PLEASE MAKE SURE YOU SOLVE THE FOLLOWING USING MATLAB ONLY T

PLEASE MAKE SURE YOU SOLVE THE FOLLOWING USING MATLAB ONLY!!!! THANKS

Solving the following Control Systems Problems using MATLAB. The following problems are to be solved by the TFtool. Perform partial-fraction expansion of the following functions. G(s) = 10(s + 1)/s^2(s + 4)(s + 6) G(s) = 5e^-2s/(s + 1)(s^2 + s + 1)

Solution

a )

>> syms a s
>> G = (10*s+10)/(s^2*(s+4)*(s+1))
>> ilaplace(G)

OUTPUT :-

(5*t)/2 + 5/(8*exp(4*t)) - 5/8

d)

>> ilaplace(5*(exp(-2*s))/((s + 1)*(s^2+s+1)), s, t)

output :-

5*heaviside(t - 2)*(exp(2 - t) - exp(1 - t/2)*(cos((3^(1/2)*(t - 2))/2) - (3^(1/2)*sin((3^(1/2)*(t - 2))/2))/3))

Hence using command we can find inverse laplace transform of given transfer function.

heaviside function will give three outputs depends on input argument to heavisside i.e

if

t < 0 heaviside(-1) = 0

t > 0 heaviside(1) = 1

t = 0 heaviside(0) = 1/2