ECE 101 LAB 5 FEEDBACK
STABILIZATION: STICK BALANCING | 2026
UPDATE WITH COMPLETE SOLUTIONS.
150 Questions with Answers and Detailed Rationales
100 PERCENT GUARANTEED PASS
INSTANT DOWNLOAD ANSWERS INCLUDED
IMPORTANCE OF THIS DOCUMENT
This comprehensive examination preparation guide has been meticulously developed to help you succeed in the
ECE 101 LAB 5 FEEDBACK STABILIZATION: STICK BALANCING | 2026 UPDATE WITH COMPLETE
SOLUTIONS.. It contains 150 carefully selected questions that reflect the most current exam content and testing
strategies. Each question is accompanied by a correct answer and a detailed rationale that explains the
underlying pathophysiology, pharmacology, or clinical reasoning.
Self-Assessment – Test your knowledge and Exam Preparation – Familiarize yourself with the
identify areas requiring further question format and content
study areas
Concept Reinforcement – Deepen your Confidence Building – Develop test-taking
understanding through strategies and reduce
evidence-based exam anxiety
rationales
Time Management – Practice answering
questions under simulated
exam conditions
Review Summary 150 Questions
Foundations - Application - ECE 101 LAB 5 Feedback Stabilization Stick Balancing 2026 Update WITH
Complete Solutions Control Systems / Feedback Stabilization Laboratory Undergraduate YEAR 3 Electrical
AND Computer Engineering
All answers with rationales
,Table of Contents
Content Area Questions Key Topics
System Modeling AND 1-25 Controller, Stick, Angle, Closed-loop, Primary
Transfer Functions FOR Stick
Balancing
PID Controller Design AND 26-50 Controller, Stick-balancing, Student, Closed-loop, Angle
Tuning
ROOT Locus AND POLE 51-75 Stick-balancing, Controller, Phase, Angle, Closed-loop
Placement
State-space Representation 76-100 Stick, Controller, Balancer, Student, Angle
AND Feedback Control
Stability Analysis 101-125 Controller, Stick, Angle, Closed-loop, Student
Routh-hurwitz Nyquist BODE
Sensor AND Actuator 126-150 Student, Controller, Angle, System, Stick-balancing
Dynamics IN Feedback
Loops
TOTAL 150 All questions include answers and detailed rationales
,Section A - System Modeling AND Transfer Functions FOR
Stick Balancing
Q1.
For a stick balancing on a cart, the linearized transfer function from cart acceleration to
stick angle is P(s) = 1/(s^2 - a^2), with a = sqrt(g/L). Which of the following is the primary
reason a simple proportional controller cannot stabilize this plant?
A. The plant has a right-half-plane zero. B. The plant has a pole in the right-half
plane.
C. The plant has a pair of D. The plant has a left-half-plane zero
complex-conjugate poles on the imaginary causing phase lead.
axis.
Correct: B - The plant has a pole in the right-half plane.
Rationale:The denominator s^2 - a^2 factors as (s - a)(s + a), giving a pole at s = +a in the
right-half plane. A proportional controller cannot move this pole into the left-half plane;
feedback with sufficient phase lead is required. The plant has no zeros and no imaginary-axis
poles, and a LHP zero would not preclude proportional stabilization.
Why the other answers are wrong:
A. The transfer function has no zeros, so a RHP zero is not present.
C. The poles are real and one is positive, not complex conjugates on the imaginary axis.
D. A LHP zero would actually help stabilization, but the plant has no zeros.
Reference: Åström, K.J. & Murray, R.M. (2021). Feedback Systems: An Introduction for Scientists and
Engineers, 2nd Ed., Ch. 3.
Q2.
In the stick-balancing lab, you use a potentiometer to measure the stick angle. The
potentiometer output is 0.5 V at vertical and changes by 2 V per radian. If the ADC has a
12-bit resolution over a 0-5 V range, what is the approximate angle resolution in
milliradians?
A. 0.61 mrad B. 1.22 mrad
C. 2.44 mrad D. 4.88 mrad
Correct: A - 0.61 mrad
Rationale:ADC step size = 5 V / 4096 "H 1.2207 mV. Angle change per volt = 1/2 rad/V = 0.5
rad/V. Thus angle resolution = 1.2207 mV * 0.5 rad/V 0.610 mrad. The other options are
factors of 2 or 4 too large, resulting from misplacing the decimal or using wrong bit resolution.
Why the other answers are wrong:
Page 3
, Section A - System Modeling AND Transfer Functions FOR Stick Balancing
B. This is double the correct value, likely from using 2048 steps instead of 4096.
C. This is four times the correct value, from using 1024 steps.
D. This is eight times the correct value, from using 512 steps.
Reference: Franklin, G.F., Powell, J.D., & Emami-Naeini, A. (2020). Feedback Control of Dynamic
Systems, 8th Ed., Ch. 8.
Q3.
You are tuning a PD controller for the stick balancer. Increasing the derivative gain Kd
while keeping Kp fixed will generally have which effect on the closed-loop system?
A. Decrease phase margin and reduce B. Increase phase margin and add damping.
damping.
C. Increase steady-state error. D. Decrease the system type by one.
Correct: B - Increase phase margin and add damping.
Rationale:Derivative action adds phase lead at higher frequencies, which increases phase
margin and improves damping, reducing overshoot. It does not affect steady-state error for a
type-1 system and does not change system type. Increasing Kd too much can amplify noise,
but the primary effect is added damping.
Why the other answers are wrong:
A. Derivative action adds phase lead, increasing phase margin, not decreasing it.
C. Steady-state error is unaffected by derivative gain for the same Kp.
D. System type is determined by the number of integrators in the loop, not by Kd.
Reference: Åström, K.J. & Murray, R.M. (2021). Feedback Systems: An Introduction for Scientists and
Engineers, 2nd Ed., Ch. 10.
Q4.
A digital controller is implemented with a sampling period T = 5 ms. The stick's natural
frequency is approximately 3 rad/s. Which statement best describes the effect of this
sampling rate on the achievable closed-loop performance?
A. The sampling rate is too slow; it will B. The sampling rate is adequate; phase lag
introduce significant phase lag and limit at 3 rad/s is negligible.
bandwidth.
C. The sampling rate is excessive and will D. The sampling rate has no effect because
cause numerical issues. the controller is digital.
Correct: B - The sampling rate is adequate; phase lag at 3 rad/s is negligible.
Rationale:The sampling frequency is 200 Hz (1/0.005), which is much higher than the stick's
natural frequency (3 rad/s 0.48 Hz). The phase lag from zero-order hold at 3 rad/s is about
T*/2 = 0.0075 rad, negligible. Thus performance is not limited by sampling. Options A and C
misjudge the ratio, and D incorrectly dismisses digital effects.
Page 4
STABILIZATION: STICK BALANCING | 2026
UPDATE WITH COMPLETE SOLUTIONS.
150 Questions with Answers and Detailed Rationales
100 PERCENT GUARANTEED PASS
INSTANT DOWNLOAD ANSWERS INCLUDED
IMPORTANCE OF THIS DOCUMENT
This comprehensive examination preparation guide has been meticulously developed to help you succeed in the
ECE 101 LAB 5 FEEDBACK STABILIZATION: STICK BALANCING | 2026 UPDATE WITH COMPLETE
SOLUTIONS.. It contains 150 carefully selected questions that reflect the most current exam content and testing
strategies. Each question is accompanied by a correct answer and a detailed rationale that explains the
underlying pathophysiology, pharmacology, or clinical reasoning.
Self-Assessment – Test your knowledge and Exam Preparation – Familiarize yourself with the
identify areas requiring further question format and content
study areas
Concept Reinforcement – Deepen your Confidence Building – Develop test-taking
understanding through strategies and reduce
evidence-based exam anxiety
rationales
Time Management – Practice answering
questions under simulated
exam conditions
Review Summary 150 Questions
Foundations - Application - ECE 101 LAB 5 Feedback Stabilization Stick Balancing 2026 Update WITH
Complete Solutions Control Systems / Feedback Stabilization Laboratory Undergraduate YEAR 3 Electrical
AND Computer Engineering
All answers with rationales
,Table of Contents
Content Area Questions Key Topics
System Modeling AND 1-25 Controller, Stick, Angle, Closed-loop, Primary
Transfer Functions FOR Stick
Balancing
PID Controller Design AND 26-50 Controller, Stick-balancing, Student, Closed-loop, Angle
Tuning
ROOT Locus AND POLE 51-75 Stick-balancing, Controller, Phase, Angle, Closed-loop
Placement
State-space Representation 76-100 Stick, Controller, Balancer, Student, Angle
AND Feedback Control
Stability Analysis 101-125 Controller, Stick, Angle, Closed-loop, Student
Routh-hurwitz Nyquist BODE
Sensor AND Actuator 126-150 Student, Controller, Angle, System, Stick-balancing
Dynamics IN Feedback
Loops
TOTAL 150 All questions include answers and detailed rationales
,Section A - System Modeling AND Transfer Functions FOR
Stick Balancing
Q1.
For a stick balancing on a cart, the linearized transfer function from cart acceleration to
stick angle is P(s) = 1/(s^2 - a^2), with a = sqrt(g/L). Which of the following is the primary
reason a simple proportional controller cannot stabilize this plant?
A. The plant has a right-half-plane zero. B. The plant has a pole in the right-half
plane.
C. The plant has a pair of D. The plant has a left-half-plane zero
complex-conjugate poles on the imaginary causing phase lead.
axis.
Correct: B - The plant has a pole in the right-half plane.
Rationale:The denominator s^2 - a^2 factors as (s - a)(s + a), giving a pole at s = +a in the
right-half plane. A proportional controller cannot move this pole into the left-half plane;
feedback with sufficient phase lead is required. The plant has no zeros and no imaginary-axis
poles, and a LHP zero would not preclude proportional stabilization.
Why the other answers are wrong:
A. The transfer function has no zeros, so a RHP zero is not present.
C. The poles are real and one is positive, not complex conjugates on the imaginary axis.
D. A LHP zero would actually help stabilization, but the plant has no zeros.
Reference: Åström, K.J. & Murray, R.M. (2021). Feedback Systems: An Introduction for Scientists and
Engineers, 2nd Ed., Ch. 3.
Q2.
In the stick-balancing lab, you use a potentiometer to measure the stick angle. The
potentiometer output is 0.5 V at vertical and changes by 2 V per radian. If the ADC has a
12-bit resolution over a 0-5 V range, what is the approximate angle resolution in
milliradians?
A. 0.61 mrad B. 1.22 mrad
C. 2.44 mrad D. 4.88 mrad
Correct: A - 0.61 mrad
Rationale:ADC step size = 5 V / 4096 "H 1.2207 mV. Angle change per volt = 1/2 rad/V = 0.5
rad/V. Thus angle resolution = 1.2207 mV * 0.5 rad/V 0.610 mrad. The other options are
factors of 2 or 4 too large, resulting from misplacing the decimal or using wrong bit resolution.
Why the other answers are wrong:
Page 3
, Section A - System Modeling AND Transfer Functions FOR Stick Balancing
B. This is double the correct value, likely from using 2048 steps instead of 4096.
C. This is four times the correct value, from using 1024 steps.
D. This is eight times the correct value, from using 512 steps.
Reference: Franklin, G.F., Powell, J.D., & Emami-Naeini, A. (2020). Feedback Control of Dynamic
Systems, 8th Ed., Ch. 8.
Q3.
You are tuning a PD controller for the stick balancer. Increasing the derivative gain Kd
while keeping Kp fixed will generally have which effect on the closed-loop system?
A. Decrease phase margin and reduce B. Increase phase margin and add damping.
damping.
C. Increase steady-state error. D. Decrease the system type by one.
Correct: B - Increase phase margin and add damping.
Rationale:Derivative action adds phase lead at higher frequencies, which increases phase
margin and improves damping, reducing overshoot. It does not affect steady-state error for a
type-1 system and does not change system type. Increasing Kd too much can amplify noise,
but the primary effect is added damping.
Why the other answers are wrong:
A. Derivative action adds phase lead, increasing phase margin, not decreasing it.
C. Steady-state error is unaffected by derivative gain for the same Kp.
D. System type is determined by the number of integrators in the loop, not by Kd.
Reference: Åström, K.J. & Murray, R.M. (2021). Feedback Systems: An Introduction for Scientists and
Engineers, 2nd Ed., Ch. 10.
Q4.
A digital controller is implemented with a sampling period T = 5 ms. The stick's natural
frequency is approximately 3 rad/s. Which statement best describes the effect of this
sampling rate on the achievable closed-loop performance?
A. The sampling rate is too slow; it will B. The sampling rate is adequate; phase lag
introduce significant phase lag and limit at 3 rad/s is negligible.
bandwidth.
C. The sampling rate is excessive and will D. The sampling rate has no effect because
cause numerical issues. the controller is digital.
Correct: B - The sampling rate is adequate; phase lag at 3 rad/s is negligible.
Rationale:The sampling frequency is 200 Hz (1/0.005), which is much higher than the stick's
natural frequency (3 rad/s 0.48 Hz). The phase lag from zero-order hold at 3 rad/s is about
T*/2 = 0.0075 rad, negligible. Thus performance is not limited by sampling. Options A and C
misjudge the ratio, and D incorrectly dismisses digital effects.
Page 4
