How would I write a code to solve a system of equations?
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I need to solve a system of equations but I do not know the syntax for doing so. The equations are:
q1 = (1.53*10^-5)*t1^4 + (1.67*10^-2)*t1^3 + 6.85*t1^2 + 2746*t1 - 57793
q2 = 13.3*(t1-t2)
q3 = (1.53*10^-5)*t2^4 + (1.67*10^-2)*t2^3 + 6.85*t2^2 + 4846*t2 - 49161
also; q1=q2=q3
I'm new to MATLAB and not sure how to handle this many variables along with the scientific notation.
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回答(4 个)
sixwwwwww
2013-10-20
编辑:sixwwwwww
2013-10-20
Dear Omar, you can solve your system of equations using the following way:
t = sym('t%d', [1 2]);
q1 = 1.53e-5 * t(1)^4 + 1.67e-2 * t(1)^3 + 6.85 * t(1)^2 + 2746 * t(1) - 57793;
q2 = 13.3 * (t(1) - t(2));
q3 = 1.53e-5 * t(2)^4 + 1.67e-2 * t(2)^3 + 6.85 * t(2)^2 + 4846 * t(2) - 49161;
[solutions_t1, solutions_t2] = solve(q1 == q2 == q3, t(1), t(2))
Or
[solutions_t1, solutions_t2] = solve(q1 == q2, q2 == q3, t(1), t(2))
You can check which solutions are better because in first case you will get 4 solutions for both t1 and t2 and in second case you will get 16 solutions for both t1 and t2. I hope it helps. Good luck!
Walter Roberson
2013-10-20
{q = 2003.839045, t1 = -819.5264017, t2 = -970.1909915},
{q = -10982.94224, t1 = -817.9943073, t2 = 7.790823431},
{q = 133.2164095, t1 = 20.04280634, t2 = 10.02653495},
{q = 13235.45859, t1 = 24.30348638, t2 = -970.8437757}
provided that you only want real-valued solutions.
This was done by substituting t1 for t(1) and t2 for t(2), and then plugging the three q equations into solve()
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David
2013-10-21
编辑:David
2013-10-21
In addition to the answers already posted, be sure to put sym() around each of your equations. That is to say, do the following:
syms t1 t2
q1 = sym( 1.53e-5*t(1)^4 + 1.67e-2*t(1)^3 + 6.85*t(1)^2 + 2746*t(1) - 57793 );
q2 = sym( 13.3*(t(1) - t(2)) );
q3 = sym( 1.53e-5*t(2)^4 + 1.67e-2*t(2)^3 + 6.85*t(2)^2 + 4846*t(2) - 49161 );
[solutions_t1, solutions_t2] = solve(q1 == q2, q2 == q3, t1, t2);
solve requires that your equations be symbolic objects which is guaranteed by using sym().
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Walter Roberson
2013-10-21
As long as anything in the equation is sym, the whole expression will be treated as sym. So
t = sym('t%d', [1 2]);
is enough to make the equations sufficiently sym() without requiring sym() around the equations.
David
2013-10-22
Oh? This seemed to correct a problem I was having earlier in using the solve function. You actually saw that question and made useful suggestions, though suggestions that did not quite do the trick. Maybe we are both missing something or maybe it's just me...
anjali wavhale
2020-12-1
how to do least square estimation for system with the prbs as input to it
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