Step 3 − Use Rule 1 for blocks $(G_3 + G_4)$ and $G_5$. The modified block diagram is shown in the following figure. (BS) Developed by Therithal info, Chennai. Block Diagram Reduction Rules – Control System. This is the simplified block diagram. Each input has its own appropriate plus or minus sign. Repeat the above-discussed steps to have a simplified system. Obtain the transfer function for the system shown in the fig, 3. ... First, see the procedural steps to be followed for solving block diagram reduction problems: The directly connected blocks in series must be reduced to a single block. A control system may consist of a number of components. BLOCK DIAGRAM SIMPLIFICATIONS Figure 5: Cascade (Series) Connections Figure 6: Parallel Connections . Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail, Block diagram reduction Techniques - Transfer Function, Transfer functions of elements inside the blocks, Very simple to construct block diagram for a complicated system, Function of individual element can be visualized, Individual & Overall performance can be studied. Let us simplify (reduce) this block diagram using the block diagram reduction rules. A block diagram of a system is a pictorial representation of the functions performed by each component and of the flow of signals. Rule 4 − If there is difficulty with take-off point while simplifying, shift it towards right. The directly connected blocks in series must be reduced to a single block. Rule 3 − Check for the blocks connected in feedback loop and simplify. Rule 6 − Repeat the above steps till you get the simplified form, i.e., single block. So, to overcome this drawback, use signal flow graphs (representation). Because, we have to draw the (partially simplified) block diagram after each step. The modified block diagram is shown in the following figure. Now determine the transfer function of the overall closed-loop simplified system. In the next two chapters, we will discuss about the concepts related to signal flow graphs, i.e., how to represent signal flow graph from a given block diagram and calculation of transfer function just by using a gain formula without doing any reduction process. The block diagram reduction process takes more time for complicated systems. Step 1 − Find the transfer function of block diagram by considering one input at a time and make the remaining inputs as zero. No information about the physical construction, Tutorial Problems: Control Systems - Systems and their Representation, Important Short Questions, Answers: Control Systems - Systems and their Representation. o   Transfer functions of elements inside the blocks. Step 6 − Use Rule 3 for blocks connected in feedback loop. Because, we have to draw the (partially simplified) block diagram after each step. Rule 1 − Check for the blocks connected in series and simplify. Although blocks are used to identify many types of mathematical operations, operations of addition and subtraction are represented by a circle, called a summing point. The concepts discussed in the previous chapter are helpful for reducing (simplifying) the block diagrams. Block diagram reduction technique Because of their simplicity and versatility, block diagrams are often used by control engineers to describe all types of systems. Disadvantages of Block Diagram Representation, o   No information about the physical construction, Simple or Canonical form of closed loop system. The block diagram is to represent a control system in diagram form. In a block diagram all system variables are linked to each other through functional blocks. Step 4 − Use Rule 3 for blocks $(G_3 + G_4)G_5$ and $H_3$. Your email address will not be published. Use Rule 2 for blocks $G_3$ and $G_4$. Block Diagram Reduction Figure 1: Single block diagram representation ... Block diagram of a closed-loop system with a feedback element . Note − Follow these steps in order to calculate the transfer function of the block diagram having multiple inputs. Over all transfer function can be calculated easily. Also, it can be used, together with transfer functions, to represent the cause-and-effect relationships throughout the system. Step 5 − Use Rule 1 for blocks connected in series. A block diagram can be used simply to represent the composition and interconnection of a system. The modified block diagram is shown in the following figure. The reasons might be need to draw the (partially simplified) block diagram after each step. Rule 2 − Check for the blocks connected in parallel and simplify. Branches – lines showing the connection between the blocks, Arrow – associated with each branch to indicate the direction of flow of signal, Summing point – comparing the different signals, Take off point – point from which signal is taken for feed back, Advantages of Block Diagram Representation, o   Very simple to construct block diagram for a complicated system, o   Function of individual element can be visualized, o   Individual & Overall performance can be studied. Functional block – each element of the practical system represented by block with its T.F. The block diagram reduction process takes more time for complicated systems. Step 3 − Get the overall transfer function by adding all those transfer functions. Because of their simplicity and versatility, block diagrams are often used by control engineers to describe all types of systems. Obtain the Transfer function of the given block diagram, 2. block diagram representation of the control system, Difference Between Half Wave and Full Wave Rectifier, Difference between Half Adder and Full Adder, Difference between Centre Tapped and Bridge Rectifier, Intelligent Electronic Devices (IED) in SCADA. The transfer function is given inside the block. The block diagram reduction process uses more time for complicated systems. A block diagram can be used simply to represent the composition and interconnection of a system. The modified block diagram is shown in the following figure. Transfer Function is defined as the relationship between an input signal and an output signal to a device. A takeoff point is used to allow a signal to be used by more than one block or summing point. Further, reduce the parallely connected block into a single block. A pictorial representation of the functions performed by each component and of the flow of signals. Therefore, the transfer function of the system is, $$\frac{Y(s)}{R(s)}=\frac{G_1G_2G_5^2(G_3+G_4)}{(1+G_1G_2H_1)\lbrace 1+(G_3+G_4)G_5H_3\rbrace G_5-G_1G_2G_5(G_3+G_4)H_2}$$. Follow these rules for simplifying (reducing) the block diagram, which is having many blocks, summing points and take-off points. Use Rule 4 for shifting take-off point after the block $G_5$. Copyright © 2018-2021 BrainKart.com; All Rights Reserved.

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