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From: JCH on 19 Nov 2009 03:21

"pnachtwey" <pnachtwey(a)gmail.com> schrieb im Newsbeitrag
news:171a1cc5-0723-47f5-9980-4e846f08eb2e(a)x25g2000prf.googlegroups.com...
> On Nov 17, 11:40 pm, "JCH" <ja...(a)nospam.arcornews.de> wrote:
>> "Edward Jensen" <edw...(a)jensen.invalid> schrieb im
>> Newsbeitragnews:hdubk2$psm$1(a)news.net.uni-c.dk...
>>
>>
>>
>>
>>
>> > Hi.
>>
>> > I'm working on modeling a system which have resulted in a system of
>> > first
>> > order nonlinear differential equations
>> > s'(t) = f(t, s(t), u(t))
>> > with state vector s(t) and control input u(t) and s(t), u(t) \in R^3
>> > The measurements are simply given by y(t) = s(t).
>>
>> > The continuous time model is embedded in a digital control loop where
>> > there output y(n) is a sampled version of y(t) with zero order hold and
>> > Ts
>> > = 0.1 s. Similarly the discrete control inputs u(n) is converted
>> > through
>> > zero order hold to u(t) with the same sample time.
>>
>> > I now want to write this model as: s(n + 1) = g(n, s(n), u(n)). I know
>> > how
>> > to do this is for a linear continous time continous model s'(t) = Ax(t)
>> > +
>> > Bu(t) with the c2d fuction but I am in doubt how to do this for the
>> > nonlinear model.
>>
>> > Should I linearize the continous time differential equation first or
>> > what
>> > is the best method?
>>
>> EXAMPLE
>>
>> Linearizing a nonlinear differential equation (DE):
>>
>> *http://home.arcor.de/janch/janch/_control/20091118-non-linear-ode/
>>
>> Red points: nonlinear DE
>> Black points: approximated linear DE
>>
>> If system is load dependent then optimize the controller (PID) on at
>> least 3
>> load points and adjust the controller parameters automatically using a
>> polynomial.
>>
>> See Note in Math Model: Model Adaptation 2
>>
>> --
>> Regards JCH
> Stop your nonsense. You have been able to identify any of the systems
> I have provided in the past. Your system identification doesn't have
> an concept of a ambient value, dead time or know the difference
> between type 0 and type 1 systems. It is easy to do what you are
> doing if you know the solution and then generate the problem.
>


Again, the TOPIC was:

>> Linearizing a nonlinear differential equation (DE):
>>
>> * http://home.arcor.de/janch/janch/_control/20091118-non-linear-ode/


--
Regards JCH


From: JCH on 20 Nov 2009 13:08

"pnachtwey" <pnachtwey(a)gmail.com> schrieb im Newsbeitrag
news:171a1cc5-0723-47f5-9980-4e846f08eb2e(a)x25g2000prf.googlegroups.com...
> On Nov 17, 11:40 pm, "JCH" <ja...(a)nospam.arcornews.de> wrote:
>> "Edward Jensen" <edw...(a)jensen.invalid> schrieb im
>> Newsbeitragnews:hdubk2$psm$1(a)news.net.uni-c.dk...
>>
>>
>>
>>
>>
>> > Hi.
>>
>> > I'm working on modeling a system which have resulted in a system of
>> > first
>> > order nonlinear differential equations
>> > s'(t) = f(t, s(t), u(t))
>> > with state vector s(t) and control input u(t) and s(t), u(t) \in R^3
>> > The measurements are simply given by y(t) = s(t).
>>
>> > The continuous time model is embedded in a digital control loop where
>> > there output y(n) is a sampled version of y(t) with zero order hold and
>> > Ts
>> > = 0.1 s. Similarly the discrete control inputs u(n) is converted
>> > through
>> > zero order hold to u(t) with the same sample time.
>>
>> > I now want to write this model as: s(n + 1) = g(n, s(n), u(n)). I know
>> > how
>> > to do this is for a linear continous time continous model s'(t) = Ax(t)
>> > +
>> > Bu(t) with the c2d fuction but I am in doubt how to do this for the
>> > nonlinear model.
>>
>> > Should I linearize the continous time differential equation first or
>> > what
>> > is the best method?
>>
>> EXAMPLE
>>
>> Linearizing a nonlinear differential equation (DE):
>>
>> *http://home.arcor.de/janch/janch/_control/20091118-non-linear-ode/
>>
>> Red points: nonlinear DE
>> Black points: approximated linear DE
>>
>> If system is load dependent then optimize the controller (PID) on at
>> least 3
>> load points and adjust the controller parameters automatically using a
>> polynomial.
>>
>> See Note in Math Model: Model Adaptation 2
>>
>> --
>> Regards JCH
> Stop your nonsense. You have been able to identify any of the systems
> I have provided in the past. Your system identification doesn't have
> an concept of a ambient value, dead time or know the difference
> between type 0 and type 1 systems. It is easy to do what you are
> doing if you know the solution and then generate the problem.


What is the bigger problem? Have a data set and find the differential
equation(s)? Or vice versa?

It's much easier to solve e.g. 8 known non-linear differential equations,
even on higher order:

EXAMPLE FOR 1st ORDER SYSTEM

* http://home.arcor.de/janch/janch/_control/20091120-non-linear-de/

Nothing is better than use the 'real' data values!


--
Regards JCH

From: Jerry Avins on 20 Nov 2009 16:24
iman way wrote:

إخفاء النص المقتبس -

>> - عرض النص المقتبس -
>
> I am happy to be a member of this group and I consider you my friends.

No friend would be as disruptive as you. You haven't even the decency to
start your own (off topic) thread. You hijack an unrelated one. Shame!

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
From: Tim Wescott on 20 Nov 2009 22:38
On Fri, 20 Nov 2009 16:24:42 -0500, Jerry Avins wrote:

> iman way wrote:
>
> إخفاء النص المقتبس -
>
>>> - عرض النص المقتبس -
>>
>> I am happy to be a member of this group and I consider you my friends.
>
> No friend would be as disruptive as you. You haven't even the decency to
> start your own (off topic) thread. You hijack an unrelated one. Shame!

Jerry, I think it's a bot. This stuff gets splattered all over a number
of newsgroups; I doubt that there's any human there to read any replies.

--
www.wescottdesign.com
From: Jerry Avins on 20 Nov 2009 23:00
Tim Wescott wrote:
> On Fri, 20 Nov 2009 16:24:42 -0500, Jerry Avins wrote:
>
>> iman way wrote:
>>
>> إخفاء النص المقتبس -
>>
>>>> - عرض النص المقتبس -
>>> I am happy to be a member of this group and I consider you my friends.
>> No friend would be as disruptive as you. You haven't even the decency to
>> start your own (off topic) thread. You hijack an unrelated one. Shame!
>
> Jerry, I think it's a bot. This stuff gets splattered all over a number
> of newsgroups; I doubt that there's any human there to read any replies.

I know the origin is gmail and groups.google.com. I gurss they think
it might not be PC to kill the account.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
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