1- For the problems below document the design process. Clearly show the final compensator that you have obtained.
engineering
Description
NOTE:
1- For the
problems below document the design process. Clearly show the final compensator
that you have obtained.
2-If you had to redesign (a compensator) briefly indicate what assumptions you
had and the compensator you obtained (omit all other details in your final
report).
3-If you were
unable to a satisfactory design a compensator for a given problem after several
trials, follow the step 2 however include your best results with more details
as indicated by step 1.
4- Provide a nice / organized
/ clean report, including matlab script file of your work along with required figures
(simulation, bode plots, etc.). Do not just print out Matlab command window,
error messages, etc.
Problems:
1- For a unity feedback
control system with plant transfer function of
Design
phase-lag compensator such that the resulting controlled system has a Phase
Margin of at least 45°
and at
most 65° with a static error
constant coefficient in the range of 115 to 130.
Document the design process.
Verify your
design by determining/showing the explicit form of the compensator, resulting
Phase Margin, Gain Margin of the compensated system, as well as including step
responses of the uncompensated system, gain adjusted system, and
lag-compensated system.
2- Design a phase-lead
compensator for the system given in problem 1 (use the same values of Phase
Margin and error coefficient).
3- Compare and contrast the
resulting compensated systems of problem 1 and 2. Is there any clear reason why
one is a better choice than the other?
4- Design a PID compensator for a unity feedback
system with plant transfer function
Design a PID
compensator that meets the following specifications:
a-
The closed-loop system transfer function has exactly two poles.
b-
The closed loop controlled system has dominant poles with
damped
frequency of 4.5 rad/s and damping ratio greater than
0.707.
c-
The closed-loop system exhibit zero steady state error due to a unit step
input.
Clearly show
the rational for the design, final compensator transfer function, and step
response of closed-loop compensated system.
