MAE 488 Final Exam Review UPDATED
ACTUAL Exam Questions and CORRECT
Answers
What are required assumptions for a full state feedback controller? - CORRECT
ANSWER - The original system is controllable. This could be checked if the
controllability matrix is full rank.
If the A = [2 4; 0 1] and B = [0; 1], what are the size of C and D? - CORRECT ANSWER -
C is 2x2, D is 2x1, same as A and B matrix.
If the A = [2 4; 0 1] and B = [0; 1], what is the closed loop characteristic polynomial? -
CORRECT ANSWER - Steps:
1) A_hat = A - BK where K is size B'
2) | lambda * I - A_hat | = 0
Where lambda is s, I is identity
3) Take determinant
4) Solve for s polynomial
s^2 +(K2-2)s + (4K1 - 2K2 + 2) = 0
If zeta = sqrt(2)/2 and omega_n = 2*sqrt(2), what is the desired closed loop polynomial? -
CORRECT ANSWER - Steps:
Using standard form of characteristic polynomial:
s^2 + 2*zeta*omega_n*s + omega_n^2
substitute and solve
s^2 + 4s + 8 = 0
What are three reasons why control is used? - CORRECT ANSWER - 1) To modify the
dynamic response
2) Compensate for a disturbance
, 3) Stabilize an unstable plant
NOT) Change the input
What is the output of an ideal closed loop control system if the input is a unit ramp? -
CORRECT ANSWER - Same as the input
A proportional controller results in a response with too much steady-state error. Which controller
will help reduce that error? - CORRECT ANSWER - Integrator
A PI controller results in a response with too much overshoot. What will help this? - CORRECT
ANSWER - A derivative term or differentiator
The poles of a transfer function are the _________ of the equation obtained by setting the
_________ polynomial of the transfer function to zero. - CORRECT ANSWER - zeros,
denominator
The zeros of a transfer function are the _________ of the equation obtained by setting the
_________ polynomial of the transfer function to zero. - CORRECT ANSWER - zeros,
numerator
Pole placement is a control design technique based on equating the
_________________________ and the ________________________ which is expressed in
terms of the unknown gains. - CORRECT ANSWER - desired closed loop characteristic
polynomial, actual closed loop characteristic polynomial
Define Control - CORRECT ANSWER - Influencing or forcing a desired behavior of a
system
Care must be taken when using a differentiator due to - CORRECT ANSWER -
amplifying noise
ACTUAL Exam Questions and CORRECT
Answers
What are required assumptions for a full state feedback controller? - CORRECT
ANSWER - The original system is controllable. This could be checked if the
controllability matrix is full rank.
If the A = [2 4; 0 1] and B = [0; 1], what are the size of C and D? - CORRECT ANSWER -
C is 2x2, D is 2x1, same as A and B matrix.
If the A = [2 4; 0 1] and B = [0; 1], what is the closed loop characteristic polynomial? -
CORRECT ANSWER - Steps:
1) A_hat = A - BK where K is size B'
2) | lambda * I - A_hat | = 0
Where lambda is s, I is identity
3) Take determinant
4) Solve for s polynomial
s^2 +(K2-2)s + (4K1 - 2K2 + 2) = 0
If zeta = sqrt(2)/2 and omega_n = 2*sqrt(2), what is the desired closed loop polynomial? -
CORRECT ANSWER - Steps:
Using standard form of characteristic polynomial:
s^2 + 2*zeta*omega_n*s + omega_n^2
substitute and solve
s^2 + 4s + 8 = 0
What are three reasons why control is used? - CORRECT ANSWER - 1) To modify the
dynamic response
2) Compensate for a disturbance
, 3) Stabilize an unstable plant
NOT) Change the input
What is the output of an ideal closed loop control system if the input is a unit ramp? -
CORRECT ANSWER - Same as the input
A proportional controller results in a response with too much steady-state error. Which controller
will help reduce that error? - CORRECT ANSWER - Integrator
A PI controller results in a response with too much overshoot. What will help this? - CORRECT
ANSWER - A derivative term or differentiator
The poles of a transfer function are the _________ of the equation obtained by setting the
_________ polynomial of the transfer function to zero. - CORRECT ANSWER - zeros,
denominator
The zeros of a transfer function are the _________ of the equation obtained by setting the
_________ polynomial of the transfer function to zero. - CORRECT ANSWER - zeros,
numerator
Pole placement is a control design technique based on equating the
_________________________ and the ________________________ which is expressed in
terms of the unknown gains. - CORRECT ANSWER - desired closed loop characteristic
polynomial, actual closed loop characteristic polynomial
Define Control - CORRECT ANSWER - Influencing or forcing a desired behavior of a
system
Care must be taken when using a differentiator due to - CORRECT ANSWER -
amplifying noise
