1. Lab Assignment 02 Modern and Classical Control Theory
Instructions:
v Any MATLABR
tool can be selected for solution of Problems
v MATLAB R
and SimulinkR
file names should be yourname section.m (e.g.
John A.m) & yourname Section alpha.slx (e.g John A alpha.slx) respectively
2. Copy&Paste of assignment is strictly prohibited
v Submit Report(generated from MATLABR
for m-files and SimulinkR
if any)
only
v Attach results figures seperately for SimulinkR
files only, else everything should
be in generated report
Problem 1. Mathematical Modelling (15 points.)
VC1 =
Va
C1R1
−
1
C1R1
+
1
C1R2
VC1 +
VC2
C1R2
(1)
VC2 =
Vb
C2R3
−
1
C2R3
+
1
C2R2
VC2 +
VC1
C2R2
(2)
Where Va and Vb are the inputs.
w Implement the above system in SimulinkR
by using the random values of parameters
and show the step, ramp and impulse responses.
w Determine the general form of state space representation of the system.
w Determine the state space representation by using the random values of parameters
Show the step response of the state space by using the SimulinkR
(overshoot, peak
value, settling time, rise time if any)
Problem 2. Partial Fraction (10 points.) Determine the partial fraction of the following
transfer function
G(s) =
10s4 − 2s3 + 3s2 − s + 10
s6 + s5 − 4s3 − 8s2 − s + 25
Problem 3. Symbolic Math (5 points.) Implement the following function in the given
format and determine the Laplace of the given function.
y(t) = 2te−2t
+
10
17
cos(t3
− 60) − 4t4
e(5−t2)
Engr. Qazi Ejaz Ur Rehman Graduate Research Assistant
Aerospace Astronautics Department
3. Problem 4. Bode Plots (20 points.) For the following open loop transfer function
G(s) =
18(s2 + 5s + 10)
s(s3 + 1.2s + 9)
, H(s) = 1
* Plot the step response of the open loop transfer function of the system
* Plot the step response of the closed loop transfer function of the system
* Draw the bode plot of the given transfer function
Use the frequency range from 0.01-10000 rad/sec
Use the magnitude range from -60dB to +60dB
* Add title, labels and grid to all plots. Plots should be in doted lines in part 3 (optional)
Problem 5. Controller Design (25 points.) Design PID Controller for the following system
G(s) =
1
s(s + 1)(s + 5)
Plot the step response of the system without controller (SimulinkR
/MATLABR
)
Plot the step response of the system with controller (SimulinkR
/MATLABR
)
Compare the results of part 1 and part 2 (overshoot, settling time, rise time)
Problem 6. Controller Design (25 points.)
G(s) =
4
s(s + 2)
φ = 55o
s = −2 ± 2
√
3j
@ Design Compensator for the given system
@ Plot the compensated and uncompensated responses on the same window
Add title, labels and grid to all plots. Plots should be in doted lines (optional)
NOTE: Submit the Softcopy before Result finalization.
Engr. Qazi Ejaz Ur Rehman Graduate Research Assistant
Aerospace Astronautics Department
