“Inn the name off God, the most merciful”
Ferdowsi Unniversity of Mashhad
M
Linea
ar Control Sysstems, Fall 2010, Instructoor: Dr. M-R. AkbarzadehA
T.
Mini-projject #2 (subbmission deaadline: 13th of
o Azar)
Analy
ysis of an Attitude Control System
S
off an Aircrraft
A linearizzed model off an attitude control systtem of an airrcraft is desccribed
in Examp
ple 4-11-1. Please
P
read thhis case studdy example carefully
c
andd then
answer th
he following questions.
I addition to
In
o employing the conventtional method
ds (by hand)), use Contro
ol System
Toolbox, ACSYS and Simulink in MATLAB
M
to
o solve the fo
ollowing prob
blems.
1. Firrst, read Sectiion 5-8 carefuully where K is a proportional controller (P controlller). Substitutte
this proportional
p
controller
c
witth
(a particular lag controlller) and repeat all steps of
o
Sectioon 5-8 (with
h all details)) for the thiird order
of Exam
mple 4-11-1. Compare thhe
perforrmance of theese two contrrollers from the
t viewpointts of stabilityy, transient annd steady statte
responnse. Simulatee the designed control sysstem in Simullink and illusstrate its perfo
formance usinng
differrent command
d/output plotss. If you are allowed to change
c
the zeero of the aboove-mentioneed
controoller (z = -10
00), how will you change it
i to improvee the performaance of the coontrol system
m?
Explaain your answ
wer using the Root
R
Loci.
2. Solve Problem 5-58 for the third order ‫ܩ‬௣ ሺ‫ݏ‬ሻ of Example 4-11-1. Simulate the designed control
system in Simulink and illustrate its performance using different command/output plots. Consider
the internal stability (all signals = internal stability) of the designed control system.
3. Solve Problem 8-61 for the third order ‫ܩ‬௣ ሺ‫ݏ‬ሻ of Example 4-11-1 using the frequency domain
analysis techniques. Use Bode Diagram, Nyquist Stability Criterion and Nichols Chart to analyze
the stability and transient/steady-state performance of the control system with explaining all
details. Describe the relationship between the Root Loci (time-domain analysis) and the Nyquist
Plot (frequency-domain analysis) on this control problem.
4. Plot the Bode Diagram of open loop and closed loop transfer functions of the designed control
systems in Questions 1 and 2. For each one, use Bode Plot to analyze the performance of the
designed control system and determine the frequency range of the allowed command signals that
can be accurately tracked by the control system.
5. In addition to Command Tracking, a real-world control system should have the ability of
Disturbance/Noise Rejection. Introduce a disturbance (or a noise) signal for the above control
system and simulate them in Simulink. Find the TF between the disturbance and output. Use Root
Loci and Bode Plot to answer the following questions. How do your designed control systems in
Questions 1 and 2 perform disturbance attenuation? How about noise attenuation? How can you
improve the performance of the control system to simultaneously perform command tracking and
disturbance/noise attenuation? Use Bode Plot to determine the frequency range of the
disturbance/noise signals that can be rejected by this control system.
6. In control engineering especially in conventional control theory, the controller is usually
designed based on a mathematical model of the actual plant. In comparison with the actual plant,
the model usually has some inaccuracy (called Plant Uncertainty) in terms of parametric
uncertainty and neglected dynamics. Thus, a real-world control system should be Robust, i.e., the
controller must not be sensitive to the plant uncertainty and it must keep stability and
performance of the control system even in the presence of plant uncertainty. Consider two
parametric uncertainties in the above plant and simulate them in Simulink. How do these
uncertainties influence the Root Loci? How do they take effect on the Bode Diagram of the openloop and closed-loop transfer functions? Use Root Loci to describe the effect of these parametric
uncertainties on the stability and performance of the closed loop control system. How do you do
this work using Bode/Nyquist/Nichols Plots? How can you increase the robustness of the
controller?