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ELEC3114 Control Systems

Online Tutorial 1 Question Sheet

Problem 1: Let F(s) be the Laplace transform of f(t). Show the following properties of the Laplace transform (a) (b)

(c)

L [e−at f (t)] = F (s + a)   df (t) L = sF (s) − f (0− ) dt  Z t F (s) f (τ )dτ = L s 0−

Hint: for (b) and (c) use the integration by parts formula

Z

b

udv = a

uv]ba

−

Z

b

vdu

a

Problem 2: Determine the Laplace transforms of the following functions f(t). Use Laplace transform table and properties of Laplace transforms. (a) f(t) = 3e-2t sin(2t)u(t) + δ(t). (b) f(t) = 3e-2(t-5) sin(2(t-5)) u(t-5). (c) f(t) = dg(t)/dt + 2 g(t), with g(t) = 1+ t + 3e-2t u(t). (d) Same as (c) but with g(t) = (1+t + 3e-2t )u(t)

Also following problems from Nise’s Control Systems Engineering Problem 1.5 (1.4 in 8th edition) Problem 2.7 (2.8 in 7th edition) Problem 1.7 (1.5 in 8th edition) Problem 2.9 See page 2 Problem 2.1-a, 2.1-b, and 2.1-c

Original version by Dr Hendra Nurdin Revised by Dr Arash Khatamianfar (T2, 2019)

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ELEC3114 Online Tutorial 1

Problem 1.5:

Problem 2.7:

Problem 2.9:

Problem 1.7:

Problem 2.1:

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