3. Use Matlab to find the partial fraction expansion of the
functions below.
a) F(s)=16(s+2)/((s+4)(s2+6s+9))
show your Matlab commands and answers in the space below
b)
F(s)=(s2+2s+2)/((s+1)2(s+4)2)
show your Matlab commands and answers in the space below
?(?) = (? + 5)/[s(s+2)(s^2+6s+10)]
Sketch the root locus by hand. You may verify your sketch using
MATLAB but you must show sufficient intermediate work for
sketching.
Use MATLAB to identify the proportional controller value (to the
tenth decimal point) that would cause your system to be unstable.
Be sure to show evidence of this value. Plot your system response
due to a step input for this controller.
(a) Determine the inverse Laplace transform of F(s) =(2s−1)/s^2
−4s + 6
(b) Solve the initial value problem using the method of Laplace
transform. d^2y/dx^2 −7dy/dx + 10y = 0, y(0) = 0, dy/dx(0) =
−3.
(c) Solve the initial value problem:
1/4(d^2y/dx^2)+dy/dx+4y = 0, y(0) = −1/2,dy/dx(0) = −1.