gains encountered on the path.**Loop gain:**Loop gain is the product of signal gains encountered in a feedback loop.**Source node:**Source nodes are nodes with only outgoing branches.**Sink nodes:**Sink nodes are nodes with only incoming branches.

It is a graphical technique that deals with the relation between the variable of a system described in the form of set of linear algebraic equation.

- Signal flow graph of Block diagram.

**Download Formulas for GATE Electrical Engineering – Electrical Machines PDF**

**Mason’s formula:**

This is a technique for reducing signal flow graphs to single transfer functions that relate the output of a system to its input. There is general gain formula, called **Mason’s rule**, that allow the determination of the input-output relations of an SFG by inspection. The transfer function of a system is given as,

Where,

K= 1, 2, 3, ………

N = no of forward path

P_{K} = Gain of K^{th} forward path

Δ_{K }= 1 – [Sum of individual loop gain not touching to K^{th} forward path] + [Sum of product of 2 non touching loop gain that not touching to k^{th} forward path]

Δ = Determinant of the graph or characteristics function

Δ = 1 – (Sum of all individual loop gain) + (Sum of gain products of all possible combinations of two non-touching loops) – (Sum of the gain products of all possible combinations of three non-touching loops) + ………

**Download Formulas for GATE Electrical Engineering – Signals and Systems**

**Analogous System**

An analogous electrical and mechanical system has differential equations of the same kind. There are two analogies that are used to go between the electrical and mechanical systems.

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