Control Engineering [Dr. Salah Ahmed Helmy]
Sheet No. 1.1
Chapter 2 MATHEMATICAL MODELING OF DYNAMIC
SYSTEMS
1- Derive the Laplace transform for the following time functions:
a. 𝑓(𝑡) = 2𝒆−𝒂𝒕
b. 𝑓(𝑡) = 5
2- For each of the following transfer functions, write the
corresponding differential equation.
𝑋(𝑠)
15
=
𝐹 (𝑠) (𝑠 + 10)(𝑠 + 11)
𝑋(𝑠)
𝑠+3
= 3
𝐹 (𝑠) 𝑠 + 11𝑠 2 + 12𝑠 + 18
3- Write the differential equation for the system shown below
𝑅(𝑠)
𝒔𝟓 + 2𝒔𝟒 + 4𝒔𝟑 + 𝒔𝟐 + 4
𝒔𝟔 + 𝟕𝒔𝟓 + 3𝒔𝟒 + 2𝒔𝟑 + 𝒔𝟐 + 5
𝐶(𝑠)
4- Find the transfer function, 𝐺(𝑠) = 𝑋1 (𝑠)/𝐹(𝑠), for the
translational mechanical system shown in Figure P4.
Figure P4
5- Find the transfer function, 𝐺(𝑠) = 𝑋2 (𝑠)/𝐹(𝑠), for the
translational mechanical network shown in Figure P5.
Figure P5
6- For the system of Figure P6 find the transfer function, 𝐺(𝑠) =
𝑋1 (𝑠)/𝐹(𝑠).
Figure P6
7- Find the transfer function, 𝐺(𝑠) = 𝑋3 (𝑠)/𝐹(𝑠), for the system
shown in Figure P7.
Figure P7
8- For the rotational mechanical systems shown in Figure P8, write
the
equations
of
motion
and
calculate
the
transfer
function 𝐺 (𝑠) = 𝜃1 (𝑠)/𝑇(𝑠).
Figure P8
9- For the mechanical systems shown in Figure P9, Draw the
equivalent electric circuit.
Figure P9