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A system can be represented in the form of state equations as:
S (n+1) =A S (n) +B x (n)
Y (n) = C S (n) +D x (n)
Where, A, B, C, D are the matrices , S(n) is the state vector , x(n) is the input and y(n) is the output . The transfer function of the system.
H (z) =Y (z)/X (z) is given by:
S (n+1) =A S (n) +B x (n)
Y (n) = C S (n) +D x (n)
Where, A, B, C, D are the matrices , S(n) is the state vector , x(n) is the input and y(n) is the output . The transfer function of the system.
H (z) =Y (z)/X (z) is given by:
- a)A(ZI – B)-1 C + D
- b)B(ZI – C)-1 D + A
- c)C(ZI – A)-1 B + D
- d)D(ZI – A)-1 C + B
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A system can be represented in the form of state equations as:S (n+1) ...
Explanation: Solving both the equations and substituting the value of the output equation into the state equation we get the value of the transfer function as obtained.
Most Upvoted Answer
A system can be represented in the form of state equations as:S (n+1) ...
Understanding the State-Space Representation
The state-space representation of a system is given by the equations:
- S(n+1) = A S(n) + B x(n)
- Y(n) = C S(n) + D x(n)
Where:
- A, B, C, D are matrices defining the system dynamics.
- S(n) is the state vector.
- x(n) is the input.
- y(n) is the output.
Transfer Function Derivation
To derive the transfer function H(z) = Y(z)/X(z), we utilize the Z-transform:
1. Z-transform of the state equation:
- Applying the Z-transform to S(n+1) leads to S(z) = A S(z) + B X(z).
- Rearranging gives: S(z)(I - AZ) = BX(z).
2. Solving for S(z):
- This can be expressed as: S(z) = (I - AZ)^(-1) B X(z).
3. Substituting into the output equation:
- The output equation in the Z-domain becomes Y(z) = C S(z) + D X(z).
- Substituting for S(z), we have Y(z) = C(I - AZ)^(-1) B X(z) + D X(z).
4. Combining terms:
- Factoring out X(z) leads to: Y(z) = [C(I - AZ)^(-1) B + D] X(z).
5. Final Transfer Function:
- Thus, we can express the transfer function as: H(z) = [C(I - AZ)^(-1) B + D].
Conclusion
The correct answer is option 'C' because it properly captures the relationship between the input and output in the Z-transform domain using the state-space representation. The final form represents the dynamics of the system effectively.
The state-space representation of a system is given by the equations:
- S(n+1) = A S(n) + B x(n)
- Y(n) = C S(n) + D x(n)
Where:
- A, B, C, D are matrices defining the system dynamics.
- S(n) is the state vector.
- x(n) is the input.
- y(n) is the output.
Transfer Function Derivation
To derive the transfer function H(z) = Y(z)/X(z), we utilize the Z-transform:
1. Z-transform of the state equation:
- Applying the Z-transform to S(n+1) leads to S(z) = A S(z) + B X(z).
- Rearranging gives: S(z)(I - AZ) = BX(z).
2. Solving for S(z):
- This can be expressed as: S(z) = (I - AZ)^(-1) B X(z).
3. Substituting into the output equation:
- The output equation in the Z-domain becomes Y(z) = C S(z) + D X(z).
- Substituting for S(z), we have Y(z) = C(I - AZ)^(-1) B X(z) + D X(z).
4. Combining terms:
- Factoring out X(z) leads to: Y(z) = [C(I - AZ)^(-1) B + D] X(z).
5. Final Transfer Function:
- Thus, we can express the transfer function as: H(z) = [C(I - AZ)^(-1) B + D].
Conclusion
The correct answer is option 'C' because it properly captures the relationship between the input and output in the Z-transform domain using the state-space representation. The final form represents the dynamics of the system effectively.
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A system can be represented in the form of state equations as:S (n+1) =A S (n) +B x (n)Y (n) = C S (n) +D x (n)Where, A, B, C, D are the matrices , S(n) is the state vector , x(n) is the input and y(n) is the output . The transfer function of the system.H (z) =Y (z)/X (z) is given by:a)A(ZI – B)-1C + Db)B(ZI – C)-1D + Ac)C(ZI – A)-1B + Dd)D(ZI – A)-1C + BCorrect answer is option 'C'. Can you explain this answer?
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A system can be represented in the form of state equations as:S (n+1) =A S (n) +B x (n)Y (n) = C S (n) +D x (n)Where, A, B, C, D are the matrices , S(n) is the state vector , x(n) is the input and y(n) is the output . The transfer function of the system.H (z) =Y (z)/X (z) is given by:a)A(ZI – B)-1C + Db)B(ZI – C)-1D + Ac)C(ZI – A)-1B + Dd)D(ZI – A)-1C + BCorrect answer is option 'C'. 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 A system can be represented in the form of state equations as:S (n+1) =A S (n) +B x (n)Y (n) = C S (n) +D x (n)Where, A, B, C, D are the matrices , S(n) is the state vector , x(n) is the input and y(n) is the output . The transfer function of the system.H (z) =Y (z)/X (z) is given by:a)A(ZI – B)-1C + Db)B(ZI – C)-1D + Ac)C(ZI – A)-1B + Dd)D(ZI – A)-1C + BCorrect answer is option 'C'. 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 A system can be represented in the form of state equations as:S (n+1) =A S (n) +B x (n)Y (n) = C S (n) +D x (n)Where, A, B, C, D are the matrices , S(n) is the state vector , x(n) is the input and y(n) is the output . The transfer function of the system.H (z) =Y (z)/X (z) is given by:a)A(ZI – B)-1C + Db)B(ZI – C)-1D + Ac)C(ZI – A)-1B + Dd)D(ZI – A)-1C + BCorrect answer is option 'C'. Can you explain this answer?.
A system can be represented in the form of state equations as:S (n+1) =A S (n) +B x (n)Y (n) = C S (n) +D x (n)Where, A, B, C, D are the matrices , S(n) is the state vector , x(n) is the input and y(n) is the output . The transfer function of the system.H (z) =Y (z)/X (z) is given by:a)A(ZI – B)-1C + Db)B(ZI – C)-1D + Ac)C(ZI – A)-1B + Dd)D(ZI – A)-1C + BCorrect answer is option 'C'. 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 A system can be represented in the form of state equations as:S (n+1) =A S (n) +B x (n)Y (n) = C S (n) +D x (n)Where, A, B, C, D are the matrices , S(n) is the state vector , x(n) is the input and y(n) is the output . The transfer function of the system.H (z) =Y (z)/X (z) is given by:a)A(ZI – B)-1C + Db)B(ZI – C)-1D + Ac)C(ZI – A)-1B + Dd)D(ZI – A)-1C + BCorrect answer is option 'C'. 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 A system can be represented in the form of state equations as:S (n+1) =A S (n) +B x (n)Y (n) = C S (n) +D x (n)Where, A, B, C, D are the matrices , S(n) is the state vector , x(n) is the input and y(n) is the output . The transfer function of the system.H (z) =Y (z)/X (z) is given by:a)A(ZI – B)-1C + Db)B(ZI – C)-1D + Ac)C(ZI – A)-1B + Dd)D(ZI – A)-1C + BCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A system can be represented in the form of state equations as:S (n+1) =A S (n) +B x (n)Y (n) = C S (n) +D x (n)Where, A, B, C, D are the matrices , S(n) is the state vector , x(n) is the input and y(n) is the output . The transfer function of the system.H (z) =Y (z)/X (z) is given by:a)A(ZI – B)-1C + Db)B(ZI – C)-1D + Ac)C(ZI – A)-1B + Dd)D(ZI – A)-1C + BCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
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