Control Systems Projects
Maglev Mathematical Design;
Goals:
Question 1: Derive the mathematical models from the electrical and mechanical systems.
Question 2:
a) Find the transfer functions,
𝐼(𝑠)/𝐸𝑖𝑛(𝑠)
and
𝑍(𝑠)/𝐼(𝑠)
b) Construct the feedback system using a proportional controller 𝐶(𝑠) = 𝐾𝑝 and plot the root
locus.
c) Now attach the lead compensator 𝐶(𝑠) = 𝐾 ∙
(𝑠+40)/(𝑠+160)
in the feedback system. Plot the root locus.
Question 3: Simulate the feedback system with a reference position 𝑧𝑟𝑒𝑓 = 0.003m.
a) Construct the SIMULINK model of maglev levitation systems with the transfer functions from (2a)
by adding the controller 𝐶(𝑠) = 1780 ∙
(𝑠+40)/(𝑠+160)+(1.2)/𝑠
Plot the time response z(t) vs. t for 1 second
using the above controller C(s).
b) Construct SIMULINK model by replacing the transfer functions by the nonlinear model from (1)
and plot the time response z(t) vs. t
c) Explain what you observed from your results.
Airplane Longitidual Mathematical Design;
Goals:
a. Derive the transfer function and state space model according to the system input and output.
Show your solutions step by step.
b.Define the transfer function and state space models in a Matlab Script.
Add the required codes into your report.
Find zeros and poles of the transfer function and comment on the stability of the system. What is thesystemorder?
c.Find the stepresponse.
d.Build a block diagram in Matlab/Simulink by using the equations and plot output by giving a step input.
Show your final Simulink model and plots.