MATLAB: Implementing a complex function in Simulink

MATLABsimulink

In Matlab's command window I obtained several equations which look like:

Tc1 = (- 2*J2*cos(t3)*sin(t1)*sin(t3)*n^2 + 2*J2*w3*sin(t3)*n)/cos(t2) - d2 + cos(t2)*(J2*cos(t3)*sin(t1)*sin(t3)*n^2 + J2*v3*sin(t1)) + J1*w1*w3 + J2*w1*w3 - J3*w1*w3 + J2*v2*cos(t1) + J2*n^2*cos(t1)*tan(t2) - J2*w2^2*cos(t1)*tan(t2) + 2*J2*w3^2*cos(t1)*tan(t2) + J2*w2^2*cos(t1)^3*tan(t2) - J2*w3^2*cos(t1)^3*tan(t2) - 2*J2*n*w2*cos(t3)*tan(t2) + 2*J2*w2*w3*sin(t1)*tan(t2) - J2*n^2*cos(t1)*cos(t3)^2*tan(t2) + 2*J2*n*w2*cos(t1)^2*cos(t3)*tan(t2) - 2*J2*w2*w3*cos(t1)^2*sin(t1)*tan(t2) - 2*J2*n*w3*cos(t1)*cos(t3)*sin(t1)*tan(t2)

In Simulink I use From and Goto blocks for all the parameters (Tc1, J1, J2, J3, t1, t2, t3 and so on).

Now I am wondering what the easiest way is to implement these long formulas in Simulink for a simulation. Normally I would just rebuild the equations using all kind of blocks in Simulink, but the equations I ended up with this time are much longer. Any ideas?

Best Answer

The only other alternative I can think of is to use the MATLAB Function block and write this out as a MATLAB function.

Related Solutions

MATLAB: Problem with simplify function used with matrices

MATLAB's symbolic toolbox is not perfect (perhaps it is impossible to make a perfect symbolic engine), and every year they make some improvements. This seems one such case. Also, "simplification" is not a well defined idea. The tips section of simplify() documentation mentions: "Simplification of mathematical expression is not a clearly defined subject. There is no universal idea as to which form of an expression is simplest. The form of a mathematical expression that is simplest for one problem might be complicated or even unsuitable for another problem."

Are you using an older release of MATLAB? In R2020b, it is simplified as you described in your comment

syms t1 t2 t3 t4 a1 a2 d3
M = [
cos(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)) - sin(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)), - cos(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)) - sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)), 0, a1*cos(t1) + a2*cos(t1)*cos(t2) - a2*sin(t1)*sin(t2)
cos(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)) + sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)),   cos(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)) - sin(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)), 0, a1*sin(t1) + a2*cos(t1)*sin(t2) + a2*cos(t2)*sin(t1)
                                                                                        0,                                                                                           0, 1,                                                   d3
                                                                                        0,                                                                                           0, 0,                                                   1];
                                                                                    
M_simplify = simplify(M)

Result

>> M_simplify
M_simplify =
[cos(t1 + t2 + t4), -sin(t1 + t2 + t4), 0, a2*cos(t1 + t2) + a1*cos(t1)]
[sin(t1 + t2 + t4),  cos(t1 + t2 + t4), 0, a2*sin(t1 + t2) + a1*sin(t1)]
[                0,                  0, 1,                           d3]
[                0,                  0, 0,                            1]

You may experiment with following option if you are using an older release of MATLAB

M_simplify = simplify(M, 'Seconds', 10); % specify maximum number of seconds MATLAB spent on simplification

MATLAB: How can we solve only for t1 variable in the equation P=R1 which has multiple variables such as t2 t3. Which is possible mathematically.

With respect to

syms t1 t2 t3
R1 = [
    cos(t2)*cos(t3) - sin(t2)*sin(t3),  - cos(t2)*sin(t3) - cos(t3)*sin(t2), 0, 10*cos(t2);
    (7344817515977723*cos(t2)*sin(t3))/9223372036854775808 + (7344817515977723*cos(t3)*sin(t2))/9223372036854775808, (7344817515977723*cos(t2)*cos(t3))/9223372036854775808 - (7344817515977723*sin(t2)*sin(t3))/9223372036854775808, 9007196398844849/9007199254740992, (36724087579888615*sin(t2))/4611686018427387904 + 45035981994224245/4503599627370496;
     - (9007196398844849*cos(t2)*sin(t3))/9007199254740992 - (9007196398844849*cos(t3)*sin(t2))/9007199254740992,       (9007196398844849*sin(t2)*sin(t3))/9007199254740992 - (9007196398844849*cos(t2)*cos(t3))/9007199254740992, 7344817515977723/9223372036854775808, 36724087579888615/4611686018427387904 - (45035981994224245*sin(t2))/4503599627370496;
     0, 0, 0, 1];
P = [
     (433*cos(t1))/500, -cos(t1)/2, sin(t1),  0;
    -(433*sin(t1))/500,  sin(t1)/2, cos(t1), 0;
    -1/2, 433/500, 0, 0;
    0,  0, 0, 1];

there is no possible solution for R1 == P.

Compare R1(3,3) = 7344817515977723/9223372036854775808 to P(3,3) = 0. These are constants but do not equal each other, so it is not possible to find t1, t2, t3 that will make the matrices equal.

Best Answer

Related Solutions

MATLAB: Problem with simplify function used with matrices

MATLAB: How can we solve only for t1 variable in the equation P=R1 which has multiple variables such as t2 t3. Which is possible mathematically.

Related Question