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Control Process Engineering
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MATLAB EXERCISE LAPLACE TRANSFORMS
HANS STIGTER AND TON VAN BOXTEL
(1) Find the Laplace transforms of the following functions (i) by hand calcula-tion, and (ii) with the help of MATLAB’s symbolic toolbox:(a) f(t) = 2 t3
(b) f(t) = cos (5 t)(c) f(t) = t e2 t
(d) f(t) = (t + 1)(2) Solve the differential equations
(a) dx(t)dt
− x(t) = 0, x(0) = −1
(b) dx(t)dt
+ a x(t) = 0, x(0) = b,
(c) d2x(t)
dt2+ 3 dx(t)
dt+ 2x(t) = 0, x(0) = −1,
dx(t)dt
= 1(3) Calculate the initial and final value limits for
(a) F (s) = 5(3 s+1) s
(b) F (s) = 73 s3+2 s2+3 s
(c) F (s) = 2 s+5(s+2) s
(4) Apply partial fraction expansion of the following expressions (i) by hand,and (ii) by Matlab(a) F (s) = 7
3 s3+2 s2+3 s
(b) F (s) = s+33 s2+2 s+3
(c) F (s) = s3+s+1
s2+2 s+3
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