AE ME 351 - Answer Sheet Soft Copy

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BACHELOR OF SCIENCE (B.Sc.)

IN ENGINEERING DISCIPLINES

Spring Semester (2012)

ANSWER SHEET – Soft Copy

Student Name: ______________________________________

Student ID: _____________________________________

Course: Feedback Control Systems Lab (AE 351 / ME 351)

Examiner: Mr. Mohammad Abdul Majid Siddiqi

Date: 30/April/2012

Duration: 2.5 hours

Instructions:

This Answer Sheet Word document includes only those questions where you are asked to saveMATLAB code, snapshots of Simulink models or response plots.

- For questions where you are asked to create Simulink models, create a folder on the

Desktop (name it as: Student ID–Student Name) and save all your models in this folder.

The names to be used for these models are mentioned in the respective questions.

- For questions where you are asked to write MATLAB Code, copy your MATLAB code

in the space provided in this Word document (in the soft copy).

Page 1 of 12



Part I: System Modeling

Question 1.3: [25 pts.]

Using basic blocks in Simulink (Integrator, Gain, etc.), model the aircraft system of equations

(i.e., equations (1), (2) and (3)), using Simulink. Save your Simulink model as“AircraftPitchModel_OpenLoop.mdl”.

[When creating the model, note that the Input to the system is the Elevator Deflection angle (δe), and theoutput of the system is the Pitch angle (θ)]

[Save model on Desktop folder. Include snapshot of model in Word doc]

Question 1.4: [10 + 10 pts.]

Simulate the open loop Simulink model created in Question 1.3, for a step input in the Elevator Deflection angle (that is, δe = 1).

Attach a snapshot of the output plot (Pitch angle (θ) versus time) for a simulation of 15 seconds, and

comment of the nature of the output plot.

[Attach snapshot of output plot in Word doc. Include comments in hard copy]

Page 2 of 12



Part II: System Representation

… Eqn. (4)


Use MATLAB to represent the above system (the aircraft pitch model transfer function shown inEqn. (4)). Save it in a variable called “acpitch_sys”.

[Include MATLAB code in Word doc]Input

thata=[1.15 0.18];

dlta=[1 0.739 0.921 0];

acpitch_sys=tf(thata,dlta)Output

Transfer function:1.15 s + 0.18

-------------------------s^3 + 0.739 s^2 + 0.921 s

Question 2.3: [15 pts.]Use MATLAB to obtain the step response of the “acpitch_sys” system created in Question 2.2, for asimulation of 15 seconds.

Attach a snapshot of the step response plot.

[Include MATLAB code and step response plot in Word doc]

Inputthata=[1.15 0.18];dlta=[1 0.739 0.921 0];

acpitch_sys=tf(thata,dlta)step ([0:1:15],acpitch_sys)

Output

Page 3 of 12




For the System Transfer Function given by Equation (4), use MATLAB to obtain the State-Space

representation. Save the State-Space matrices in variables called A, B, C and D.

[Include MATLAB code in Word doc]

Inputthata=[1.15 0.18];dlta=[1 0.739 0.921 0];

[A,B,C,D]=tf2ss(thata,dlta)

Output

A =

-0.7390 -0.9210 0

1.0000 0 0

0 1.0000 0

B =

1

0

0

Page 4 of 12



C =

0 1.1500 0.1800

D =

0


Use the SS function in MATLAB to create a state-space object that represents the system (use the A, B,C and D matrices obtained in Question 2.4). Save your system in a variable called “sys_ss”.

[Include MATLAB code in Word doc]

Inputthata=[1.15 0.18];

dlta=[1 0.739 0.921 0];

[A,B,C,D]=tf2ss(thata,dlta);sys_ss = ss(A,B,C,D)

Output

a =

x1 x2 x3

x1 -0.739 -0.921 0

x2 1 0 0x3 0 1 0

b =u1

x1 1

x2 0x3 0

c =

x1 x2 x3

y1 0 1.15 0.18

d =u1

y1 0

Page 5 of 12




Use MATLAB to obtain the step response of the “sys_ss” system created in Question 2.6, for a

simulation of 15 seconds.

Attach a snapshot of the step response plot.[Note that this response must be the same as the response plot obtained in Question 2.3]


Input:thata=[1.15 0.18];

dlta=[1 0.739 0.921 0];

[A,B,C,D]=tf2ss(thata,dlta);sys_ss = ss(A,B,C,D);

step ([0:1:15],sys_ss)

Output:

Page 6 of 12



Part IV: Controller Design

Question 4.1: Proportional Control – Simulink [20+5+5 pts.]

a. Using the “AircraftPitchModel_OpenLoop.mdl” Simulink model (created in Question 1.3)as the starting point, create a closed-loop Simulink model (similar to the configuration shown in

Fig. 1 on Page 9) with a Proportional Controller (gain Kp).

Save your model as “PitchController_ClosedLoop_P.mdl”. b. Attach a snapshot of the output plot (Theta versus time) for a 50 seconds simulation for a value of

Kp = 1.

[Note that Theta commanded is equal to 0.2 radians]c. Comment on the nature of the output response plot (obtained in (b) above). Do the overshoot and

settling time meet the controller design specifications that were mentioned in Part III?

[Save model on Desktop folder. Include snapshot of model in Word doc. Write comments in hard copy]

Page 7 of 12



Question 4.2: Proportional Control – MATLAB [15+10+10+5 pts.]

a. Using the “acpitch_sys” variable created in Question 2.2, use MATLAB to obtain the closed-looptransfer function of the system with a Proportional Controller Kp (use a gain value of

Kp = 1).

Save the closed-loop transfer function in a variable called “sys_cl_p”. b. Use MATLAB to obtain the step response of the “sys_cl_p” system (created in (a)) for a

simulation of 50 seconds (value of Kp = 1).

Attach a snapshot of the step response plot.c. Use MATLAB to plot the step response plots of the “sys_cl_p” system (created in (a)) for the

following values of Proportional Gain: Kp = 2, 3, 5, 7.

Attach a snapshot of the step response plots (all step responses on a single plot) for a simulationof 20 seconds.

d. Comment on the nature of the step response plots obtained in (c). How do the following performance parameters vary with increasing values of Proportional Gain (Kp):

o Overshoot, Steady-State Error and Settling Time

[the step response in part (b) will be similar to that obtained using Simulink – in Question 4.1]


a)thata=[1.15 0.18];

dlta=[1 0.739 0.921 0];acpitch_sys=tf(thata,dlta);kp=1;

h=1;ff=series(kp,acpitch_sys);

sys_cl_p=feedback(ff,h);

b)thata=[1.15 0.18];

dlta=[1 0.739 0.921 0];

acpitch_sys=tf(thata,dlta);

kp=1;h=1;

ff=series(kp,acpitch_sys);sys_cl_p=feedback(ff,h);

step([0:1:50],sys_cl_p)

Page 8 of 12



c)thata=[1.15 0.18];dlta=[1 0.739 0.921 0];

acpitch_sys=tf(thata,dlta);kp=[2 3 5 7];

h=1;

for i=1:4

ff=series(kp(i),acpitch_sys);sys_cl_p=feedback(ff,h);

step([0:1:50],sys_cl_p)hold on

end

legend (kp=2

Page 9 of 12



Question 4.3: PID Controller Design – Simulink [15+10+10+5 pts.]

Create a copy of the “PitchController_ClosedLoop_PD.mdl” Simulink model created in Question 4.3,

and rename it as “PitchController_ClosedLoop_PID.mdl”.a. Modify the Controller block so that it now represents a Proportional-Integral-Derivative (PID)

Controller with gain Proportional Gain (Kp), Integral Gain (Ki) and Derivative Gain (Kd).

Be sure to save your model as “PitchController_ClosedLoop_PID.mdl”.

Page 10 of 12



b. Modify the Controller Gains Kp, Ki and Kd so that the response meets all the design

specifications (make sure none of these gains exceeds a value of 20). Write down these designedvalues of Controller gains (Kp, Ki and Kd).

c. Attach a snapshot of the output plot (Theta versus time) for a 30 seconds simulation for the

designed values of Kp, Ki and Kd.

[Note that Theta commanded is equal to 0.2 radians]d. Comment on the nature of the output response plot (obtained in (c) above). Are all the Controller

design specifications (mentioned in Part III) met?

[Save model on Desktop folder. Include snapshot of model in Word doc. Write comments in hard copy]

Page 11 of 12



Page 12 of 12

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AE ME 351 - Answer Sheet Soft Copy