The question asks to identify the incorrect statement regarding the Transfer Function of a linear Time-Invariant (LTI) system.
Analyzing Transfer Function Statements
Let's analyze each statement:
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Statement A: "The ratio of Laplace transform of the output to the Laplace transform of the input variable under the assumption that all initial conditions are zero."
This is the correct definition of a transfer function for an LTI system. Mathematically, if $ Y(s) $ is the Laplace transform of the output $ y(t) $ and $ U(s) $ is the Laplace transform of the input $ u(t) $, then the transfer function $ G(s) $ is given by:
$ G(s) = \frac{Y(s)}{U(s)} \quad \text{(with zero initial conditions)} $
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Statement B: "The ratio of Fourier transform of the output to Fourier transform of the input variable."
This statement is incorrect. The transfer function is fundamentally defined using the Laplace transform, not the Fourier transform. While the frequency response $ G(j\omega) $ (related to the Fourier transform) can be derived from the transfer function $ G(s) $ by setting $ s = j\omega $, the definition itself is based on Laplace transforms.
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Statement C: "The higher power of the complex variable 's' in the denominator of the transfer function determines the order of the system."
This is a correct statement. The order of an LTI system is defined by the degree of the denominator polynomial of its transfer function $ G(s) $.
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Statement D: "It is an expression in s-domain relating the output and input of linear time invariant system in terms of the system parameters and is independent of the input."
This statement accurately describes the characteristics of a transfer function. It represents the system's input-output relationship in the s-domain, depends only on system parameters (not the input), and is valid for LTI systems.
Conclusion
Based on the analysis, the incorrect statement regarding the Transfer Function of an LTI system is the one defining it as the ratio of Fourier transforms instead of Laplace transforms.
Important Questions from Basics of Control Systems
- Match the LIST-I with LIST-IIChoose the correct answer from the options given below:
LIST-I LIST-II A. Nyquist Criterion I. Polar Plots B. Bode Plot II. Rectangular Plots C. Phase Margin III. Amount of additional phase lag at the gain crossover frequency required to bring the system to the verge of instability D. Gain Margin IV. It is the reciprocal of the magnitude $|G(j\omega)|$ at the frequency at which the phase angle is $-180^\circ$. A. In any open loop control system, the output is not compared with the reference input.
B. Traffic control by means of signals operated on a time basis is an example of closed loop control.
C. Closed loop control always implies the use of feedback control action in order to reduce system error.
D. Washing machine is an example of open loop system.
E. Stability is a major concern in open loop control system.
Choose the correct answer from the options given below:
Read the following statements about the transfer function of a system :
(a) The transfer function provides complete insight into the structure of the system.
(b) It offers a symbolic picture about the dynamic characteristics of the system.
(c) It does not give any insight into the structure of the system.
(d) If the transfer functions of individual components of the system are known, the overall characteristics of the system can be determined just by taking their product.
Which of the above statements are correct ?
The mass-spring-damper system shown in the following figure represents :
The error detector element in a control system gives
