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How many of you know Laplace transforms?

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PNachtwey

PNachtwey

Electrical
Oct 9, 2004
772
Why do I ask?
I was on a Chinese hydraulic servo forum. There is an on going dispute about different kinds of servo control. The problem I have is that no one understands Laplace transforms.
I can show the relative strengths of PID, PD, PI and P only control using Laplace transforms but no one seems to understand Laplace transforms, transfer functions, time constants and bandwidth. A common problem we have in China, and even the EU, is that people not aware of even the basics of how to control a hydraulic servo system or to select cylinder diameter and valve size.

A second question.
Many of you know that I write magazine articles related to hydraulic servo control. Are there any topics you would like me to cover?


Peter Nachtwey
Delta Computer Systems
 
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Had one specific math class covering LaPlace and transfer functions.
After that they appeared again in the Automatic control theory class.
Also Bode diagrams, Nyqvist diagrams.
 
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Don't really use them in my current role but used to be fairly conversant with them in my twenties and early thirties. I could probably pick it up again given a few hours with a decent text and some examples to work through.
 
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Mathematicians understand Laplace Transforms, and the EEs who apparently had them in several classes. At least in my controls class there were a majority of C's and one A. The A went to a EE who had nearly the identical course under a different name.

For me, I'd say that a basic understanding of back pressure in hydraulic lines would have resolved the most costly problems.

What percentage of hydraulic systems don't have a human operator closing the position and velocity loops?
 
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The reason I ask is because I am trying to explain the difference in response when a P only, PI, PD, PID or PID2 is used to control a hydraulic actuator. The problem is that no one seems to understands my examples or they doubt them.
What I want to know is that if anybody could ask intelligent questions about this simple example using a P only control for a hydraulic actuator.
On the first page I show how to generate the closed loop transfer function for a hydraulic actuator using P only control. Then I find the actual and desired characteristic equation . Does anybody follow this?

Should I do this here on this forum or on my own?

What percentage of hydraulic systems don't have a human operator closing the position and velocity loops?
Click to expand...
It depends. Mobile equipment still is largely manual control. Industrial equipment is very sophisticated now and mostly computer controlled. If the industrial equipment isn't computer controlled it soon will be.






Peter Nachtwey
Delta Computer Systems
 
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It certainly isn't completely alien to me, but I would need time to get back up to speed with Laplace: it's been quite a few years since I used it properly, and right now I'd say that I'm aware of Laplace rather than fluent. It's set out in a format which is fairly straightforward to follow for anyone who's seen it before.

I think the difficulty many people will have is that they'll study Laplace in university, but if they don't have cause to use it during their work then over time it will fade into unfamiliarity. I imagine that calculus suffers the same fate for many practicing engineers.
 
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OK, I have queried on a couple different forums. No one really knows Laplace transforms.

I am a moderator on a Chinese hydraulic website. What I can say is that in China they have far more hydraulic schools that in the US. They teach hydraulic in the universities. I know. I have been there and have given presentations. However I don't think the universities there are any better than the universities here or even as good. It doesn't seem to make a difference where we go, US, CN, or EU the engineers learn Laplace transforms if they math students or EE students. This was mentioned above. The sad thing is they the students instantly forget what they have learned. This seems to be universal.
No I can't say universal, just global.

I am stuck. I can't make a point. I was hoping to find 1 person that really knows Laplace transforms.



Peter Nachtwey
Delta Computer Systems
 
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I know that all mechanical and aerospace engineers who have studied to bachelors level in the UK in the last 10 years have had to be able to solve laplace transforms to pass their degree. The unfortunate thing about laplace transforms is I feel that it is something you can learn to solve by "rote" without actually understanding what you are doing, so how many graduates actually understand Laplace transforms I can't say, but they should at least be familiar with the concept. Although as others have said I don't doubt that it is a skill that falls in to disuse for the vast majority of mechanical and aerospace engineers, and I suspect most have little interest in keeping their skills in the area sharp.

GSTP

Graduate Mechanical Design Engineer
UK
 
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So, sure, I had a class specifically for Laplace transforms, and a couple of classes where we used them, but I've not touched them except in a very peripheral way in the last 40 yrs. Unless you're actually teaching classes or doing modeling that specifically requires them, I doubt very much you'd remember enough. Although, if you've learned them, you should at least remember how they're supposed to be used.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! faq731-376 forum1529 Entire Forum list
 
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@IRstuff, I know you have Mathcad and sometime post in the control theory group. Do you understand the first page of my pdf?

@Everyone, if you want to see Laplace transforms used for control theory then visit my Peter Ponders PID YouTube channel. Warning, most people stop watching after 3 minutes because they don't understand Laplace transforms and control theory at that level.


Peter Nachtwey
Delta Computer Systems
 
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Hi Peter,

I don't think we instantly forget, but it's inevitable that it fades over time through disuse. I understand enough of it to be able to pick it up faster than someone who has never seen it before, but in the last 25 years I've had no practical use for it either.

I imagine some of the engineers such as yourself who actually design turbine governor servo controllers know Laplace inside out. I have to operate and maintain what guys like you have designed alongside the myriad other powerplant systems I have to operate and maintain. I'm unlikely to ever be an expert in any of them, but I have to know a reasonable amount about almost all of them. You're at the other end of the spectrum in a role where you can specialise in one field and truly master it.
 
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The 1st page looks pretty straightforward. A standard closed loop transfer function; don't really need LTs to understand that, other than to know it's essentially in frequency space. The second half (Polish airline passing over the Statue of Liberty on starboard side; Poles on the right hand side of plane = bad) places 3 stable poles to presumably solve for the 2 unknowns with the values in the characteristic equation. We did pieces of this in high school and freshman electronics.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! faq731-376 forum1529 Entire Forum list
 
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What about page 2 where 3 equations are used to solve for 3 unknowns, Kp, alpha and beta?
There optimal proportional gain, Kp, is calculated symbolically. The optimal value for Kp is a function of the open loop gain, natural frequency and damping factor. This really shows that the performance of a servo hydraulic system using proportional only control is all up to the hydraulic and mechanical designers, not the person adjusting the proportional control.

Peter Nachtwey
Delta Computer Systems
 
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Looks likewise straightforward until middle of page 3 where the inverse Laplace transform is invoked.
3rd from last equation appears to be truncated.
simplification for position equation
derivative of position to get velocity, presumably.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! faq731-376 forum1529 Entire Forum list
 
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@IRStuff, you are correct. The inverse Laplace transform extends pages to the right. I had to simplify manually. This is one of by pet peeves with Mathcad. It doesn't simplify recursively.
Notice that that pos(t) is making a step change in position r. This can be any distance that doesn't saturate the control output. Notice that the error decays as a function of ⍺. r can be 1mm or 10mm it will still take 5 time constants to move within the set point r. The time constant is the inverse of ⍺. ⍺=2*ζ*⍵/3 so 5 time constants will take 7.5/(ζ*⍵).

The point here is that the shortest time constant is determined by the damping factor and natural frequency and these are determined by the hydraulic and mechanical designer. There is NOTHING the control person can do to optimize the proportional gain, Kp beyond the formula.

I just want to cover proportional gain only control but one should ask if the optimal time constants are determined by the natural frequency and damping factor for PI, PD or PID control? The answer is yes. Are there control algorithms that get around the natural frequency and damping factor limitation? The answer is yes. More on this at another time.

So good so far. Now on to page 4.
Do you agree with the calculation for the time constant?
You can see the step response reaches within 1% of the set point in the predicted amount of time.


Peter Nachtwey
Delta Computer Systems
 
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My controls theory is pretty hazy, at best, but what you have looks mathematically correct. I would caveat your 1st paragraph with the admonition that underdamping to crank the effective time constant down is not a winner, since that leads to ringing. Which suggests that you need to include the calculation for critical damping factor that minimizes settling time.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! faq731-376 forum1529 Entire Forum list
 
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I would caveat your 1st paragraph with the admonition that underdamping to crank the effective time constant down is not a winner, since that leads to ringing.
Click to expand...
You are correct. In the pdf the distance to move to changes instantly so oscillations are introduced. The frequency of acceleration and deceleration needs to be many times lower than the natural frequency but that hurts production. What is necessary is a control algorithm that places the closed loop poles on or near the negative real axis. In other word, minimize β.

Which suggests that you need to include the calculation for critical damping factor that minimizes settling time.
Click to expand...
The damping factor is determined by the hydraulic and mechanical designers. The control guy can't do much with proportional only control. The question that can be asked is "does adding a derivative gain help". What about a PID? I have done the same calculations with a PID too. The point is the damping factor and natural frequency determine how errors will decay. The hydraulic and mechanical designers really determine limit of how fast the errors will decay.

Is there a solution? Yes, but not with a P, PI, PD or PID controller.


Peter Nachtwey
Delta Computer Systems
 
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"but not with a P, PI, PD or PID controller"

Agree, there are supposed to be solutions using brute force approaches.
Click to expand...
There are solutions but they are not brute force.
I can't say more because it would be considered advertising but look for recent articles on the magazines.
You can also e-mail me. My e-mail address is not hard to find.
On top of that you can alway watch my "Peter Ponders PID" videos. The videos are for the advanced users.
Most people give up after watch about 3 minutes because they don't understand the basics.


Peter Nachtwey
Delta Computer Systems
 
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