How to Read Block Diagrams Control Systems
In the last tutorial, we learnt about transfer functions. In this tutorial nosotros shall learn near block diagrams in control systems. A block diagram is an intuitive way of representing a organisation. Information technology is a graphical representation that shows us how the systems are interconnected and how the indicate flows between them. In other words, block diagrams are mathematical drawings of the system. While a transfer function does not requite the internal details of the system, cake diagrams can be made to show the required internal details.
Let's at present get started with learning about block diagrams by understanding the bones terminologies involved.
ane) Blocks
A cake represents a organisation or a sub system. The block commonly has the transfer role of that detail organization of subsystem which information technology represents.
2) Arrows
Arrows represent the direction of the flow of signal or data. This will tell us how the individual systems/subsystems are connected.
3) Summing Point
The summing points add or subtract signals. Information technology is a small circle with a modest "+" or "-" near the entry of each betoken telling usa if the signals are existence added or subtracted.
We tin as well include a small X within the circle and write the "+-" signs inside. Information technology would look similar,
You can follow whichever representation you are comfortable with.
4) Take Off Point
When nosotros need to use the same signal to feed into multiple systems, we brand use of take off points.
With this, nosotros are all set to describe our first cake diagram.
Remember the example of a microwave cooking a potato from our first tutorial? Its block diagram would be:
This was quite simple and should assistance you get familiarized with the terminologies.
Now, allow's move on to something more circuitous. We shall now depict the block diagram of a series RLC excursion which has been our go-to example!
In general, drawing a cake diagram for a arrangement involves breaking down the equations and presenting it in the grade of blocks. While doing so, nosotros ever consider the input variable commencement and so we end with the output variable. This instance of a series RLC circuit volition make this articulate.
Applying Kirchhoff'due south voltage law to the loop shown above,
Laplace transformation of the in a higher place equations with initial weather condition causeless cypher will be:
Here Vi (due south) is the input variable, 5o (s) is the output variable and I(due south) is an intermediate variable. Ordinarily a system has more intermediate variables and block diagrams helps u.s. in visualizing these intermediate variables.
A general procedure that is followed is that we beginning with making use of the input variable and other required variables to class the intermediate variable(s) and use them to form the output.
In this case, we shall form I(southward) using Vi (due south) and 5o (s) and and then using this I(s), we shall form Fiveo (s) all in accordance with the arrangement equations which nosotros formed above.
At present,
First we shall employ a summing point.
The output of the summing point is passed through a block of transfer function:
Next, we shall utilize the other equation,
We combine the in a higher place two blocks and then with the assist of a take off point, we connect the output to the summing bespeak where we need the output variable as ane of the inputs.
The above is the block diagram representation of the serial RLC excursion.
Though block diagrams are unproblematic, it becomes actually confusing when a large number of blocks are present. This gives us a demand to reduce the block diagrams for our convenience. We shall now talk over a few rules that will help united states of america reduce complex block diagrams. In fact, using these rules, we tin can reduce whatever number of blocks into a single block which somewhen represents the transfer function of the entire system. These rules are often referred to as block diagram algebra and nosotros shall now look at them one by one.
one) Blocks in cascade.
When in that location are two or more blocks in a cascade (one side by side to the other), the resultant block would merely be the production of the transfer functions of individual blocks.
2) Blocks in parallel.
When there are two or more blocks in parallel, the resultant block would just exist the sum of the transfer functions of individual blocks.
3) Eliminating a feedback loop.
Consider a unproblematic feedback loop with a system block G(due south) and feedback block H(s).
If we simply look at the cake Yard(s) with E(southward) as input and C(s) as output,
Where E(s) is the difference or sum of the input and the feedback depending upon the type of feedback. For a feedback that is negative, E(s) is the departure of the input and the feedback and for a feedback that is positive, E(s) is the sum of the input and the feedback.
Now,
Hence, the above loop tin can be replaced by,
4) Moving a take off point to the left of the cake.
When we demand to motility a take off point to the left of a cake, we introduce a block with the aforementioned transfer role in that branch of a take off betoken. The diagram beneath will brand information technology clear.
5) Moving a have off point to the right of the block.
Similar to the previous ane, when we accept to movement a take off point to the right of a cake, we introduce a block with the reciprocal of the transfer function in that branch of the take off point.
6) Moving a summing point to the right of block.
When a summing point has to be moved to the right of the summing block, the post-obit modifications are to be made.
vii) Moving a summing point to the left of a block.
When a summing point has to be moved to the left of the summing block, the following modifications are to be made.
8) Interchanging summing points.
The summing points can be interchanged without any modifications.
9) Moving a take off point to the right of the summing point.
When we move the accept off point to the correct of the summing betoken, nosotros need to compensate for the arithmetics changes so the value of the branch of the take off bespeak as well equally the output doesn't change.
10) Moving a take off signal to the left of the summing signal.
Similar to the previous rule, when we move the take off point to the left of the summing point, we need to recoup for the arithmetic changes every bit shown.
Okay, at present nosotros are done! The thought behind these rules are just to continue the resulting values the aforementioned by slightly modifying the block diagram which shall compensate for the changes. Take your time and get through this once more.
It'south time for u.s. to try out these rules and reduce a slightly complicated block diagram into a single block.
As nosotros can see, blocks K iii and G iv are in cascade, and so nosotros tin combine them according to the starting time rule we learnt.
Now, the circled section forms a closed loop and we tin reduce it using the third rule that nosotros learnt.
Yous encounter that take off point there, nosotros can move that to the right of the block with the help of the fifth rule.
Next, we can meet that G 2 and the cake next to it are in cascade, and hence, they tin can be combined easily.
The circled portion is a closed loop which can exist reduced using the 3rd rule.
Again we can run across that G i and the block adjacent to information technology are in cascade and hence tin exist combined.
And again, this is a elementary closed loop which we can reduce using the 3rd rule having a petty patience while calculating.
And voila!! We have reduced that large block diagram into a single cake. It is to be noted that reducing a block diagram to a single block is not always required and nosotros reduce block diagrams every bit for our convenience of understanding.
To summarize, in this tutorial we learnt what block diagrams are, the basic terminologies involved. Then we learnt how to describe cake diagrams for a organisation followed by the rules for reducing circuitous block diagrams. In the next tutorial, we shall learn virtually bespeak catamenia graphs. Till then, endeavour reducing this block diagram into a unmarried block and verify it with the given answer.
Exercise
Answer:
Authored Past
Kushal Gowda
An Electrical and Electronics Engineer. Loves playing Table Tennis, Cricket and Badminton . Always ready to learn and teach. His fields of interest include power electronics, east-Drives, control theory and battery systems.
Source: https://www.circuitbread.com/tutorials/block-diagrams-1-4
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