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Simple RLC circuit calculation not working correctly -- why?

Hi, kind of a Matlab newbie here, so maybe this will be a no-brainer for Matlab pros, but I can use some help. Am trying to simulate a simple RLC circuit to obtain the steady state response. I can get a correct answer with Mathcad, but not with Matlab. Here's the process:

EDU>> circuit1 = '2*pi*2000/( (2*pi*2000)^2 + s^2) = (470 + .033*s + (10^7)/s) * I'; % 'I' is the current, so I am using V = I * Z

The term on the left is the Laplace transform of a sinusoidal source, and the terms on the right are for the RLC circuit. (Multiplying, on the left, by a 1/s term for a step function does not change the outcome shown below.)

EDU>> Ifr = solve(circuit1,'I') % Ifr stands for I_frequency_domain Ifr = .126e8*s/(.742e14*s+.470e6*s^3+.152e11*s^2+33.*s^4+.158e19)

EDU>> Itd = ilaplace(Ifr); % Itd stands for I_time_domain

EDU>> simple(Itd) ans =

-.104e-2*exp(-.713e4*t)*cos(.159e5*t)

-.149e-2*exp(-.713e4*t)*sin(.159e5*t)

+.104e-2*exp(11.5*t)*cos(.126e5*t) +.129e-2*exp(11.5*t)*sin(.126e5*t)

If we ignore the two exponentially decaying terms, the remaining two terms grow exponentially, which is simply not the correct steady-state solution. The frequencies give for the second two terms are correct (they equal 2 * 2000 pi, which is the source frequency, but the exponentially growing terms are a problem.

One possibility I can imagine: The Matlab documentation makes clear that "pi" is treated as a number, not a symbolic value, so that for example 'sin(pi)' does not come out to exactly zero. Perhaps this throws off the calculations somehow!? Any help or suggestions would be appreciated.

Steve O.

"Spying On The College Of Your Choice" -- How to pick the college that is the Best Match for a high school student's needs.

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Reply to
Steven O.
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Best Match for a high school student's needs.

This probably has more to do with the fact that you are asking Matlab to factor a 4th-order polynomial. The polynomial _should_ have roots at s = +/- j12.5e3, but isn't factoring correctly because of numerical problems.

Polynomial factoring is notoriously sensitive to errors in the coefficients, and you're doing this math in floating point. I think you're just asking too much of the algorithm (MathCad, obviously, is either using more precision or playing fancy tricks to make things come out right, which is cool for them, but doesn't help you if you must use MatLab).

I honestly don't know what precision MatLab uses when it does these calculations; it might be worth some digging to find out what precision they use and what algorithm -- then you could calculate the expected precision of the result and see if things match up.

I use SciLab, which easily lets you express systems in a state space form. If I had to get this answer numerically from that tool I would keep the RLC system in state space, and build a system who's impulse response was a cosine wave. Then I'd cascade them (keeping them state space) and see what sort of response came out. This has the advantage that the state-space system representation can have much better numerical conditioning* than the polynomial form.

You could also get the impulse response for the filter in terms of the sum of two complex single-order systems, and break the cosine wave down with the Euler identity into the sum of two complex single-order signals. Then you could take these four elements, multiply them out (remember FOIL**?), solve for all the bits & pieces, and put it back together again.

  • OTOH, it can be just as bad, or worse -- you have to know what'll be good going in.
** First Outer Inner Last, although LOIF, FLOI, FOLI and other combinations work as well. 
--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google?  See http://cfaj.freeshell.org/google/
Reply to
Tim Wescott

To understand simple L and C tuned circuits you can do no better than download program QL_QC and program LCR from website below.

Download programs in a few seconds and run immediately under DOS-Windows. Not zipped up.

---- ........................................................... Regards from Reg, G4FGQ For Free Radio Design Software go to

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Reply to
Reg Edwards

I'm sure it's a great program, but Matlab is required for the class.

Steve O.

"Spying On The College Of Your Choice" -- How to pick the college that is the Best Match for a high school student's needs.

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Reply to
Steven O.

The problem is that you only have 3 digits in your coefficients in this expression. Leave everything in factored form:

4E6*pi*s ---------------------------------------------- ((2*pi*2000)^2 + s^2)*(1E10 + 47E4*s + 33*s^2)

or keep more digits, 12 perhaps, in your coefficients and you will get the right roots.

Best Match for a high school student's needs.

Reply to
The Phantom

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