ENME 585 Lab 4 Report (Section B06)
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Date
Dec 6, 2023
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ENME 585 Fall 2022 Lab 04 β Stabilization of a Cart and Pole Lab Submission Worksheet
Page 1
of 10
YOUR GROUP INFORMATION Lab section
: Date: B06 November 10, 2023
Laptop #
: Hardware #
: 5 Q8USB: 07; VoltPAQ:03; LinearServo: 01 First Name 1: Allen Last Name 1: Okanovic First Name 2: Pranab Last Name 2: Barua First Name 3: Marcus Last Name 3: Gregory First Name 4: Raksha Last Name 4: Achar First Name 5: Ayman Last Name 5: Malkawi YOUR FEEDBACK A. How would you rate the difficulty of this lab? Medium B. Were there any aspects of this lab that you struggled with or found confusing? If so, which? None. C. How long did it take you/your group to do the lab, including finishing this submission form? 2 hours. D. Suggest improvements, if any. Type here.
Page 2
of 10
QUESTIONS: Cart Model Identification via Step Response (12/32 marks)
Q1.
Insert the figure of the scope output for the 5V step input, complete with your selected data points shown. Enter your determined values for π
and π
in the table below.
Constant Value π
[m/sV]
0.1702
π
[s] 0.114
Page 3
of 10
Q2.
Insert the overlay plot output from the MATLAB script using physical system response values of c and π
, with the figure title and axis labels. Provide possible reasons for the difference between the actual linear cart output and the theoretical step response.
The reasons for the difference between the actual and linear output. ο·
Friction between the rod and where the cart sits on the rod as it moves along the rod. ο·
Friction between the gear and where the gear sits. ο·
In the theoretical response, inductance is neglected. In the actual response, inductance is accounted for which makes up the variation between the theoretical and actual step responses.
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Page 4
of 10
Q3.
Insert the overlay plot output from the MATLAB script using theoretical system response values of c and π
determined using Quanserβs values from the prelab, with the figure title and axis labels. Provide possible reasons for the difference between the actual DC motor output and the theoretical step response.
The main differences between the theoretical and actual step response are because the parameter bec is larger than bec in the actual step response. This is because Quanser supplies mean values for all their equipment which means it assumes a constant mass through the equipment whereas in the actual response, the mass varies.
Page 5
of 10
Q4.
Calculate π
ΰ―ΰ―
and π
from the experimental values of π
and π
and Quanserβs value of π
ΰ―ΰ―
= 0.500
kg. How do these compare with the values provided by Quanser?
Constant Value π
ΰ―ΰ―
[Ns/m]
4.386
π
[N/v] 0.746 The Quanser values are larger than the experimental values.
Page 6
of 10
QUESTIONS: Proportional Position Control of the Cart (4/32 marks)
Q5.
Insert the figure of the scope output for the 5 cm step input for the position control of the cart. Record the value of π
ΰ―£
used (from Question 2 of the prelab). Does the cart behave as expected? Is the steady-state error zero, as expected? Constant Value π
ΰ―£
59.24
Yes. The steady error is very close to zero but not exactly zero. The differences are mainly due to friction.
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Page 7
of 10
QUESTIONS: Validation of the Pendulum Inertia (4/32 marks)
Q6.
Insert the figure of the pendulum oscillatory response with the relevant data points selected to determine the natural frequency. Enter your value for the natural frequency π
determined from the period of pole oscillations. How does it compare with the value found in Question 3 of the prelab? Constant Value π
[rad/s]
6.628
Compared to the value from the prelab of 6.5175 rad/s. This values are relatively close only off by 0.112 rad/s.
Page 8
of 10
QUESTIONS: Gantry Position Control (4/32 marks)
Q7.
Enter the calculated values for the gains for the gantry control below. Constant Value π
ΰ―£ΰ―«
200.1736
π
ΰ―ΰ―«
64.0046 π
ΰ―£ΰ°
-85.4782 π
ΰ―ΰ°
9.6389 Q8.
Insert the figure of the gantry step response below. Does the gantry behave as expected? Elaborate. Yes the system behaved as expected. The cart position moved exactly 15cm which is the same as its reference position.
Page 9
of 10
QUESTIONS: Stabilization of Cart with Inverted Pole (8/32 marks)
Q9.
Enter the calculated values (from prelab Q.4) for the gains for the inverted pole control below. Constant Value π
ΰ―£ΰ―«
-12.9285
π
ΰ―ΰ―«
-29.5742 π
ΰ―£ΰ°
64.1429 π
ΰ―ΰ°
9.0588 Q10.
Insert the figure of the step response of the inverted pole below. Does the inverted pole behave as expected? Elaborate. The system behaves close to what is expected but the error between the reference and actual position is greater than when the pole is in the down position.
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Page 10
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Q11.
Tune the control gains experimentally, and insert the figure of resulting the step response below, along with the values of the tuned gains. What aspects of the response are visibly better than those obtained in Q10? Constant Value π
ΰ―£ΰ―«
-14.9324175
π
ΰ―ΰ―«
-32.53162 π
ΰ―£ΰ°
64.1429 π
ΰ―ΰ°
9.0588 The percent overshoot and steady state error are lower than the plot from question 10.
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