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If we have a resistor of 10k and another resistor of 10k forming a voltage divider and powered with a steady DC voltage source, and a capacitor across the lower resistor, the system reaches a stead capacitor voltage of 1/2 the source voltage. So with a 10v source, we get a 5v output across the cap after a long time.
Now say we take another source like a 9v battery and small value resistor like 1k and place it across the cap so it charges the cap up to a higher voltage, and lets say that i charges up to 6v and then we remove the 9v battery and 1k resistor. So now we have the original circuit but the cap is charged to 6v now. So after a time period has passed, the cap will discharge back to 5v again. So with a 6v initial condition for the cap the output again reached equilibrium after some time, so it is stable.
I am getting old - I do not understand the above example.
(The lower resistor is reduced from 10k to 1k and at the same time the voltage is 9V instead of 10V - but the cap is charged "up to a higher voltage" of 6V?)
Therefore, I try another answer:
Initial conditions in a control loop are - for example - settings of bias points (operating points around which a signal can change) or some internal (or externally supplied) reference values.
Think of a simple linear voltage regulator. It contains an internal reference voltage. If this is altered you change initial conditions. OK?
I am getting old - I do not understand the above example.
(The lower resistor is reduced from 10k to 1k and at the same time the voltage is 9V instead of 10V - but the cap is charged "up to a higher voltage" of 6V?)
Therefore, I try another answer:
Initial conditions in a control loop are - for example - settings of bias points (operating points around which a signal can change) or some internal (or externally supplied) reference values.
Think of a simple linear voltage regulator. It contains an internal reference voltage. If this is altered you change initial conditions. OK?
Figure out how to connect a 9v battery and 1k resistor up to the original circuit such that the voltage across the cap rises to at least 6v as stated.
I never stated that the lower resistor was reduced from 10k to 1k.
Figure out how to connect a 9v battery and 1k resistor up to the original circuit such that the voltage across the cap rises to at least 6v as stated.
I never stated that the lower resistor was reduced from 10k to 1k.
As said - I am getting old. Surely, you will be right, but I can`t figure it out.
Is it a puzzle?
You did start with a voltage divider - and how does the second circuit looks like? Is it just R||C driven by 9 V (according to your verbal description)
As said - I can`t figure it out.
Perhaps PG1995 can?
Am I allowed to quote your motto (written on each of your replies)?
"one expert specification is worth a thousand tests."
Shouldn`t a specification be as clear as possible without the necessity to "figure something out"?
Q1: The curves are just predefined functions. People sometimes call functions, curves. For example, the term "curve-fitting" is fitting a functional form to a curve formed by the plotting of data.
Q2 and Q3: As far as initial values, in a more abstract form, think of your state space equations. The initial value refers to the starting value of a state variable at time=0. Hence, if x(t) is a state variable, then x(t=0+)=x(0) is the initial value.
Examples of initial values in electrical circuits are (1) capacitor voltages, as in MrAls example, and (2) coil currents. The interesting thing about nonzero initial values is that they indicate initial energy stored in the system. Hence, even with no input signals, one can look at the free response of a system when it is started with some energy. Instability would then be a system that gains more and more energy, even with no inputs, while a stable system would dissipate energy and find it's way back to an equilibrium state.
Q1: The curves are just predefined functions. People sometimes call functions, curves. For example, the term "curve-fitting" is fitting a functional form to a curve formed by the plotting of data.
Q2 and Q3: As far as initial values, in a more abstract form, think of your state space equations. The initial value refers to the starting value of a state variable at time=0. Hence, if x(t) is a state variable, then x(t=0+)=x(0) is the initial value.
Examples of initial values in electrical circuits are (1) capacitor voltages, as in MrAls example, and (2) coil currents. The interesting thing about nonzero initial values is that they indicate initial energy stored in the system. Hence, even with no input signals, one can look at the free response of a system when it is started with some energy.
Yes - everything agreed 100%.
However, the question of PG1995 was related to a CHANGE of initial conditions and the corresponding system response.
Therefore, my example with a control loop containing a reference value that can change during operation. This would be a typical example for a control loop that follows a guidance value.
W.
Yes - everything agreed 100%.
However, the question of PG1995 was related to a CHANGE of initial conditions and the corresponding system response.
Therefore, my example with a control loop containing a reference value that can change during operation. This would be a typical example for a control loop that follows a guidance value.
W.
Personally, I would characterize a reference value that changes during operation as an input signal, rather than an initial condition. I interpreted the "change in initial conditions" as a change in the state variables in the system away from an equilibrium value.
But, as usual with PG's text book, the wording is vague. Hence, PG's question is understandable.
PG will have to decide which interpretation is more consistent with the terminology and explanations that exist in other parts of the book. We, don't have access to that to make a proper judgement.
The theory states that there should be a return to equilibrium even if the initial conditions are changed. That's like saying that the final state of the system should not depend on the initial conditions. If this is not met, then it implies that the system can not reach certain states due to less than optimal initial conditions, and we dont want that because we dont want to have to supply optimal initial conditions.
As far as the secondary excitation circuit i talked about, it's a simple 1k resistor in series with a 9v battery
The initial circuit has just two 10k resistors as voltage divider with cap across lower resistor, and the final voltage is 5v of course because the supply voltage is 10v. But after the 1k resistor and 9v battery is connected to the cap, the cap charges up to a higher voltage like 6v. That's because the 9v battery supplies more current through the 1k resistor and then to the cap.
So the 1k is in series with the 9v battery, the 9v battery negative terminal is connected to ground, and the open end of the 1k resistor is connected to the cap at the junction of the two 10k resistors, and so the cap charges up more. When the voltage reaches 6v we disconnect the cap.
If you still cant visualize this, then forget the 1k resistor and 9v battery and instead simply connect a current source in parallel to the capacitor. Let it stay there until the cap reaches to 6v, then remove it. The cap voltage then after a time returns to 5v.
It's an overly simplified example i know so if either of you would like to provide another circuit feel free to do so.
The main point is that when we force a change in the initial conditions, the system possess the innate ability to return back to the equilibrium state. This is a little different than the change of the input signal(s).
MrAl,
thank you for additional explanation.
It was really not easy to visualize the example circuit you have described with words.
Perhaps you can understand my problems if you compare the two following phrases:
*post#2: small value resistor like 1k and place it across the cap
*post#9: it's a simple 1k resistor in series with a 9v battery .
But, no problem. Such things happen from time to time - we see that a drawing has some advantages.
W.
Ok it is a little understandable that you may not have been able to visualize the circuit. But what you show there is only PART of the complete sentence from post 2. If you cut up the sentence you loose information. From your post i can see that maybe you are reading the sentence a little at a time to translate it. When you translate from one language to another you have to first do a literal translation and then take a step back and render what you've found into the new language. It's not a word for word process.
I see this happen in other places too on the web. The way around it is to read the entire sentence and even entire paragraph and then try to imagine what is happening. So see you read:
"small value resistor like 1k across the cap"
and of course there can only be one meaning, that the resistor is in parallel. But look at the whole sentence:
"Now say we take another source like a 9v battery and small value resistor like 1k and place it across the cap so it charges the cap up to a higher voltage, and lets say that i charges up to 6v and then we remove the 9v battery and 1k resistor."
First we have:
"Now say we take another source like a 9v battery and small value resistor like 1k and place it across the cap..."
So see we dont just have a resistor, we have a 9v battery too. So we are starting with two things, not one. And then we have more of the sentence:
"...so it charges the cap up to a higher voltage..."
and that tells us that the 9v battery and 1k resistor are SOME HOW charging up the cap to a higher voltage, and as you know the initial condition of the cap could be the initial voltage.
Now more of the sentence:
"...and lets say that it charges up to 6v and then we remove the 9v battery and 1k resistor."
So here we have more information, that it gets up to 6v and then we remove BOTH the 9v and resistor.
What this would accomplish is a perturbation of the initial condition of the cap, the voltage, and that was the main question.
I reply like this so as to hopefully help you with your translations. I have talked to many people of different languages in their language and mine and always see translation problems both ways. The original post i gave was a little more obscure than usual so you had a harder time translating it. But when you see a question come up like this you can just remember to take a step back and try to figure out what the author meant rather than just throw questions at it. In this case the author was available for immediate questioning, but in many cases they are not anywhere to be found
But anyway, i hope you understand now that the main goal was to perturb the initial condition of the cap.
I like to supply drawings most of the time too, although this time i did not want to take the time.
wow - such a long reply just to justify a somewhat misleading description? Perhaps it was my fault - however, you can be sure that I not intentionally had problems to visualize the circuit.
It is a pity that PG1995 did not reply. I wonder if he understood from the beginning.
But - independent on this kind of misunderstanding between us (the first one?):
I am a bit surprised that the questioner (PG1995) does not respond at all.
Two days ago, he opens a thread with a question - and that`s it.
We try to give him a suitable answer, but he never tells us if he is satisfied with the answer(s) or not.
Well i have helped people with language in the past too so i like to add a few comments along those lines too sometimes. There are many differences that are not known at first, then later we find them out. I am still finding out differences i didnt know about other languages that could lead to a pretty big misunderstanding if i didnt know it. Some actually would lead to a HUGE misunderstanding.
But yes i agree, PG often asks a number of questions and then never bothers to reply as to what good they did. It's almost like he asks questions, then goes on vacation So i guess he takes a lot of vacations <chuckle>.
You are 100 percent right in that we need that feedback to know if he benefited or even understands why we are talking about a given topic. Does he even know why we talked about the extra resistor and capacitor? When i ask him about this, he tells me that he has something else he is doing like an exam or something else. So why bother asking the question then if not to stick around to learn from the answer right? So i agree with you totally here.
Maybe it would be wise to give shorter, less detailed replies so that way if he wants to know more he will have to come back and ask more.
PG if you ever get around to reading this, please reply to your questions so that we know what you need.
I have tried to clarify some of the points here which were raised above about my not responding to the replies. For my follow-on queries where most of them are just rephrased version of older ones, I will use Steve's post and both Winterstone and MrAl were also in agreement with its content. Thanks.
Q1: The curves are just predefined functions. People sometimes call functions, curves. For example, the term "curve-fitting" is fitting a functional form to a curve formed by the plotting of data.
Q2 and Q3: As far as initial values, in a more abstract form, think of your state space equations. The initial value refers to the starting value of a state variable at time=0. Hence, if x(t) is a state variable, then x(t=0+)=x(0) is the initial value.
Examples of initial values in electrical circuits are (1) capacitor voltages, as in MrAls example, and (2) coil currents. The interesting thing about nonzero initial values is that they indicate initial energy stored in the system. Hence, even with no input signals, one can look at the free response of a system when it is started with some energy. Instability would then be a system that gains more and more energy, even with no inputs, while a stable system would dissipate energy and find it's way back to an equilibrium state.
Q1: I think you have it correct. I also think cutting tool implies some type of automated factory (or machine shop) system designed to cut multiple versions of a product or part.
Q2: Design criteria do not relate to component values. Rather, the design itself relates to component values. Design criteria is another word for design specifications. Things like response time, control accuracy, steady state error, stability margins, disturbance rejection etc. all relate to the design criteria.
Q3: I don't follow you on this question, but I can make a couple of general comments related to this. Adding switches often creates confusion in our thinking. Switches tend to change the system structure in the sense that the state space equations that describe the system might be different in the different switch positions (although this is not always the case). When this does happen, analysis is complicated by the fact that you need to analyze the transitions from one system model to the other and initial conditions for each model become relevant at the transition. This is a more advanced type of analysis and I recommend that you not worry about this yet. Consider only simple system models without switches and use input signals to control inputs. Then, initial values of the state variables will be needed in the model.
Q4: Again, I'm not sure I understand the question, but I'll make a comment. You talked about stable and unstable equilibrium. The simplest case that describes these two situations is a ball sitting in a valley and a ball sitting on top of a hill. In both cases we have equilibrium in that the system will stay in that state for all time (theoretically). Practically, a ball in a valley can be disturbed and the ball will come back to the bottom of the valley, which implies stability. However, if you disturb a ball that is balanced perfectly on top of a hill, it will roll down the hill. Hence, this case is marginally stable, which practically means it is unstable in actual usage since there are always disturbances to any real system.
Q5: I think you are correct here. You are correct that the wording of the book is not always good and causes confusion, and I believe you are correct on your interpretation of what they said because I interpret the text the same way you said here.
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