I have got the eqaution of motion of a slider crank mechanism . I need
the following solution for that
1) A solution (in matlab code or simulink diagram ).
2) The solution for that when a fuzzy logic controller is applied to the system. |
Request for Question Clarification by
mathtalk-ga
on
04 Mar 2004 07:46 PST
Hi, lahsiv25-ga:
Unfortunately the particular equation which you want solved seems to
be missing from your Question. It can be difficult without some
experience to express a mathematical equation in a plain text format,
but if you give it a try, I'll be glad to help clear up any
ambiguities with you. Some of the previous Questions in the Science
--> Math section might serve to illustrate suitable notation.
regards, mathtalk-ga
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Clarification of Question by
lahsiv25-ga
on
04 Mar 2004 10:58 PST
Hi mathtalk-ga
I am trying to write the equation below
m(x)x(double dot) + 1/2m'(x)x(dot)^2 + K[r(x)-r(x0)]r'(x) + Kd e^2 x = Kd e d(t)
In the above equation , assume following things
1) Psi in place of x
2) double dot = second deriviative
3) dot = single deriviative
4) prime (') = denotes the deriviative with respect to psi
If u need anyhthing else Plz let me know
Lahsiv25
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Request for Question Clarification by
mathtalk-ga
on
04 Mar 2004 19:23 PST
From your description I gather the equation is a PDE (partial
differential equation), and that it involves three kinds of
derivatives.
1) On the right-hand side, the expression Kd e d(t): does this mean
the derivative of something (an unknown function e?) with respect to
time t?
2) On the left-hand side, primes denote the derivative with respect to
psi. Are the functions m(x) and r(x) known functions?
3) Again on the left-hand side, dots denote derivatives with respect
to (?) a space variable?
It would probably be a good approach for you to define the knowns and
unknowns in this equation, e.g. is K a known constant or a more
complicated term? Also, if your equation is in fact a partial
differential equation, perhaps of "evolutionary" type, then I'd expect
the equation itself to be supplemented by initial conditions and
possibly boundary conditions that make the problem well-defined.
regards, mathtalk-ga
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Clarification of Question by
lahsiv25-ga
on
05 Mar 2004 09:35 PST
Hi mathtalk-ga
1)On the right hand side Kd and e are constant and d(t) is the initial excitation.
2)Yes m(x)and r(x) are known functions.
m(psi) = Jmb + Jme +Jml((abcos(psi) - b^2)/r^2(psi))^2 + ms(absin(psi)/r(psi))^2
and r^2(psi) = a^2+b^2-2abcos(psi)
3) the dot on the left hand side denotes the deriviative with respect to time .
In the above calrification I have written psi in place of x .
so the equation can be written as
m(psi)psi(double dot) + 1/2m'(psi)psi(dot)^2 +
K[r(psi)-r(psi0)]r'(psi) + Kd e^2 psi = Kd e d(t).
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Request for Question Clarification by
mathtalk-ga
on
07 Mar 2004 11:18 PST
Hi, lahsiv25-ga:
Based on your Clarifications, I'm starting to see the problem more
clearly. If I've understood your points, this is a second-order
nonlinear ordinary differential equation for a function psi(t).
In order to specify a unique solution for such a problem, there would
need to be some additional information, such as two initial conditions
or perhaps some boundary conditions on either endpoint of a
time-interval, etc. Do you have additional data, say of the form
psi(0) and psi"dot"(0)?
regards, mathtalk-ga
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Clarification of Question by
lahsiv25-ga
on
08 Mar 2004 12:07 PST
I only have the equation for System potential energy
V = 1/2K[r(psi)-r(psi0)]^2 + 1/2Kd[d(t)-e*psi]^2
where psi0 is the static equilibrium position of the system.
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Request for Question Clarification by
mathtalk-ga
on
08 Mar 2004 13:41 PST
Okay, that may be related to my request for clarification. It seems
that the right hand side of the differential equation d(t) ("the
initial excitation") is meant to represent an instantaneous unit
impulse "force" which perturbs the system. If we assume the system is
in equilibrium prior to this "excitation" then perhaps the pieces of
the puzzle can begin to fall into place.
Is psi0 on this account a constant angle(?) ? Pressure?
-- mathtalk-ga
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Clarification of Question by
lahsiv25-ga
on
08 Mar 2004 23:20 PST
Yeah you are going on right track .
psi0 is the initial angle at the equilibrium position
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