MATLAB: How to simplify exponential symbolic equation

exponential symbolic equations

I am solving a system of equations that have exponential terms in it. The equations are as follows:

x1_temp(t) == exp(-t*theta1_temp)*u1(t);
x2_temp(t) == exp(-t*theta2_temp)*(theta1_temp*x1_temp(t) + 19)

I want to ultimately find theta1 and theta2 from these equations. How can I isolate these variables and get an explicit equation? Using solve() or vpasolve() does not give answer. It gives an error saying that the input cannot be of type 'sym'.

Best Answer

Something like this?

syms x1_temp(t) x2_temp(t) theta1_temp theta2_temp u1(t)
eq=[x1_temp(t)==exp(-t*theta1_temp)*u1(t) x2_temp(t) == exp(-t*theta2_temp)*(theta1_temp*x1_temp(t) + 19)];
solx=solve(eq,[theta1_temp,theta2_temp]);
theta1_temp(t)=solx.theta1_temp
theta2_temp(t)=solx.theta2_temp

Related Solutions

MATLAB: Replace x with x(t) in a symbolic matrix

syms theta1 theta2 theta3
T = [  cos(theta1 + theta2 + theta3), sin(theta1 + theta2 + theta3), 0,   8*cos(theta1 + theta2 + theta3) + 5*cos(theta1 + theta2) + 10*cos(theta1)
    -sin(theta1 + theta2 + theta3), cos(theta1 + theta2 + theta3), 0, - 8*sin(theta1 + theta2 + theta3) - 5*sin(theta1 + theta2) - 10*sin(theta1)
    0,                             0, 1,                                                                           0
    0,                             0, 0,                                                                           1];
syms theta4(t) theta5(t) theta6(t)
temp = subs(T, {theta1, theta2, theta3}, {theta4, theta5, theta6});
syms theta1(t) theta2(t) theta3(t)
AT1 = subs(temp, {theta4, theta5, theta6}, {theta1, theta2, theta3});

"It is also fine if there is some way I can call elements of the matrix below,"

T10(t) =

[ cos(theta1(t)), sin(theta1(t)), 0, 10*cos(theta1(t))]

That is not a matrix: it is a symbolic function that returns a matrix. You cannot access individual elements of the function through normal indexing. You can, however, use formula(T10) which will return an array result that is not a function, and then you can index the array result.

MATLAB: How to solve three equations for four unknowns

You can only solve for three out of the four variables.

syms x1t t t1t u1 x2t y gamma t2t 
eq = [ x1t == exp(-t*t1t)*u1, x2t==y-gamma, x2t == exp(-t*t2t)*(t1t*x1t+1160917147506309/70368744177664)]
sol = solve(eq, [t1t, t2t, x2t], 'returnconditions',true)

You will find that the result is parameterized in two variables, and that the "conditions" returned is mostly that the two variables are each integer. What that is saying is that there are an infinite number of solutions that differ by multiples of 2*pi*1i

If you are willing to restrict to real values, then add the word "real" at the end of the syms line. sol would then have exactly one set of solutions.

Note that asking to solve for [t1t, t2t, x1t] will not return back any values.

If you ask to solve for [t1t, x1t, x2t] assuming real values, then you will get back three solution sets. The solutions will involve different branches of the Lambert W function. After you have substituted in the known values and have substituted in t and u1, you might find that some of the solutions turn out to be complex valued.

Best Answer

Related Solutions

MATLAB: Replace x with x(t) in a symbolic matrix

MATLAB: How to solve three equations for four unknowns

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