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Consider the following properties attributed to state model of a system:
- State model is unique.
- Transfer function for the system is unique.
- State model can be derived from transfer function of the system.
Which of the above statements are correct?
- a)1, 2 and 3
- b)1 and 2 only
- c)2 and 3 only
- d)1 and 3 only
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Consider the following properties attributed to state model of a syste...
Statement 1: State model is unique.
The statement that the state model is unique is correct. The state model of a system describes the behavior of the system using a set of first-order differential equations. It represents the internal state variables of the system and their relationships. The state model is unique because it captures the specific dynamics and behavior of the system under consideration. Each system will have its own unique set of state variables and their relationships, resulting in a unique state model.
Statement 2: Transfer function for the system is unique.
The statement that the transfer function for the system is unique is correct. The transfer function is a mathematical representation of the input-output relationship of a linear time-invariant system. It describes how the system responds to input signals in the frequency domain. The transfer function is derived from the system's differential equations or state model. Since the state model is unique, the transfer function derived from it will also be unique. Different systems will have different transfer functions due to their unique dynamics and characteristics.
Statement 3: State model can be derived from the transfer function of the system.
The statement that the state model can be derived from the transfer function of the system is incorrect. The transfer function is derived from the state model, not the other way around. The transfer function is obtained by taking the Laplace transform of the system's differential equations or state equations. It represents the system's behavior in the frequency domain. However, the transfer function alone does not provide information about the internal state variables and their relationships, which are necessary to fully describe the system's dynamics. To obtain the state model from the transfer function, additional steps such as inverse Laplace transform or partial fraction expansion would be required.
Therefore, the correct statements are:
a) 1, 2, and 3
The statement that the state model is unique is correct. The state model of a system describes the behavior of the system using a set of first-order differential equations. It represents the internal state variables of the system and their relationships. The state model is unique because it captures the specific dynamics and behavior of the system under consideration. Each system will have its own unique set of state variables and their relationships, resulting in a unique state model.
Statement 2: Transfer function for the system is unique.
The statement that the transfer function for the system is unique is correct. The transfer function is a mathematical representation of the input-output relationship of a linear time-invariant system. It describes how the system responds to input signals in the frequency domain. The transfer function is derived from the system's differential equations or state model. Since the state model is unique, the transfer function derived from it will also be unique. Different systems will have different transfer functions due to their unique dynamics and characteristics.
Statement 3: State model can be derived from the transfer function of the system.
The statement that the state model can be derived from the transfer function of the system is incorrect. The transfer function is derived from the state model, not the other way around. The transfer function is obtained by taking the Laplace transform of the system's differential equations or state equations. It represents the system's behavior in the frequency domain. However, the transfer function alone does not provide information about the internal state variables and their relationships, which are necessary to fully describe the system's dynamics. To obtain the state model from the transfer function, additional steps such as inverse Laplace transform or partial fraction expansion would be required.
Therefore, the correct statements are:
a) 1, 2, and 3
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Community Answer
Consider the following properties attributed to state model of a syste...
- In the transfer function model, initial conditions are assumed to be zero. In the state-space model, transfer function is not the starting point for the system analysis, and it considers the initial conditions of the system.
- The transfer function for the system is unique.
- The transfer function is applicable only for linear time-invariant systems. The state-space model is applicable to linear time-variant systems also.
- State-space representation of a system is not unique, it may have more than one representation.
- State model can be derived from transfer function of the system.
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Consider the following properties attributed to state model of a system: State model is unique. Transfer function for the system is unique. State model can be derived from transfer function of the system.Which of the above statements are correct?a)1, 2 and 3b)1 and 2 onlyc)2 and 3 onlyd)1 and 3 onlyCorrect answer is option 'C'. Can you explain this answer?
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