1.4 Block Diagrams

Oct 26, 2026

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1.4 Block Diagrams explains how block diagrams use blocks, summing points, and take-off points to represent control systems in pictorial form. It clarifies transfer functions using examples such as G(s)=Y(s)/X(s), including how outputs are formed by algebraic addition or subtraction based on input polarity. It also shows how electrical systems like series RLC circuits can be transformed from the time domain to the s-domain and implemented with block diagrams by mapping equations to blocks and combining them into an overall representation.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages20

Reading Time50 min

AccessFree to download

Block diagrams basics

Basic elements of a block diagram

Block and transfer function

Summing point operations

Take-off point usage

Block diagram representation of electrical systems

Series RLC circuit in time and s-domain

ROHINI COLLEGE OF ENGINEERING & TECHNOLOGY 1.4 BLOCK DIAGRAMS Block diagrams consist of a single block or a combination of blocks. These are used to represent the control systems in pictorial form. Basic Elements of Block Diagram The basic elements of a block diagram are a block, the summing point and the take-off point. Let us consider the block diagram of a closed loop control system as shown in the following fig 1.4.1 to identify these elements. Figure 1.4.1: Basic elements of Block diagram [Source: “Control System Engineering” by Nagoor Kani, page : 1.50] The above block diagram consists of two blocks having transfer functions G(s) and H(s) . It is also having one summing point and one take-off point. Arrows indicate the direction of the flow of signals. Let us now discuss these elements one by one. Block The transfer function of a component is represented by a block. Block has single input and single output. The following fig 1.4.2 shows a block having input X(s), output Y(s) and the transfer function G(s) . ROHINI COLLEGE OF ENGINEERING & TECHNOLOGY Figure 1.4.2: Open loop transfer function [Source: “Control System Engineering” by Nagoor Kani, page : 1.49] Transfer Function, G(s)=Y(s) / X(s) ⇒Y(s)=G(s)X(s) Output of the block is obtained by multiplying transfer function of the block with input. Summing Point The summing point is represented with a circle having cross (X) inside it. It has two or more inputs and single output. It produces the algebraic sum of the inputs. It also performs the summation or subtraction or combination of summation and subtraction of the inputs based on the polarity of the inputs. Let us see these three operations one by one. The following figure shows the summing point with two inputs (A, B) and one output (Y) . Here, the inputs A and B have a positive sign. So, the summing point produces the output, Y as sum ofA and B. i.e.,Y = A + B. The following fig 1.4.3& fig 1.14 shows the summing point with two inputs (A, B) and one output (Y) . ROHINI COLLEGE OF ENGINEERING & TECHNOLOGY Figure 1.4.3: Summing point with two inputs [Source: “Control System Engineering” by Nagoor Kani, page : 1.50] Here, the inputs A and B are having opposite signs, i.e., A is having positive sign and B is having negative sign. So, the summing point produces the output Y asthe difference of A and B. Y = A + (-B) = A-B. Figure 1.4.4: Summing point with two inputs (difference of A & B) [Source: “Control System Engineering” by Nagoor Kani, page : 1.50] The following fig 1.4.5 shows the summing point with three inputs (A, B, C) and one output (Y) . Here, the inputs A and B are having positive signs and C is having a negative sign. So, the summing point produces the output Y as Y = A + B + (−C) = A + B − C. Figure 1.4.5: Summing point with three inputs [Source: “Control System Engineering” by Nagoor Kani, page: 1.50] Take-off Point The take-off point is a point from which the same input signal can be passed through more than one branch. That means with the help of take-off point, we can apply the same input to one or more blocks, summing points. ROHINI COLLEGE OF ENGINEERING & TECHNOLOGY In the following fig 1.4.6 shows the take-off point is used to connect the same input, R(s) to two more blocks. Figure 1.4.6: Take-off point from same input [Source: “Control System Engineering” by Nagoor Kani, page: 1.51] In the following fig 1.4.7 , the take-off point is used to connect the output C(s), as one of the inputs to the summing point. Figure 1.4.7: Take-off point from output [Source: “Control System Engineering” by Nagoor Kani, page: 1.51] ROHINI COLLEGE OF ENGINEERING & TECHNOLOGY Block Diagram Representation of Electrical Systems In this section, let us represent an electrical system with a block diagram. Electrical systems contain mainly three basic elements—resistor, inductor and capacitor. Consider a series of RLC ci

FAQs

What are the basic elements of a block diagram?

A block diagram uses blocks, a summing point, and a take-off point to represent system structure and signal flow.

How does a block diagram represent a transfer function?

A block represents a component’s transfer function, where the output is obtained by multiplying the transfer function with the input, such as G(s)=Y(s)/X(s).

How do summing points determine whether signals are added or subtracted?

The summing point produces algebraic sums or differences based on the polarity of each input (positive or negative), forming expressions like Y=A+B or Y=A-B.

Oct 26, 2026

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