Here's a study aid that I had created a while ago. It tries to pictorially summarize stability analysis using the Routh Hurwitz criterion in Control Theory.
https://preview.redd.it/icty5rphnxk51.png?width=1131&format=png&auto=webp&s=8fbe8f7ab2a69d2711fec28d3e3895d874084c1c
In my controls class, we learned the RH criterion by setting up a table to see if there are sign changes. If there are, then the system has positive real roots. However, I want to spend time understanding the proof.
What are some preliminaries necessary to understand the proof?
I took a control theory class last semester, and although I understand how control theory can be implemented using analog circuits, I'm having trouble understanding how this theory relates to modern microcontrollers and digital embedded systems. Like, do I have to consider factors like overshoot, poles on the RHS of the real-imaginary plane, etc when working with a Raspberry Pi or Arduino?
I am mainly asking about 1a)
I have been taught how to find the range of K using the Routh-Hurwitz method, but when i try to solve for this problem, i end up with an inequality with 2 variables, any advice on how to solve the problem?
https://preview.redd.it/1pror5z7cw351.png?width=888&format=png&auto=webp&s=1ffe40bf772ab51633b6d8de14d28fbf80ccbc3b
For a polynomial system equation. S^3 +3s^2 + s-2 + K(s+1). Would the Routh table column be 2 or 3? I not quit sure which is correct.
As the title states, I am searching for an easy way to explain why to define an auxiliary polynomial and to continue the Routh-Hurwitz table with the derivative of this polynomial.
I built this after one of my projects. I was surprised I couldn't find a tool online where you fed it your coefficients and it automatically did the Routh-Hurwitz criterion calculations to help determined the stability of a LTI control system.
I got pretty bored of doing them by hand over and over again, so I built this. A bit of a shameless plug here, but hopefully it's useful to you.
http://crclayton.com/projects/routhhurwitz/index.html
Link: https://www.sciencedirect.com/science/article/pii/B9781785482861500024
DOI: 10.1016/B978-1-78548-286-1.50002-4
Hope someone can help :)
Which stability paradigm in classical control can help me generalize Barkhausen's criterion and how exactly do I have a sufficient(not just necessary) condition for stable, unity-amplified oscillations? This just looks like another way of saying having a pole at origin brings an oscillator to the verge of stability.
The problem that's stumping me is from Needham's Visual Complex Analysis; this is how it's stated in the text.
If Γ denotes the contour the hint describes moving with positive (anticlockwise, by the convention in the book) sense and the semi-circular section in the left-half plane, then I can see that if all n roots of F(s) lie in the left-half plane then Γ would enclose them all as R → ∞.
The argument principle then gives me that the winding number about the origin of the image of Γ under F would be n: v[F(Γ),0] = n.
Translating this observation into F(s) rotating through nπ as s moves from -i∞ to +i∞ is giving me some trouble, though. I tried plotting out F(Γ) in numpy for a few Hurwitz (and non-Hurwitz) polynomials to try and get a feel for what rotation happened along the straight-line segment, but it didn't seem to help: either my understanding of the problem or the script itself was flawed, since the segment seemed to map to a straight line (which would correspond to a net rotation of 0 or π/2 depending on whether it lay along the real or imaginary axis?).
I'm having trouble understanding where the polynomial used in the routh array comes from. Is the routh array based on the characteristic equation (like 1 + GcGpGvGm for example) or is it the simplified combination of the numerator and the denominator? I know what to do with the polynomial after that.
It is a simple feedback with a disturbance if that helps.
Thanks in advance...
Could anyone help to derive the following expression (4.23) which is the stability criterion for type 3 digital PLL ?
"Forward Euler has a stability criterion in the form a time-step restriction ∆t < s, where s is a real number."
I need to find s, given a matrix (four of them actually) and the knowledge that for a linear ODE dy/dt=Ay and y=ynought.
"Consider the linear ODEs with A equal to each of the matrices you loaded. Find s for each matrix."
I do not have any code yet and am really unsure how to begin, its possible that I missed class. Any links to helpful places or hints would be excellent. I've been searching the web but haven't found much on this particular thing.
Thank you!
Hello community!
I’m an avid Informatics student and I’ve received a task of programming a project in any language of choice and I’ve chosen python because I wanted to learn more about it. I’m already very familiar with OOP, SOAP & REST APIs which I had written quite a bit in C#. However, my project will consist of reading the CSV files and implementing few algorithms, along with
Routh–Hurwitz stability criterion and a few graphs.
Since I’m unfamiliar with python I’d like you guys to point me in the right direction. Where exactly should I start? Is reading the documentation alone okay or should i stick to some youtube tutorials and stack overflow? I’ve noticed that Visual Studio supports python but I heard that PyCharm is a lot better, so should i stick to the latter? If you have any advice to support a beginner in a right path I will be so thankful.
Greetings everyone,
With this quarantine, and exams coming in June (Europe) i have been lagging behind on study's on the classes mentioned in the title.
I want to begin studying those, but the teacher's material is lackluster, although they have lot's of exercises but no explanations and i find them difficult.
Is there any recommended books, or online resources that you can help tackle these?
Bellow i will transcript a summary of what they teach in this classes.
Telec:
- The Communication Process
- Introduction.Signals and Systems
- Continuous-wave modulations
- Noise
- PCM
- Baseband pulse transmission
- Digital passband transmission; PSK, FSK, QPSK, QAM.
Systems Theory:
- Review of basic mathematical concepts:- Laplace transform;- Transfer function.
- Construction and manipulation of block diagrams
- Modeling of dynamical systems:- Electric, electronic, mechanical, hydraulic, thermal.
- Systems analysis in the time domain
- Stability Criterion Routh-Hurwitz.
- Analysis of feedback systems in the time domain
- Systems analysis in the frequency domain
- PID Controllers
Thanks!
I have written up my question clearly below:
https://i.imgur.com/zchVRxb.png
The stator dynamics have 2 states and has 2 eigenvalues; the rotor dynamics have 2 states and has 2 eigenvalues, yielding a total of 4 eigenvalues for the 4 state induction machine.
Would I get the same eignevalues if i combined the rotor and stator states together and calculate the eigenvalues of the resulting 4x4 "A" matrix?
I feel I should be able to do this. I just wanted to double check with someone here.
Hello r/ControlTheory,
I had an argument with my professor about finding the steady state error of an unstable system. You see we had this question in the exam where we were asked to find the steady state error of an unstable system.
Apparently the answer is 'Not applicable', however I ended finding the steady state error anyway without stating that the system's unstable. And just like that I received zero points for the question.
I know that finding the steady state error for unstable systems is meaningless, but on the other hand I don't see why it's unjustifiable to solve for it. Especially when useless methods such as the Routh–Hurwitz stability criterion are used to check the stability of clearly unstable systems (can be done numerically).
The professor promised me a full mark on my test if I justified to her finding the steady state error of an unstable system. My GPA's in jeopardy, help is appreciated!
Also it would be great if you have references to support my claim. Many thanks.
TL;DR
My professor will give me a full score if I justified finding the steady state error of an unstable system, will you help me?
I have a system with g(s) = 1/(s^3+2s^2-s+6). g(s) is unstable with two roots in the RHP. I need to add element K somewhere in the system to make it stable. What do i make K and where do i add it?
https://preview.redd.it/js24kqtik0z71.png?width=1138&format=png&auto=webp&s=04d1345a3296475210d082db6bf78b35a51c4ada
There is investing and there is trading. The difference between “investors” and “traders” is subtle, but there is a difference. It’s hard to get a straight answer from experts on exactly what the difference is. There is, after all, nothing fundamentally different about investing and trading: they are both buying and selling securities. And yet there is a real difference between an investor and a trader.
I didn’t used to know the term “trader” as it pertains to financial markets until recently. I had no concept of a “trader.” My understanding of finance began in my teenage years, when I read my parent’s copy of Rick Edelman’s The Truth About Money. I learned in that book that one should not buy and sell securities on a short term basis because it was a money loser - a game that only Wall Street professionals can play profitably. It never occurred to inquire further about these Wall Street professionals and how they were making money.
What I had learned in Edelman’s book was that over any 20 year time span throughout history, a diversified stock market portfolio would have earned a very good annual return. I believe the book stated 8% annually. And it was an absurdly old trend too - going back to something like the 1600s. One should save as much per month as they can as early as they can to take advantage of compounding returns.
Edelman cautioned against investing in one's own home. The reason was basically that one’s house is their home, not an investment. One’s home is not an investment property because you can’t liquidate it as soon as prices are high and the return is good because it’s your home - and you want to live there. Also, to take full advantage of a price cycle, you might get stuck in a house you don’t want to live in.
Edelman gave a warning about investing in real estate, saying that real estate is a business - not an investment. He said not to invest in property equity unless you want to make it your career. He distinguished between speculators and developers when it came to investing in property, and essentially said it was unwise to buy property as an investment if they did not intend to develop it - which is a job, not an investment. There was also the fact that the return on real estate is historically much lower than the stock market’s, (this book was a 1996 edition)
Edelman was very clear on one point in particular: an investor should not try to time the market. I remember this very distinctly from Edelman’s book because it
... keep reading on reddit ➡
Hello r/ElectricalEngineering,
I had an argument with my Control Theory professor about finding the steady state error of an unstable system. You see we had this question in the exam where we were asked to find the steady state error of an unstable system.
Apparently the answer is 'Not applicable', however I ended finding the steady state error anyway without stating that the system's unstable. And just like that I received zero points for the question.
I know that finding the steady state error for unstable systems is meaningless, but on the other hand I don't see why it's unjustifiable to solve for it. Especially when useless methods such as the Routh–Hurwitz stability criterion are used to check the stability of clearly unstable systems (can be done numerically).
The professor promised me a full mark on my test if I justified to her finding the steady state error of an unstable system. My GPA's in jeopardy, help is appreciated!
Also it would be great if you have references to support my claim. Many thanks.
TL;DR
My professor will give me a full score if I justified finding the steady state error of an unstable system, will you help me?
