# Signal Flow Graph Question

Discussion in 'Homework Help' started by sailmike, Dec 6, 2015.

1. ### sailmike Thread Starter Member

Nov 11, 2013
143
3
I need to answer a question on signal flow graphs. I've answered part A of the question and I hope I got it right. I don't have any idea how to solve parts B and C. My instructor never mentioned those two topics relating to signal flow graphs. I hope someone can check my answer to part A. I've attached the pdf file.

Thanks,
Mike

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2. ### MrAl Well-Known Member

Jun 17, 2014
2,438
492
Hi there,

I checked your part A and i am happy to report that you got the right result. I did it a different way (you must have used Mason's but i did not) and got the same result.

My question would be why would the instructor give you parts B and C without ever teaching you anything about that? Could you have missed a chapter in the book or something?
In other words what i am saying is that usually a teacher does not give a student a multiplication problem without ever first teaching them how to multiply, or at least giving them a hint as to what text to read in order to learn how to multiply.

Also, it is not entirely clear what they are asking in part B. Saturation occurs in a real system, where the signal levels reach a level too high for the components to withstand. That would indicate a redesign as noted in your text, but it's not entirely clear what they mean by "Z1, 10Z2", etc., unless they mean change the intermediate gains to those gains, and that would make the gains 1, 10, 4, and 1/2. If that is the case then that part should be easy.
What you could do to investigate this is to calculate the outputs for each and every node in the system and then examine them to see if any of them would reach a level that seems too high. If so, then try to create the same system but tailor the gains such that no single node reaches a high level but you get the same output response.

The last part usually requires that you use a certain procedure, and there are many. I would wonder what procedure the instructor wants you to use. The real parts of the denominator roots are most responsible for the fastness or slowness of a system, so you could investigate that to start with and see what you can figure out.
Since they are asking for a 100 fold increase in speed, that would indicate that the dominant exponential part exponents be increased by a factor of 100 so that the evolution of the system takes place 100 times faster.

Some of these questions have to be answered based on what you have done in the course already. If you have never seen this before that is very strange. Maybe you should ask the instructor more about this.
I see this from time to time, people asking questions that they are given and have no idea whatsoever how to approach the problem. I have to wonder what is going on in education these days or is it just that the student was absent one day and missed that part of the course work.

The attachment shows the original response (blue) with the system changed to have a much faster response (green). The old system is slow to settle but has less overshoot, while the new system is much faster to settle but has more overshoot. That's just one solution that comes from increasing ALL the exponential part exponents by the same amount (100 fold).

• ###### ResponseSpeedIncrease-1.gif
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Last edited: Dec 7, 2015
3. ### sailmike Thread Starter Member

Nov 11, 2013
143
3
I learned this stuff in a different class. One instructor taught signal flow graphs and another gave me this problem. Would you mind explaining parts B and C a little more?

Thanks,
Mike

4. ### MrAl Well-Known Member

Jun 17, 2014
2,438
492
Hello again,

Well, from what was found in that text it appears that they want you to change the intermediate gains but i cant be sure about this because that would be revealed in the course itself. They would have given you other problems like this one and that way you would know what they are looking for.

Also, this is not strictly a signal flow graph topic, it is a design topic using a signal flow graph. So learning about a signal flow graph alone does not necessarily mean you will know how to design or redesign something. You would have had a class that taught you to design something using a signal flow graph.

So for part B there is a question of what they really want you to do. That's why i suggested you look into this a bit more and ask the instructor what they are looking for here. It appears that some of the nodes may reach a value too high and others too low, but the gains may or may not result in a similar response unless perhaps they allow changing the feedback gains to also.

As for part C, one way of doing this means making the real part of the roots larger. Have you ever done anything like this before? I ask because there are various ways to handle this besides just making the real part of the roots larger, but that's really a design problem and i am not sure how simple or complex they want you to do it. I suppose we could start with the simplest way to do it, but then i have to wonder what kind of grade you would get if they really wanted you to do it a different way. Will you actually be graded on this?