GATE EC 2015 Set 2 — Question 29
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Control Systems → System Modelling → Block Diagram Reduction
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Question
By performing cascading and/or summing/differencing operations using transfer function blocks and , one CANNOT realize a transfer function of the form
Correct answer
(B) (G₁(s))/(G₂(s))
Solution
The basic operations allowed are:
1.Cascading: Results in the product of transfer functions, e.g., . This matches option (A).
2.Summing/Differencing: Results in the sum or difference of transfer functions, e.g., .
Analyzing the other options:- Option (C): . This can be realized by summing a unity gain path (wire) with the cascaded blocks and .
- Option (D): . This can be realized by differencing a unity gain path with the cascaded blocks.
- Option (B): requires the inversion of a transfer function block, which is not possible using only cascading, summing, or differencing. Inversion typically requires a feedback configuration. Therefore, it CANNOT be realized with the given operations.
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