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Read the statements regarding controllability and observability and mark the answer as true and false.
- For a system to be controllable, |Qc| = 0.
- For the system to be observable, |Q0| = 0.
- For the system to be controllable and observable, |Qc| ≠ 0 and |Qo| ≠ 0.
- a)True, True, False
- b)False, False, True
- c)False, False, False
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Read the statements regarding controllability and observability and ma...
Explanation:
Controllability and observability are two important concepts in control theory that determine whether a system can be controlled and whether its internal state can be determined from its outputs, respectively. Let's break down the statements and analyze them:
For a system to be controllable, |Qc| = 0:
- This statement is false. In fact, for a system to be controllable, the controllability matrix (Qc) should have full rank, meaning |Qc| ≠ 0. A system is controllable if it is possible to drive the system state from any initial state to any desired state in a finite time.
For the system to be observable, |Q0| = 0:
- This statement is false. In order for a system to be observable, the observability matrix (Q0) should have full rank, meaning |Q0| ≠ 0. Observability ensures that the internal state of the system can be determined from its outputs.
For the system to be controllable and observable, |Qc| ≠ 0 and |Q0| ≠ 0:
- This statement is true. For a system to be both controllable and observable, both the controllability matrix (Qc) and the observability matrix (Q0) should have full rank, indicating that the system can be fully controlled and its internal state can be fully determined from its outputs.
Therefore, the correct answer is option B, which states that the first two statements are false, and the third statement is true.
Controllability and observability are two important concepts in control theory that determine whether a system can be controlled and whether its internal state can be determined from its outputs, respectively. Let's break down the statements and analyze them:
For a system to be controllable, |Qc| = 0:
- This statement is false. In fact, for a system to be controllable, the controllability matrix (Qc) should have full rank, meaning |Qc| ≠ 0. A system is controllable if it is possible to drive the system state from any initial state to any desired state in a finite time.
For the system to be observable, |Q0| = 0:
- This statement is false. In order for a system to be observable, the observability matrix (Q0) should have full rank, meaning |Q0| ≠ 0. Observability ensures that the internal state of the system can be determined from its outputs.
For the system to be controllable and observable, |Qc| ≠ 0 and |Q0| ≠ 0:
- This statement is true. For a system to be both controllable and observable, both the controllability matrix (Qc) and the observability matrix (Q0) should have full rank, indicating that the system can be fully controlled and its internal state can be fully determined from its outputs.
Therefore, the correct answer is option B, which states that the first two statements are false, and the third statement is true.
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Read the statements regarding controllability and observability and ma...
The correct answer is option '2'
Concept:
Controllability:
A system is said to be controllable if it is possible to transfer the system state from any initial state x(t0) to any desired state x(t) in a specified finite time interval by a control vector u(t)
Kalman’s test for controllability:
ẋ = Ax + Bu
Qc = {B AB A2B … An-1 B]
Qc = controllability matrix
If |Qc| = 0, system is not controllable
If |Qc|≠ 0, system is controllable
Observability:
A system is said to be observable if every state x(t0) can be completely identified by measurement of output y(t) over a finite time interval.
Kalman’s test for observability:
Q0 = [CT ATCT (AT)2CT …. (AT)n-1 CT]
Q0 = observability testing matrix
If |Q0| = 0, system is not observable
If |Q0| ≠ 0, system is observable.
Concept:
Controllability:
A system is said to be controllable if it is possible to transfer the system state from any initial state x(t0) to any desired state x(t) in a specified finite time interval by a control vector u(t)
Kalman’s test for controllability:
ẋ = Ax + Bu
Qc = {B AB A2B … An-1 B]
Qc = controllability matrix
If |Qc| = 0, system is not controllable
If |Qc|≠ 0, system is controllable
Observability:
A system is said to be observable if every state x(t0) can be completely identified by measurement of output y(t) over a finite time interval.
Kalman’s test for observability:
Q0 = [CT ATCT (AT)2CT …. (AT)n-1 CT]
Q0 = observability testing matrix
If |Q0| = 0, system is not observable
If |Q0| ≠ 0, system is observable.
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Read the statements regarding controllability and observability and mark the answer as true and false. For a system to be controllable, |Qc| = 0. For the system to be observable, |Q0| = 0. For the system to be controllable and observable, |Qc| ≠ 0 and |Qo| ≠ 0.a)True, True, Falseb)False, False, Truec)False, False, Falsed)None of theseCorrect answer is option 'B'. Can you explain this answer?
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Read the statements regarding controllability and observability and mark the answer as true and false. For a system to be controllable, |Qc| = 0. For the system to be observable, |Q0| = 0. For the system to be controllable and observable, |Qc| ≠ 0 and |Qo| ≠ 0.a)True, True, Falseb)False, False, Truec)False, False, Falsed)None of theseCorrect answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Read the statements regarding controllability and observability and mark the answer as true and false. For a system to be controllable, |Qc| = 0. For the system to be observable, |Q0| = 0. For the system to be controllable and observable, |Qc| ≠ 0 and |Qo| ≠ 0.a)True, True, Falseb)False, False, Truec)False, False, Falsed)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Read the statements regarding controllability and observability and mark the answer as true and false. For a system to be controllable, |Qc| = 0. For the system to be observable, |Q0| = 0. For the system to be controllable and observable, |Qc| ≠ 0 and |Qo| ≠ 0.a)True, True, Falseb)False, False, Truec)False, False, Falsed)None of theseCorrect answer is option 'B'. Can you explain this answer?.
Read the statements regarding controllability and observability and mark the answer as true and false. For a system to be controllable, |Qc| = 0. For the system to be observable, |Q0| = 0. For the system to be controllable and observable, |Qc| ≠ 0 and |Qo| ≠ 0.a)True, True, Falseb)False, False, Truec)False, False, Falsed)None of theseCorrect answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Read the statements regarding controllability and observability and mark the answer as true and false. For a system to be controllable, |Qc| = 0. For the system to be observable, |Q0| = 0. For the system to be controllable and observable, |Qc| ≠ 0 and |Qo| ≠ 0.a)True, True, Falseb)False, False, Truec)False, False, Falsed)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Read the statements regarding controllability and observability and mark the answer as true and false. For a system to be controllable, |Qc| = 0. For the system to be observable, |Q0| = 0. For the system to be controllable and observable, |Qc| ≠ 0 and |Qo| ≠ 0.a)True, True, Falseb)False, False, Truec)False, False, Falsed)None of theseCorrect answer is option 'B'. Can you explain this answer?.
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