# Block diagram summing junction diagram base website

02.02.2021 By Nilar

Any system can be described by a set of differential equations, or it can be represented by the schematic diagram that contains all the components and their connections. However, these methods do not work for complicated systems. The Block diagram representation is a combination of these two methods.

A block diagram is a representation of a system using blocks. For representing any system using block diagram, it is necessary to find the transfer function of the system which is the ratio of Laplace of output to Laplace of input. Summing Point : When we want to apply a different input signal to the same block then the resultant input signal is the summation of all the inputs. The summation of an input signal is represented by a crossed circle called summing point which is shown in the figure below.

Take off Point : When there is more than one block, and we want to apply the same input to all the blocks, we use a take-off point. By the use of a take-off point, the same input propagates to all the blocks without affecting its value. Representation of same input to more than one block is shown in the below diagram. Now the output I s is given to another block containing element SL and the output of this block is V0. A system in which a feedback path is there is called a closed-loop control system.

In this system, the output is feedback into the error detector and then it is compared with the input signal. The feedback signal can be negative or positive. When two or more blocks are connected in seriesthen the resultant block is the product of the individual blocks. When two or more blocks are connected in parallel, then the resultant block is the sum of the individual blocks.

When the take-off point is moved ahead of a block before the blockthen the same transfer function is introduced in the take-off point branch. When the take-off point is moved after the block, then a block with reciprocal of a transfer function is introduced in the take-off point branch.

JavaTpoint offers too many high quality services. Mail us on hr javatpoint. Please mail your requirement at hr javatpoint. Duration: 1 week to 2 week. Control Systems. Control Systems Electrical Machines. Next Topic Signal flow graphs. Digital E. Affiliate M. Fuzzy Logic.

Verbal A. Angular 7. Compiler D. Software E. Web Tech. Cyber Sec. Control S. Data Mining.This site uses cookies to optimize functionality. Click Learn More to read our privacy policy. The following is a basic overview, with descriptions and meanings, of the most common flowchart symbols - also commonly called flowchart shapesflow diagram symbols or process mapping symbolsdepending upon what type of diagram you're creating.

The table below lists the flowchart symbol drawing, the name of the flowchart symbol in Microsoft Office with aliases in parenthesesand a short description of where and how the flowchart symbol is used. Caveat: The descriptions given above are written from the perspective of someone using them to create process flow chartswhereas many of the flowchart symbols actually have their roots in the data processing diagrams and programming flow charts.

So, not all the flowcharting shapes shown below may be relevant to your needs. The flowchart symbol names in parentheses are common alternates for a given shape. Sometimes a flowchart shape can have more than one meaning, as with the Circle shape, which depicts a jump node in flow charts and inspection point in business process mapping. Other times, there are just multiple names for the same flow chart symbol - such as Terminator and Terminal Point.

The majority of flowcharts rely on just a few of the process-related symbols to do all the heavy lifting: TerminatorProcessDecisionDocumentand Connector.

In fact, if you use other flowcharting shapes, many people won't know what they are for, so you may want to add a symbol key to your flowchart. You might think that an expensive flowchart software package is required to make presentation-quality flowcharts.

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It isn't. All the shapes used in this article were created in Microsoft Excel. FlowBreeze is an Excel add-in that automates the steps to create a flowchart. It simplifies the task of creating flowcharts by converting your text into flowchart shapes, automatically applying styles, routing connector arrows, positioning symbols, and much more. Try a free day trial today! Spreadspeed is a time saving Excel add-in for performing operations on workbooks, worksheets, ranges, tables, text, numbers, dates, data, and more.

The Spreadspeed auditing features are a set of risk assessment and error reduction tools for ensuring the quality of your spreadsheets. Toggle navigation BreezeTree Software. Toggle cookie consent banner.

Learn More Accept. Excel Flowchart Wizard FlowBreeze is a flowchart add-in for Microsoft Excel that makes creating flowcharts simple and pain free.

### Control Systems - Block Diagram Reduction

Spreadspeed Excel Utilities Spreadspeed is a time saving Excel add-in for performing operations on workbooks, worksheets, ranges, tables, text, numbers, dates, data, and more. FlowBreeze Samples See more screenshots Most Popular Articles What is a Flowchart?

Show a Process or action step. This is the most common symbol in both process flowcharts and process maps. A Predefined Process symbol is a marker for another process step or series of process flow steps that are formally defined elsewhere.

This shape commonly depicts sub-processes or subroutines in programming flowcharts. If the sub-process is considered "known" but not actually defined in a process procedure, work instruction, or some other process flowchart or documentation, then it is best not to use this symbol since it implies a formally defined process.This shape tells you where the flowchart begins and ends. It shows the entry point of your flowchart and the exit point.

To designate the start of your flowchart, you would fill this shape with words like Start or Begin. The words you use are up to you. To designate the ending point of the chart, this shape is filled with words like EndExitor Return. Usually a flowchart has one starting point. However, a flowchart can have as many ending points as needed.

Sometimes you see this shape drawn as an oval as shown below. That is fine. Lines with Arrows You read a flowchart by following the lines with arrows from shape to shape.

The lines with arrows determine the flow through the chart. Flowcharts are usually drawn from top to bottom or left to right. Numbering shapes is optional. Numbering is helpful if you have to refer to a shape in a discussion. Numbering does not determine the flow of control. That is determined by the lines with arrows. If two lines cross, you ignore the perpendicular line and continue following the line to the next shape. If there may be confusion as to the path, you can insert a bridge or crossover, which is a little bump on crossed lines.

Rectangle In most flowcharts, the rectangle is the most common shape. It is used to show a process, task, action, or operation. It shows something that has to be done or an action that has to be taken. The text in the rectangle almost always includes a verb. Decision A decision asks a question. The answer to the question determines which arrow you follow out of the decision shape. For example, in the shape below, if it is cloudy, you follow the arrow down near the word Yes.

If it is not cloudy, you follow the arrow to the right near the word No.

## Flowchart Symbols Defined

The arrows flowing from the decision shape are usually labeled with YesNo or TrueFalse. But you can label them any way you want as long as the meaning is clear. This shape has one input arrow. It is usually at the top, but can be on any corner. The decision shape can have two or three exit points.

If you need more than 3 exit points, then you can use either of the methods shown below. Circle If you need to connect to another page or another section of the chart, and can't draw a line, you can use a circle.The summing amplifier is a one kind of circuit and the configuration of this circuit is based upon the standard inverting op-amp. Input of the resistor will be end up with another op-amp circuit named as a summing amplifier. The term summing amplifier is also named as adder, which is used to add two signal voltages.

The circuit of the voltage adder is so simple to construct and it enables to add many signals together. These kind of amplifiers is used in a wide range of electronic circuits. For instance, on a precise amplifier you have to add a small voltage to terminate the offset error of the operational amplifier.

An audio mixer is another example to add the waveforms together from various channels before sending the mixed signal to a recorder. Just recollect that the circuit of the inverting summing amplifier changes the input signals. The summing amplifier circuit is shown below. In the circuit below Va, Vb and Vc are input signals. These input signals are given to the inverting terminal of the operational amplifier using input resistors like Ra, Rb and Rc.

Here, Rf is feedback resistor and RL is the load resistor. Noninverting terminal of the operational amplifier is given to the ground terminal using Rm resistor.

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By applying KCL at node V2 we can get the following equation. The input resistance of an ideal operational amplifier is near to infinity, so we can neglect V2 and Ib.

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If the values of resistors Ra, Rb and Rc are same then the above equation can be written as. Summing amplifier is a versatile device, used to combine the signals. These amplifiers add the signals directly or scale them to fit some prearranged combination rule. A summing amplifier is a one kind of circuit which is used to add when the two or more signals need to be combined like in audio mixing applications. These different signal sources will be added together by this amplifier, and the added signal is directed to an audio amplifier.

The circuit diagram of audio mixer using a summing amplifier is shown below. The working principle of the summing amplifier is like a multi-channel audio mixer for several audio channels. No interference will happen because each signal is given through a resistor, with its other end connected to GND terminal. A DAC converts the binary data which is applied to its input into an analogue voltage value.

Digital to analog conversion is mainly used in Real-time industrial control applications like microcomputers. The circuit diagram of the 4-bit digital to analog circuit using a summing amplifier is shown below.

These inputs represents 5V to logic 1 and Ov to logic 0. The exactness of such a DA digital to analogue converter circuit is imperfect by the accuracy of the values of the resistor employed and the differences in denoting the logic levels. Thus, this is all about summing amplifier, summing amplifier circuit and its applications of op amp.Editor's note: InPart 1 of this series, the basic structural elements and grammar of ablock diagram methodology was described.

In this part, methods formanipulating block diagrams as an aid to analyzing system behavior areoutlined. Manipulating block diagrams Initially, one usually draws a structural block diagram. This is adiagram that shows how a system is put together. At some point, onewill wish to reduce this structural block diagram into a behavioraldiagram.

While this can be done by the techniques shown in Part1such techniques immediately sever the connection betweenthe block diagram and the behavioral model, and can be verycounter-intuitive to use. It is often better to reduce a block diagram using themanipulation rules presented here. There are four tools that you have on hand to manipulate blockdiagrams.

Given a block diagram that is described fully in the z domain or theLaplace domainthese tools will allow you to fully analyzethe block diagram to extract the overall system behavior.

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If you observe their limitations, you can also use these tools on avariety of other block diagrams. The four tools that you have are: cascading gainblocks, moving summing junctions, combining summingjunctionsand reducing loops. The block diagram manipulations shown here will always work if theblocks in question contain pure transfer functions.

Derive Transfer Function from Block Diagrams 2-FE/EIT Exam

All of the examplesbelow show block manipulations on blocks containing transfer functionsin the z domain ;however,these manipulations can be carried out onblocks in the Laplace domain as well. Stating when a block operation cannot be carried out is moredifficult. In general, these operations depend on superposition andcannot be performed when the blocks contain nonlinear operation. In addition, time varying operations like sampling and zero-orderholds can sometimes be moved around and sometimes cannot—generallyifyou can review this section and make the mathematical equations fit,then you can perform the operation with a block diagram.

Loop Reduction When a block diagram indicates a feedback loop ,you can reduce the loopto a single transfer function block as shown in Figure 4. If you look atthe equations that govern the behavior of this block diagram, you cansee that the output signal is a function of the forward gain G and the errorsignal e:. Using Loop Reduction A feedback control system has a forward gain.

Draw its block diagram, and find the overall transfer function forthe system. The block diagram is a simple feedback loop with thespecified gains:. Cascading Gains When two blocks are cascaded directly, the transfer function of thecombination is the product of the two transfer functions, as in Figure 4. Looking at theequations that govern the behavior of the block diagram you can seethat.

A feedback controlsystem has a plant with a gain of. Draw its block diagram, and find the overalltransfer function for the system. Summing Junctions If a loop contains more than one summing junction, it cannot be reducedby simple loop reduction, and cascading gains will not eliminate theextra junction.

In order to reduce such a loop, the summing junctions must be movedaround until there is a loop with just one summing junction.

This isdone by propagating a transfer function backward through the junction,or its inverse forward through the junction, as shown in Figure 4. Any manipulations you do here are just for the purposes of makingthe math easy, and if the system starts as a physically realizable onethen any contradictions will disappear by the time you get yoursolution.

In the top case of Figure When designing or analyzing a system, often it is useful to model the system graphically. Block Diagrams are a useful and simple method for analyzing a system graphically. A "block" looks on paper exactly what it means:. When two or more systems are in series, they can be combined into a single representative system, with a transfer function that is the product of the individual systems.

If we have two systems, f t and g twe can put them in series with one another so that the output of system f t is the input to system g t. Now, we can analyze them depending on whether we are using our classical or modern methods. If two or more systems are in series with one another, the total transfer function of the series is the product of all the individual system transfer functions. But, in the frequency domain we know that convolution becomes multiplication, so we can re-write this as:.

If we have two systems in series say system F and system Gwhere the output of F is the input to system G, we can write out the state-space equations for each individual system. And we can write substitute these equations together form the complete response of system H, that has input u, and output y G :.

Blocks may not be placed in parallel without the use of an adder. Blocks connected by an adder as shown above have a total transfer function of:. Since the Laplace transform is linear, we can easily transfer this to the time domain by converting the multiplication to convolution:. The state-space equations, with non-zero A, B, C, and D matrices conceptually model the following system:. In this image, the strange-looking block in the center is either an integrator or an ideal delay, and can be represented in the transfer domain as:.

Depending on the time characteristics of the system. If we only consider continuous-time systems, we can replace the funny block in the center with an integrator:. The state space model of the above system, if ABCand D are transfer functions A sB sC s and D s of the individual subsystems, and if U s and Y s represent a single input and output, can be written as follows:. We will explain how we got this result, and how we deal with feedforward and feedback loop structures in the next chapter.

Some systems may have dedicated summation or multiplication devices, that automatically add or multiply the transfer functions of multiple systems together. Block diagrams can be systematically simplified. Control Systems.

From Wikibooks, open books for an open world. The Wikibook of: Control Systems. Category : Book:Control Systems. Namespaces Book Discussion.Why do we use block diagrams in control systems? Standard representation of blocks 3. Simplification or reduction of block diagrams 1. Block diagrams have become more popular in linear control systems because of its simplicity and easy to manipulate. Not only in control systems, block diagram representation is deployed in other areas like software engineering, process engineering, economics etc. It is particularly important when we wanted to discuss the output or behaviour of a complete system as one unit while keeping the inside electronic undisclosed or insignificant. No matter how complicated is the circuit diagram we are now dealing with a simple block diagram with a mathematical representation in s-domain. Similarly we can use many blocks to represent various circuit elements that we find in circuit diagrams. F, G s Since we defined that the T. G 3 s X s Y s When plants are cascaded we can get the products of functions to find the output. Simplify the blocks to get an OLTF. When we manually simplify the numerator and denominator s on numerator and s in the denominator cancel off. But program doesnt know how to do it it is not programmed to handle that situation Hence we have to write a different programme.