Re: Completion of Controller Synhesis

JCH wrote:
<pnachtwey@xxxxxxxxx> schrieb im Newsbeitrag news:1183069737.711573.234920@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


Process input value v2 (e.g. 4...20mA)
Process output value v1 (e.g. 0...10meter)

This is where you are all screwed up. You don't understand the difference between a non-integrating process ( type 0 ) and an integrating process ( type 1 )






Time behavior measured for total system F1(s)=v1/v2!
See red box in Page 3.

One is for the
crane position as a function of the control output. The other is the
one you have always had which is the load position as a function of
the crane position. Combine the two and simulate. It will be
messy. I have it done the simulation both ways. The easiest is to
just control the crane motor and use the crane position for
feedback. The hardest way is using load position feedback. One must
calculate many dervatives ( 3 ) if the load is to be controlled. This
means one would need an accelerometer on the load as well as the
position feedback.



Evaluating a step process transfer function F1(s) and using sytem identification methods you get approximated T, e.g.

1
F1(s) = -------------------------
T^2*s^2 + 2*delta*T*s + 1

Time domain:

T^2*v1'' + 2*delta*T*v1' + v1 = K1*v2

Feedback via math model

v1 = load position
v1' = load speed
v1'' = load acceleration (no accelerometer necessary!)

So if v2 goes to 1 then v1 will approach at steady position at K1*1?
If the controller suddenly loses power and v2 go to 0 then v1 will go to 0 too?

Where is the crane or cart position then? What does it do?

The formulas you need are here:
v'=-a*v+G*a*u(t)
x'=v
theta'' = -2*zeta*omega*theta'-omega^2*sin(theta)+omega^2*x

Where:
v is the cart velocity in meters per second
v' is the cart acceleration in meters per second^2
a=2*PI. alpha is the pole or bandwidth. 1 Hz in this case
G=0.04 G is the crane motor gain in meters per second per % control output
u(t) is the controller output with a range of -100% to +100%
x is the crane position.
x' is the same as v
theta is the load angle.
zeta=0.001 is the damping factor
omega=1=sqrt(g/l) omega is the natural frequency.
g = 9.807 m/s^2
L = 9.807 m
Note, one can be more accurate by using sqrt((g/L)*sin(theta)) for omega
also, it would be better yet if this was done in terms of force instead of just position because the load will swing and vary the effort required to move the crane or cart.

At this time I don't care about the difference between using the cart position or the angle. It is the fact you don't use the first two equations to compute the cart position as a function of the control output that has been wrong. Note, I wouldn't have cared about this until you said it was a crane. As long as you stuck to a type 0 under damped system you were OK except for you claim that you can do better than a PID. See below.

You need to move the crane or cart to move the load ( actually to apply force since it is force that moves the load not position ), and the cart doesn't move instantly. How can you ignore this? If you are going to ignore this then why show a cart in your example?

are known and used: See Page 1, Fig.1
http://home.arcor.de/janch/janch/_control/20070613-pd2(pid)z1z2/

Other compensations are necessary for controlling disurbances z1 and z2. See formulae in Page 1.

Just using PID wouldn't work. See Page 6 (NEW)
I told you that you just don't know how to tune a PID or you are making PIDs look bad to serve a purpose. I see the fuzzy logic people do this too.
Explain this:
ftp://ftp.deltacompsys.com/public/NG/Mathcad%20-%20T0C1%20I-PD%20JCH.pdf
This how I would control JCH's system using his model. I only use a PID and my response is faster and just as smooth as yours. Unlike you I have shown all the numbers and formulas required to duplicate these results. I told you that I could do this and you just ignored me instead of asking how. Note to others, this is only an example of how to control a type 0 under damped system and has nothing to do with cranes or loads. JCH's example is not realistic yet. It is only a type 0 under damped system.


Note:
F1(s) can be any plausible process transfer function of any order. It must be known and match the system behavior as good as possible! One can't do more and should be happy if at least it works.
See my link above. You have no idea of what can or can't be done. You can't until you can model your systems correctly and learn how to calculate controller gains. You still haven't figured out how I can control the load with only the cart position feedback. I was informed of this technique back in the early 90's.
ftp://ftp.deltacompsys.com/public/NG/t1p1%20i-pv%20c1%20ol.pdf.
This more realistic and actually very simple example only using a PID and no feed forwards. I do play some tricks with the target generator.

Peter Nachtwey


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Relevant Pages

  • Re: Completion of Controller Synhesis
    ... v2 is NOT the position of the cart. ... So if v2 is not a control signal, ... says the load will move back to the 0 position. ... as the crane slows the load down. ...
    (sci.engr.control)
  • Re: Completion of Controller Synhesis
    ... v2 is NOT the position of the cart. ... says the load will move back to the 0 position. ... as the crane slows the load down. ... possible without breaking the laws of physics. ...
    (sci.engr.control)
  • Re: Completion of Controller Synhesis
    ... v2 is NOT the position of the cart. ... So if v2 is not a control signal, ... says the load will move back to the 0 position. ... as the crane slows the load down. ...
    (sci.engr.control)
  • Re: Completion of Controller Synhesis
    ... So if v2 is not a control signal, ... You need another transfer function to move the cart! ... says the load will move back to the 0 position. ... as the crane slows the load down. ...
    (sci.engr.control)
  • Re: Completion of Controller Synhesis
    ... v2 is NOT the position of the cart. ... So if v2 is not a control signal, ... says the load will move back to the 0 position. ... as the crane slows the load down. ...
    (sci.engr.control)