MATLAB: More laplace inverse problems

Question

I can not get a distinct answer from the ilaplace function almost ever This is incredibly annoying.

This transfer function is not that complicated

There is no built in ramp function in matlab which means in order to plot it in matlab i need to either take the transfer function in s and multiple it by 1/s^2 —> take the inverse of it and plot it

or

take the inverse of the transfer function and multiple that by t and plot that

Neither of which matlab can accomplish Not being able to plot a ramp response without simulink is getting extremely old Can someone help me with a solutions

num = [10 10];
dem = [1, 6, 10 ,18, 10];
sys  = tf(num,dem)
tf_inverse = ilaplace(tf2sym(sys)) %just ignore the tf2sym functions its       %just converting tf type to symbolic
ramp_response = t*(tf_inverse) 
ezplot(ramp_response)

I just can not wrap my head around the fact that something as powerful as matlab can not take the inverse of a 4th order laplace

Answer 1

ezplot(vpa(ramp_response))

We went through this before. The inverse laplace of transfer function with maximum degree N in the denominator generally involves the sum of N roots of the polynomial that is the denominator. By default the symbolic engine leaves the root in symbolic form for degree 4 or higher.

The exact value of tf_inverse is

(1 / 189864) * (( - (30 * 1i) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) + (10386 * 1i) * 3^(1 / 2) + ( - (363 * 1i) * 3^(1 / 2) * (1774 + 54 * 1465^(1 / 2))^(2 / 3) + (37752 * 1i) * 3^(1 / 2)) / (1774 + 54 * 1465^(1 / 2))^(1 / 3)) * (( - 14 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) + (1774 + 54 * 1465^(1 / 2))^(2 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3) + 90 * 3^(1 / 2) / (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2))^(1 / 2) + (210 * ((1774 + 54 * 1465^(1 / 2))^(1 / 3) - (1 / 14) * (1774 + 54 * 1465^(1 / 2))^(2 / 3) + 52 / 7) / ((1774 + 54 * 1465^(1 / 2))^(1 / 3) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2)) + 5082 * 3^(1 / 2) * ( - 2615 / 1694 + ( - (1 / 14) * (1774 + 54 * 1465^(1 / 2))^(2 / 3) + 52 / 7) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) - 1350 * 3^(1 / 2) / (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) - 210 + (15 * (1774 + 54 * 1465^(1 / 2))^(2 / 3) - 1560) / (1774 + 54 * 1465^(1 / 2))^(1 / 3) + ((121 * 1i) * (((((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) * (1774 + 54 * 1465^(1 / 2))^(2 / 3) + 90 * 3^(1 / 2) * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 14 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) - 104 * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2)) / ((1774 + 54 * 1465^(1 / 2))^(1 / 3) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2)))^(3 / 2) + 121 * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(3 / 2)) * 3^(1 / 2)) * exp( - (1 / 6) * (1i * 3^(1 / 2) * (( - 14 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) + (1774 + 54 * 1465^(1 / 2))^(2 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3) + 90 * 3^(1 / 2) / (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2))^(1 / 2) - 3^(1 / 2) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) + 9) * t) + (1 / 189864) * (((30 * 1i) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) - (10386 * 1i) * 3^(1 / 2) + ((363 * 1i) * 3^(1 / 2) * (1774 + 54 * 1465^(1 / 2))^(2 / 3) - (37752 * 1i) * 3^(1 / 2)) / (1774 + 54 * 1465^(1 / 2))^(1 / 3)) * (( - 14 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) + (1774 + 54 * 1465^(1 / 2))^(2 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3) + 90 * 3^(1 / 2) / (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2))^(1 / 2) + (210 * ((1774 + 54 * 1465^(1 / 2))^(1 / 3) - (1 / 14) * (1774 + 54 * 1465^(1 / 2))^(2 / 3) + 52 / 7) / ((1774 + 54 * 1465^(1 / 2))^(1 / 3) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2)) + 5082 * 3^(1 / 2) * ( - 2615 / 1694 + ( - (1 / 14) * (1774 + 54 * 1465^(1 / 2))^(2 / 3) + 52 / 7) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) - 1350 * 3^(1 / 2) / (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) - 210 + (15 * (1774 + 54 * 1465^(1 / 2))^(2 / 3) - 1560) / (1774 + 54 * 1465^(1 / 2))^(1 / 3) + ( - (121 * 1i) * (((((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) * (1774 + 54 * 1465^(1 / 2))^(2 / 3) + 90 * 3^(1 / 2) * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 14 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) - 104 * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2)) / ((1774 + 54 * 1465^(1 / 2))^(1 / 3) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2)))^(3 / 2) + 121 * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(3 / 2)) * 3^(1 / 2)) * exp((1 / 6) * (1i * 3^(1 / 2) * (( - 14 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) + (1774 + 54 * 1465^(1 / 2))^(2 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3) + 90 * 3^(1 / 2) / (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2))^(1 / 2) + 3^(1 / 2) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) - 9) * t) + (1 / 189864) * (( - 30 * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) - 10386 * 3^(1 / 2) + (363 * 3^(1 / 2) * (1774 + 54 * 1465^(1 / 2))^(2 / 3) - 37752 * 3^(1 / 2)) / (1774 + 54 * 1465^(1 / 2))^(1 / 3)) * ((14 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - (1774 + 54 * 1465^(1 / 2))^(2 / 3) + 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3) + 90 * 3^(1 / 2) / (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2))^(1 / 2) + (210 * ((1774 + 54 * 1465^(1 / 2))^(1 / 3) - (1 / 14) * (1774 + 54 * 1465^(1 / 2))^(2 / 3) + 52 / 7) / ((1774 + 54 * 1465^(1 / 2))^(1 / 3) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2)) - 5082 * 3^(1 / 2) * ( - 2615 / 1694 + ( - (1 / 14) * (1774 + 54 * 1465^(1 / 2))^(2 / 3) + 52 / 7) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) + 1350 * 3^(1 / 2) / (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) - 210 + (15 * (1774 + 54 * 1465^(1 / 2))^(2 / 3) - 1560) / (1774 + 54 * 1465^(1 / 2))^(1 / 3) + (121 * (( - (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) * (1774 + 54 * 1465^(1 / 2))^(2 / 3) + 90 * 3^(1 / 2) * (1774 + 54 * 1465^(1 / 2))^(1 / 3) + 14 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) + 104 * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2)) / ((1774 + 54 * 1465^(1 / 2))^(1 / 3) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2)))^(3 / 2) - 121 * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(3 / 2)) * 3^(1 / 2)) * exp( - (1 / 6) * (3^(1 / 2) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) - 3^(1 / 2) * ((14 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - (1774 + 54 * 1465^(1 / 2))^(2 / 3) + 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3) + 90 * 3^(1 / 2) / (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2))^(1 / 2) + 9) * t) - (121 / 189864) * exp( - (1 / 6) * (3^(1 / 2) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) + 3^(1 / 2) * ((14 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - (1774 + 54 * 1465^(1 / 2))^(2 / 3) + 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3) + 90 * 3^(1 / 2) / (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2))^(1 / 2) + 9) * t) * (( - (30 / 121) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) - (10386 / 121) * 3^(1 / 2) + (3 * 3^(1 / 2) * (1774 + 54 * 1465^(1 / 2))^(2 / 3) - 312 * 3^(1 / 2)) / (1774 + 54 * 1465^(1 / 2))^(1 / 3)) * ((14 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - (1774 + 54 * 1465^(1 / 2))^(2 / 3) + 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3) + 90 * 3^(1 / 2) / (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2))^(1 / 2) + ( - (210 / 121) * ((1774 + 54 * 1465^(1 / 2))^(1 / 3) - (1 / 14) * (1774 + 54 * 1465^(1 / 2))^(2 / 3) + 52 / 7) / ((1774 + 54 * 1465^(1 / 2))^(1 / 3) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2)) + 42 * 3^(1 / 2) * ( - 2615 / 1694 + ( - (1 / 14) * (1774 + 54 * 1465^(1 / 2))^(2 / 3) + 52 / 7) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) - (1350 / 121) * 3^(1 / 2) / (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) + 210 / 121 + ( - (15 / 121) * (1774 + 54 * 1465^(1 / 2))^(2 / 3) + 1560 / 121) / (1774 + 54 * 1465^(1 / 2))^(1 / 3) + ((( - (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) * (1774 + 54 * 1465^(1 / 2))^(2 / 3) + 90 * 3^(1 / 2) * (1774 + 54 * 1465^(1 / 2))^(1 / 3) + 14 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2) + 104 * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2)) / ((1774 + 54 * 1465^(1 / 2))^(1 / 3) * (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(1 / 2)))^(3 / 2) + (((1774 + 54 * 1465^(1 / 2))^(2 / 3) + 7 * (1774 + 54 * 1465^(1 / 2))^(1 / 3) - 104) / (1774 + 54 * 1465^(1 / 2))^(1 / 3))^(3 / 2)) * 3^(1 / 2))

Well that's pretty clear, right?